Andrey received a postcard from Irina. It contained only the words "Hello, Andrey!", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt it.Andrey noticed that snowflakes and candy canes always stand after the letters, so he supposed that the message was encrypted as follows. Candy cane means that the letter before it can be removed, or can be left. A snowflake means that the letter before it can be removed, left, or repeated several times.For example, consider the following string:   This string can encode the message «happynewyear». For this, candy canes and snowflakes should be used as follows:   candy cane 1: remove the letter w,  snowflake 1: repeat the letter p twice,  candy cane 2: leave the letter n,  snowflake 2: remove the letter w,  snowflake 3: leave the letter e.   Please note that the same string can encode different messages. For example, the string above can encode «hayewyar», «happpppynewwwwwyear», and other messages.Andrey knows that messages from Irina usually have a length of $$$k$$$ letters. Help him to find out if a given string can encode a message of $$$k$$$ letters, and if so, give an example of such a message.

The first line contains the string received in the postcard. The string consists only of lowercase Latin letters, as well as the characters «*» and «?», meaning snowflake and candy cone, respectively. These characters can only appear immediately after the letter. The length of the string does not exceed $$$200$$$. The second line contains an integer number $$$k$$$ ($$$1 \leq k \leq 200$$$), the required message length.

Print any message of length $$$k$$$ that the given string can encode, or «Impossible» if such a message does not exist.


Alice has a string $$$s$$$. She really likes the letter "a". She calls a string good if strictly more than half of the characters in that string are "a"s. For example "aaabb", "axaa" are good strings, and "baca", "awwwa", "" (empty string) are not.Alice can erase some characters from her string $$$s$$$. She would like to know what is the longest string remaining after erasing some characters (possibly zero) to get a good string. It is guaranteed that the string has at least one "a" in it, so the answer always exists.

The first line contains a string $$$s$$$ ($$$1 \leq |s| \leq 50$$$) consisting of lowercase English letters. It is guaranteed that there is at least one "a" in $$$s$$$.

Print a single integer, the length of the longest good string that Alice can get after erasing some characters from $$$s$$$.

NoteIn the first example, it's enough to erase any four of the "x"s. The answer is $$$3$$$ since that is the maximum number of characters that can remain.In the second example, we don't need to erase any characters.


Gaius Julius Caesar, a famous general, loved to line up his soldiers. Overall the army had n1 footmen and n2 horsemen. Caesar thought that an arrangement is not beautiful if somewhere in the line there are strictly more that k1 footmen standing successively one after another, or there are strictly more than k2 horsemen standing successively one after another. Find the number of beautiful arrangements of the soldiers. Note that all n1 + n2 warriors should be present at each arrangement. All footmen are considered indistinguishable among themselves. Similarly, all horsemen are considered indistinguishable among themselves.

The only line contains four space-separated integers n1, n2, k1, k2 (1 ≤ n1, n2 ≤ 100, 1 ≤ k1, k2 ≤ 10) which represent how many footmen and horsemen there are and the largest acceptable number of footmen and horsemen standing in succession, correspondingly.

Print the number of beautiful arrangements of the army modulo 100000000 (108). That is, print the number of such ways to line up the soldiers, that no more than k1 footmen stand successively, and no more than k2 horsemen stand successively.

NoteLet's mark a footman as 1, and a horseman as 2.In the first sample the only beautiful line-up is: 121In the second sample 5 beautiful line-ups exist: 12122, 12212, 21212, 21221, 22121


The Smart Beaver from ABBYY has once again surprised us! He has developed a new calculating device, which he called the "Beaver's Calculator 1.0". It is very peculiar and it is planned to be used in a variety of scientific problems.To test it, the Smart Beaver invited n scientists, numbered from 1 to n. The i-th scientist brought ki calculating problems for the device developed by the Smart Beaver from ABBYY. The problems of the i-th scientist are numbered from 1 to ki, and they must be calculated sequentially in the described order, since calculating each problem heavily depends on the results of calculating of the previous ones.Each problem of each of the n scientists is described by one integer ai, j, where i (1 ≤ i ≤ n) is the number of the scientist, j (1 ≤ j ≤ ki) is the number of the problem, and ai, j is the number of resource units the calculating device needs to solve this problem.The calculating device that is developed by the Smart Beaver is pretty unusual. It solves problems sequentially, one after another. After some problem is solved and before the next one is considered, the calculating device allocates or frees resources.The most expensive operation for the calculating device is freeing resources, which works much slower than allocating them. It is therefore desirable that each next problem for the calculating device requires no less resources than the previous one.You are given the information about the problems the scientists offered for the testing. You need to arrange these problems in such an order that the number of adjacent "bad" pairs of problems in this list is minimum possible. We will call two consecutive problems in this list a "bad pair" if the problem that is performed first requires more resources than the one that goes after it. Do not forget that the problems of the same scientist must be solved in a fixed order.

The first line contains integer n — the number of scientists. To lessen the size of the input, each of the next n lines contains five integers ki, ai, 1, xi, yi, mi (0 ≤ ai, 1 < mi ≤ 109, 1 ≤ xi, yi ≤ 109) — the number of problems of the i-th scientist, the resources the first problem requires and three parameters that generate the subsequent values of ai, j. For all j from 2 to ki, inclusive, you should calculate value ai, j by formula ai, j = (ai, j - 1 * xi + yi) mod mi, where a mod b is the operation of taking the remainder of division of number a by number b. To get the full points for the first group of tests it is sufficient to solve the problem with n = 2, 1 ≤ ki ≤ 2000. To get the full points for the second group of tests it is sufficient to solve the problem with n = 2, 1 ≤ ki ≤ 200000. To get the full points for the third group of tests it is sufficient to solve the problem with 1 ≤ n ≤ 5000, 1 ≤ ki ≤ 5000.

On the first line print a single number — the number of "bad" pairs in the optimal order. If the total number of problems does not exceed 200000, also print  lines — the optimal order of the problems. On each of these lines print two integers separated by a single space — the required number of resources for the problem and the number of the scientist who offered this problem, respectively. The scientists are numbered from 1 to n in the order of input.

NoteIn the first sample n = 2, k1 = 2, a1, 1 = 1, a1, 2 = 2, k2 = 2, a2, 1 = 3, a2, 2 = 4. We've got two scientists, each of them has two calculating problems. The problems of the first scientist require 1 and 2 resource units, the problems of the second one require 3 and 4 resource units. Let's list all possible variants of the calculating order (each problem is characterized only by the number of resource units it requires): (1, 2, 3, 4), (1, 3, 2, 4), (3, 1, 2, 4), (1, 3, 4, 2), (3, 4, 1, 2), (3, 1, 4, 2).Sequence of problems (1, 3, 2, 4) has one "bad" pair (3 and 2), (3, 1, 4, 2) has two "bad" pairs (3 and 1, 4 and 2), and (1, 2, 3, 4) has no "bad" pairs.


Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?Given an integer sequence a1, a2, ..., an of length n. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each of which has an odd length and begins and ends with odd numbers.A subsegment is a contiguous slice of the whole sequence. For example, {3, 4, 5} and {1} are subsegments of sequence {1, 2, 3, 4, 5, 6}, while {1, 2, 4} and {7} are not.

The first line of input contains a non-negative integer n (1 ≤ n ≤ 100) — the length of the sequence. The second line contains n space-separated non-negative integers a1, a2, ..., an (0 ≤ ai ≤ 100) — the elements of the sequence.

Output "Yes" if it's possible to fulfill the requirements, and "No" otherwise. You can output each letter in any case (upper or lower).

NoteIn the first example, divide the sequence into 1 subsegment: {1, 3, 5} and the requirements will be met.In the second example, divide the sequence into 3 subsegments: {1, 0, 1}, {5}, {1}.In the third example, one of the subsegments must start with 4 which is an even number, thus the requirements cannot be met.In the fourth example, the sequence can be divided into 2 subsegments: {3, 9, 9}, {3}, but this is not a valid solution because 2 is an even number.


Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.Consider the point (x, y) in the 2D plane such that x and y are integers and 0 ≤ x, y. There is a tree in such a point, and it has x + y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation . Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.Okabe is sure that the answer does not exceed 1018. You can trust him.

The first line of input contains two space-separated integers m and b (1 ≤ m ≤ 1000, 1 ≤ b ≤ 10000).

Print the maximum number of bananas Okabe can get from the trees he cuts.

Note  The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas.


There are well-known formulas: , , . Also mathematicians found similar formulas for higher degrees.Find the value of the sum  modulo 109 + 7 (so you should find the remainder after dividing the answer by the value 109 + 7).

The only line contains two integers n, k (1 ≤ n ≤ 109, 0 ≤ k ≤ 106).

Print the only integer a — the remainder after dividing the value of the sum by the value 109 + 7.


As a tradition, every year before IOI all the members of Natalia Fan Club are invited to Malek Dance Club to have a fun night together. Malek Dance Club has 2n members and coincidentally Natalia Fan Club also has 2n members. Each member of MDC is assigned a unique id i from 0 to 2n - 1. The same holds for each member of NFC.One of the parts of this tradition is one by one dance, where each member of MDC dances with a member of NFC. A dance pair is a pair of numbers (a, b) such that member a from MDC dances with member b from NFC.The complexity of a pairs' assignment is the number of pairs of dancing pairs (a, b) and (c, d) such that a < c and b > d.You are given a binary number of length n named x. We know that member i from MDC dances with member  from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (109 + 7).Expression  denotes applying «XOR» to numbers x and y. This operation exists in all modern programming languages, for example, in C++ and Java it denotes as «^», in Pascal — «xor».

The first line of input contains a binary number x of lenght n, (1 ≤ n ≤ 100). This number may contain leading zeros.

Print the complexity of the given dance assignent modulo 1000000007 (109 + 7).


Lakhesh loves to make movies, so Nephren helps her run a cinema. We may call it No. 68 Cinema.However, one day, the No. 68 Cinema runs out of changes (they don't have 50-yuan notes currently), but Nephren still wants to start their business. (Assume that yuan is a kind of currency in Regulu Ere.)There are three types of customers: some of them bring exactly a 50-yuan note; some of them bring a 100-yuan note and Nephren needs to give a 50-yuan note back to him/her; some of them bring VIP cards so that they don't need to pay for the ticket.Now n customers are waiting outside in queue. Nephren wants to know how many possible queues are there that they are able to run smoothly (i.e. every customer can receive his/her change), and that the number of 50-yuan notes they have after selling tickets to all these customers is between l and r, inclusive. Two queues are considered different if there exists a customer whose type is different in two queues. As the number can be large, please output the answer modulo p.

One line containing four integers n (1 ≤ n ≤ 105), p (1 ≤ p ≤ 2·109), l and r (0 ≤ l ≤ r ≤ n).

One line indicating the answer modulo p.

NoteWe use A, B and C to indicate customers with 50-yuan notes, customers with 100-yuan notes and customers with VIP cards respectively.For the first sample, the different possible queues that there are 2 50-yuan notes left are AAAB, AABA, ABAA, AACC, ACAC, ACCA, CAAC, CACA and CCAA, and the different possible queues that there are 3 50-yuan notes left are AAAC, AACA, ACAA and CAAA. So there are 13 different queues satisfying the first sample. Similarly, there are 35 different queues satisfying the second sample.


If an integer a is divisible by another integer b, then b is called the divisor of a.For example: 12 has positive 6 divisors. They are 1, 2, 3, 4, 6 and 12.Let’s define a function D(n) — number of integers between 1 and n (inclusive) which has exactly four positive divisors.Between 1 and 10 only the integers 6, 8 and 10 has exactly four positive divisors. So, D(10) = 3.You are given an integer n. You have to calculate D(n).

The only line contains integer n (1 ≤ n ≤ 1011) — the parameter from the problem statement.

Print the only integer c — the number of integers between 1 and n with exactly four divisors.


On the Literature lesson Sergei noticed an awful injustice, it seems that some students are asked more often than others.Seating in the class looks like a rectangle, where n rows with m pupils in each. The teacher asks pupils in the following order: at first, she asks all pupils from the first row in the order of their seating, then she continues to ask pupils from the next row. If the teacher asked the last row, then the direction of the poll changes, it means that she asks the previous row. The order of asking the rows looks as follows: the 1-st row, the 2-nd row, ..., the n - 1-st row, the n-th row, the n - 1-st row, ..., the 2-nd row, the 1-st row, the 2-nd row, ...The order of asking of pupils on the same row is always the same: the 1-st pupil, the 2-nd pupil, ..., the m-th pupil.During the lesson the teacher managed to ask exactly k questions from pupils in order described above. Sergei seats on the x-th row, on the y-th place in the row. Sergei decided to prove to the teacher that pupils are asked irregularly, help him count three values:  the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei. If there is only one row in the class, then the teacher always asks children from this row.

The first and the only line contains five integers n, m, k, x and y (1 ≤ n, m ≤ 100, 1 ≤ k ≤ 1018, 1 ≤ x ≤ n, 1 ≤ y ≤ m).

Print three integers:   the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei.

NoteThe order of asking pupils in the first test:   the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table; The order of asking pupils in the second test:   the pupil from the first row who seats at the first table;  the pupil from the first row who seats at the second table;  the pupil from the second row who seats at the first table;  the pupil from the second row who seats at the second table;  the pupil from the third row who seats at the first table;  the pupil from the third row who seats at the second table;  the pupil from the fourth row who seats at the first table;  the pupil from the fourth row who seats at the second table, it means it is Sergei;  the pupil from the third row who seats at the first table;


We call a positive integer x a k-beautiful integer if and only if it is possible to split the multiset of its digits in the decimal representation into two subsets such that the difference between the sum of digits in one subset and the sum of digits in the other subset is less than or equal to k. Each digit should belong to exactly one subset after the split.There are n queries for you. Each query is described with three integers l, r and k, which mean that you are asked how many integers x between l and r (inclusive) are k-beautiful.

The first line contains a single integer n (1 ≤ n ≤ 5·104), indicating the number of queries. Each of the next n lines describes a query, containing three integers l, r and k (1 ≤ l ≤ r ≤ 1018, 0 ≤ k ≤ 9).

For each query print a single number — the answer to the query.

NoteIf 1 ≤ x ≤ 9, integer x is k-beautiful if and only if x ≤ k.If 10 ≤ x ≤ 99, integer x = 10a + b is k-beautiful if and only if |a - b| ≤ k, where a and b are integers between 0 and 9, inclusive.100 is k-beautiful if and only if k ≥ 1.


Our good friend Mole is trying to code a big message. He is typing on an unusual keyboard with characters arranged in following way:qwertyuiopasdfghjkl;zxcvbnm,./Unfortunately Mole is blind, so sometimes it is problem for him to put his hands accurately. He accidentally moved both his hands with one position to the left or to the right. That means that now he presses not a button he wants, but one neighboring button (left or right, as specified in input).We have a sequence of characters he has typed and we want to find the original message.

First line of the input contains one letter describing direction of shifting ('L' or 'R' respectively for left or right). Second line contains a sequence of characters written by Mole. The size of this sequence will be no more than 100. Sequence contains only symbols that appear on Mole's keyboard. It doesn't contain spaces as there is no space on Mole's keyboard. It is guaranteed that even though Mole hands are moved, he is still pressing buttons on keyboard and not hitting outside it.

Print a line that contains the original message.


The year 2015 is almost over.Limak is a little polar bear. He has recently learnt about the binary system. He noticed that the passing year has exactly one zero in its representation in the binary system — 201510 = 111110111112. Note that he doesn't care about the number of zeros in the decimal representation.Limak chose some interval of years. He is going to count all years from this interval that have exactly one zero in the binary representation. Can you do it faster?Assume that all positive integers are always written without leading zeros.

The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 1018) — the first year and the last year in Limak's interval respectively.

Print one integer – the number of years Limak will count in his chosen interval.

NoteIn the first sample Limak's interval contains numbers 510 = 1012, 610 = 1102, 710 = 1112, 810 = 10002, 910 = 10012 and 1010 = 10102. Two of them (1012 and 1102) have the described property.


Limak is a little polar bear. Polar bears hate long strings and thus they like to compress them. You should also know that Limak is so young that he knows only first six letters of the English alphabet: 'a', 'b', 'c', 'd', 'e' and 'f'.You are given a set of q possible operations. Limak can perform them in any order, any operation may be applied any number of times. The i-th operation is described by a string ai of length two and a string bi of length one. No two of q possible operations have the same string ai.When Limak has a string s he can perform the i-th operation on s if the first two letters of s match a two-letter string ai. Performing the i-th operation removes first two letters of s and inserts there a string bi. See the notes section for further clarification.You may note that performing an operation decreases the length of a string s exactly by 1. Also, for some sets of operations there may be a string that cannot be compressed any further, because the first two letters don't match any ai.Limak wants to start with a string of length n and perform n - 1 operations to finally get a one-letter string "a". In how many ways can he choose the starting string to be able to get "a"? Remember that Limak can use only letters he knows.

The first line contains two integers n and q (2 ≤ n ≤ 6, 1 ≤ q ≤ 36) — the length of the initial string and the number of available operations. The next q lines describe the possible operations. The i-th of them contains two strings ai and bi (|ai| = 2, |bi| = 1). It's guaranteed that ai ≠ aj for i ≠ j and that all ai and bi consist of only first six lowercase English letters.

Print the number of strings of length n that Limak will be able to transform to string "a" by applying only operations given in the input.

2 8
af e
dc d
cc f
bc b
da b
eb a
bb b
ff c

NoteIn the first sample, we count initial strings of length 3 from which Limak can get a required string "a". There are 4 such strings: "abb", "cab", "cca", "eea". The first one Limak can compress using operation 1 two times (changing "ab" to a single "a"). The first operation would change "abb" to "ab" and the second operation would change "ab" to "a".Other three strings may be compressed as follows:   "cab"  "ab"  "a"  "cca"  "ca"  "a"  "eea"  "ca"  "a" In the second sample, the only correct initial string is "eb" because it can be immediately compressed to "a".


Tattah is asleep if and only if Tattah is attending a lecture. This is a well-known formula among Tattah's colleagues.On a Wednesday afternoon, Tattah was attending Professor HH's lecture. At 12:21, right before falling asleep, he was staring at the digital watch around Saher's wrist. He noticed that the digits on the clock were the same when read from both directions i.e. a palindrome.In his sleep, he started dreaming about such rare moments of the day when the time displayed on a digital clock is a palindrome. As soon as he woke up, he felt destined to write a program that finds the next such moment.However, he still hasn't mastered the skill of programming while sleeping, so your task is to help him.

The first and only line of the input starts with a string with the format "HH:MM" where "HH" is from "00" to "23" and "MM" is from "00" to "59". Both "HH" and "MM" have exactly two digits.

Print the palindromic time of day that comes soonest after the time given in the input. If the input time is palindromic, output the soonest palindromic time after the input time.


As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as , where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

The first input line contains an integer n (1 ≤ n ≤ 109).

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

NoteIn the first sample number .In the second sample number 512 can not be represented as a sum of two triangular numbers.


You are solving the crossword problem K from IPSC 2014. You solved all the clues except for one: who does Eevee evolve into? You are not very into pokemons, but quick googling helped you find out, that Eevee can evolve into eight different pokemons: Vaporeon, Jolteon, Flareon, Espeon, Umbreon, Leafeon, Glaceon, and Sylveon.You know the length of the word in the crossword, and you already know some letters. Designers of the crossword made sure that the answer is unambiguous, so you can assume that exactly one pokemon out of the 8 that Eevee evolves into fits the length and the letters given. Your task is to find it.

First line contains an integer n (6 ≤ n ≤ 8) – the length of the string. Next line contains a string consisting of n characters, each of which is either a lower case english letter (indicating a known letter) or a dot character (indicating an empty cell in the crossword).

Print a name of the pokemon that Eevee can evolve into that matches the pattern in the input. Use lower case letters only to print the name (in particular, do not capitalize the first letter).

NoteHere's a set of names in a form you can paste into your solution:["vaporeon", "jolteon", "flareon", "espeon", "umbreon", "leafeon", "glaceon", "sylveon"]{"vaporeon", "jolteon", "flareon", "espeon", "umbreon", "leafeon", "glaceon", "sylveon"}


You are given a sequence of integers $$$a_1, a_2, \dots, a_n$$$. You need to paint elements in colors, so that:   If we consider any color, all elements of this color must be divisible by the minimal element of this color.  The number of used colors must be minimized. For example, it's fine to paint elements $$$[40, 10, 60]$$$ in a single color, because they are all divisible by $$$10$$$. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.For example, if $$$a=[6, 2, 3, 4, 12]$$$ then two colors are required: let's paint $$$6$$$, $$$3$$$ and $$$12$$$ in the first color ($$$6$$$, $$$3$$$ and $$$12$$$ are divisible by $$$3$$$) and paint $$$2$$$ and $$$4$$$ in the second color ($$$2$$$ and $$$4$$$ are divisible by $$$2$$$). For example, if $$$a=[10, 7, 15]$$$ then $$$3$$$ colors are required (we can simply paint each element in an unique color).

The first line contains an integer $$$n$$$ ($$$1 \le n \le 100$$$), where $$$n$$$ is the length of the given sequence. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 100$$$). These numbers can contain duplicates.

Print the minimal number of colors to paint all the given numbers in a valid way.

NoteIn the first example, one possible way to paint the elements in $$$3$$$ colors is:  paint in the first color the elements: $$$a_1=10$$$ and $$$a_4=5$$$,  paint in the second color the element $$$a_3=3$$$,  paint in the third color the elements: $$$a_2=2$$$, $$$a_5=4$$$ and $$$a_6=2$$$. In the second example, you can use one color to paint all the elements.In the third example, one possible way to paint the elements in $$$4$$$ colors is:  paint in the first color the elements: $$$a_4=4$$$, $$$a_6=2$$$ and $$$a_7=2$$$,  paint in the second color the elements: $$$a_2=6$$$, $$$a_5=3$$$ and $$$a_8=3$$$,  paint in the third color the element $$$a_3=5$$$,  paint in the fourth color the element $$$a_1=7$$$.


Limak is a little polar bear. He plays by building towers from blocks. Every block is a cube with positive integer length of side. Limak has infinitely many blocks of each side length.A block with side a has volume a3. A tower consisting of blocks with sides a1, a2, ..., ak has the total volume a13 + a23 + ... + ak3.Limak is going to build a tower. First, he asks you to tell him a positive integer X — the required total volume of the tower. Then, Limak adds new blocks greedily, one by one. Each time he adds the biggest block such that the total volume doesn't exceed X.Limak asks you to choose X not greater than m. Also, he wants to maximize the number of blocks in the tower at the end (however, he still behaves greedily). Secondarily, he wants to maximize X.Can you help Limak? Find the maximum number of blocks his tower can have and the maximum X ≤ m that results this number of blocks.

The only line of the input contains one integer m (1 ≤ m ≤ 1015), meaning that Limak wants you to choose X between 1 and m, inclusive.

Print two integers — the maximum number of blocks in the tower and the maximum required total volume X, resulting in the maximum number of blocks.

NoteIn the first sample test, there will be 9 blocks if you choose X = 23 or X = 42. Limak wants to maximize X secondarily so you should choose 42.In more detail, after choosing X = 42 the process of building a tower is:  Limak takes a block with side 3 because it's the biggest block with volume not greater than 42. The remaining volume is 42 - 27 = 15.  The second added block has side 2, so the remaining volume is 15 - 8 = 7.  Finally, Limak adds 7 blocks with side 1, one by one. So, there are 9 blocks in the tower. The total volume is is 33 + 23 + 7·13 = 27 + 8 + 7 = 42.


Manao is working for a construction company. Recently, an order came to build wall bars in a children's park. Manao was commissioned to develop a plan of construction, which will enable the company to save the most money.After reviewing the formal specifications for the wall bars, Manao discovered a number of controversial requirements and decided to treat them to the company's advantage. His resulting design can be described as follows:  Let's introduce some unit of length. The construction center is a pole of height n.  At heights 1, 2, ..., n exactly one horizontal bar sticks out from the pole. Each bar sticks in one of four pre-fixed directions.  A child can move from one bar to another if the distance between them does not exceed h and they stick in the same direction. If a child is on the ground, he can climb onto any of the bars at height between 1 and h. In Manao's construction a child should be able to reach at least one of the bars at heights n - h + 1, n - h + 2, ..., n if he begins at the ground.   The figure to the left shows what a common set of wall bars looks like. The figure to the right shows Manao's construction Manao is wondering how many distinct construction designs that satisfy his requirements exist. As this number can be rather large, print the remainder after dividing it by 1000000009 (109 + 9). Two designs are considered distinct if there is such height i, that the bars on the height i in these designs don't stick out in the same direction.

A single line contains two space-separated integers, n and h (1 ≤ n ≤ 1000, 1 ≤ h ≤ min(n, 30)).

In a single line print the remainder after dividing the number of designs by 1000000009 (109 + 9).

NoteConsider several designs for h = 2. A design with the first bar sticked out in direction d1, the second — in direction d2 and so on (1 ≤ di ≤ 4) is denoted as string d1d2...dn.Design "1231" (the first three bars are sticked out in different directions, the last one — in the same as first). A child can reach neither the bar at height 3 nor the bar at height 4.Design "414141". A child can reach the bar at height 5. To do this, he should first climb at the first bar, then at the third and then at the fifth one. He can also reach bar at height 6 by the route second  →  fourth  →  sixth bars.Design "123333". The child can't reach the upper two bars.Design "323323". The bar at height 6 can be reached by the following route: first  →  third  →  fourth  →  sixth bars.


After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus.  Initially, there is a pile that contains x 100-yen coins and y 10-yen coins.  They take turns alternatively. Ciel takes the first turn.  In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins.  If Ciel or Hanako can't take exactly 220 yen from the pile, she loses.  Determine the winner of the game.

The first line contains two integers x (0 ≤ x ≤ 106) and y (0 ≤ y ≤ 106), separated by a single space.

If Ciel wins, print "Ciel". Otherwise, print "Hanako".

NoteIn the first turn (Ciel's turn), she will choose 2 100-yen coins and 2 10-yen coins. In the second turn (Hanako's turn), she will choose 1 100-yen coin and 12 10-yen coins. In the third turn (Ciel's turn), she can't pay exactly 220 yen, so Ciel will lose.


Two participants are each given a pair of distinct numbers from 1 to 9 such that there's exactly one number that is present in both pairs. They want to figure out the number that matches by using a communication channel you have access to without revealing it to you.Both participants communicated to each other a set of pairs of numbers, that includes the pair given to them. Each pair in the communicated sets comprises two different numbers.Determine if you can with certainty deduce the common number, or if you can determine with certainty that both participants know the number but you do not.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 12$$$) — the number of pairs the first participant communicated to the second and vice versa. The second line contains $$$n$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from first participant to the second. The third line contains $$$m$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from the second participant to the first. All pairs within each set are distinct (in particular, if there is a pair $$$(1,2)$$$, there will be no pair $$$(2,1)$$$ within the same set), and no pair contains the same number twice. It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.

If you can deduce the shared number with certainty, print that number. If you can with certainty deduce that both participants know the shared number, but you do not know it, print $$$0$$$. Otherwise print $$$-1$$$.

NoteIn the first example the first participant communicated pairs $$$(1,2)$$$ and $$$(3,4)$$$, and the second communicated $$$(1,5)$$$, $$$(3,4)$$$. Since we know that the actual pairs they received share exactly one number, it can't be that they both have $$$(3,4)$$$. Thus, the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, and at this point you already know the shared number is $$$1$$$.In the second example either the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, or the first has $$$(3,4)$$$ and the second has $$$(6,4)$$$. In the first case both of them know the shared number is $$$1$$$, in the second case both of them know the shared number is $$$4$$$. You don't have enough information to tell $$$1$$$ and $$$4$$$ apart.In the third case if the first participant was given $$$(1,2)$$$, they don't know what the shared number is, since from their perspective the second participant might have been given either $$$(1,3)$$$, in which case the shared number is $$$1$$$, or $$$(2,3)$$$, in which case the shared number is $$$2$$$. While the second participant does know the number with certainty, neither you nor the first participant do, so the output is $$$-1$$$.


Mashmokh works in a factory. At the end of each day he must turn off all of the lights. The lights on the factory are indexed from 1 to n. There are n buttons in Mashmokh's room indexed from 1 to n as well. If Mashmokh pushes button with index i, then each light with index not less than i that is still turned on turns off.Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed m distinct buttons b1, b2, ..., bm (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button bi is actually bi, not i.Please, help Mashmokh, print these indices.

The first line of the input contains two space-separated integers n and m (1 ≤ n, m ≤ 100), the number of the factory lights and the pushed buttons respectively. The next line contains m distinct space-separated integers b1, b2, ..., bm (1 ≤ bi ≤ n). It is guaranteed that all lights will be turned off after pushing all buttons.

Output n space-separated integers where the i-th number is index of the button that turns the i-th light off.

NoteIn the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off.


Vanya got an important task — he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers.Vanya wants to know how many digits he will have to write down as he labels the books.

The first line contains integer n (1 ≤ n ≤ 109) — the number of books in the library.

Print the number of digits needed to number all the books.

NoteNote to the first test. The books get numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, which totals to 17 digits.Note to the second sample. The books get numbers 1, 2, 3, 4, which totals to 4 digits.


Iahub and his friend Floyd have started painting a wall. Iahub is painting the wall red and Floyd is painting it pink. You can consider the wall being made of a very large number of bricks, numbered 1, 2, 3 and so on. Iahub has the following scheme of painting: he skips x - 1 consecutive bricks, then he paints the x-th one. That is, he'll paint bricks x, 2·x, 3·x and so on red. Similarly, Floyd skips y - 1 consecutive bricks, then he paints the y-th one. Hence he'll paint bricks y, 2·y, 3·y and so on pink.After painting the wall all day, the boys observed that some bricks are painted both red and pink. Iahub has a lucky number a and Floyd has a lucky number b. Boys wonder how many bricks numbered no less than a and no greater than b are painted both red and pink. This is exactly your task: compute and print the answer to the question.

The input will have a single line containing four integers in this order: x, y, a, b. (1 ≤ x, y ≤ 1000, 1 ≤ a, b ≤ 2·109, a ≤ b).

Output a single integer — the number of bricks numbered no less than a and no greater than b that are painted both red and pink.

NoteLet's look at the bricks from a to b (a = 6, b = 18). The bricks colored in red are numbered 6, 8, 10, 12, 14, 16, 18. The bricks colored in pink are numbered 6, 9, 12, 15, 18. The bricks colored in both red and pink are numbered with 6, 12 and 18.


A divisor tree is a rooted tree that meets the following conditions:   Each vertex of the tree contains a positive integer number.  The numbers written in the leaves of the tree are prime numbers.  For any inner vertex, the number within it is equal to the product of the numbers written in its children. Manao has n distinct integers a1, a2, ..., an. He tries to build a divisor tree which contains each of these numbers. That is, for each ai, there should be at least one vertex in the tree which contains ai. Manao loves compact style, but his trees are too large. Help Manao determine the minimum possible number of vertices in the divisor tree sought.

The first line contains a single integer n (1 ≤ n ≤ 8). The second line contains n distinct space-separated integers ai (2 ≤ ai ≤ 1012).

Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers ai.

NoteSample 1. The smallest divisor tree looks this way: Sample 2. In this case you can build the following divisor tree: Sample 3. Note that the tree can consist of a single vertex.


In Bubbleland a group of special programming forces gets a top secret job to calculate the number of potentially infected people by a new unknown virus. The state has a population of $$$n$$$ people and every day there is new information about new contacts between people. The job of special programming forces is to calculate how many contacts in the last $$$k$$$ days a given person had. The new virus has an incubation period of $$$k$$$ days, and after that time people consider as non-infectious. Because the new virus is an extremely dangerous, government mark as suspicious everybody who had direct or indirect contact in the last $$$k$$$ days, independently of the order of contacts.This virus is very strange, and people can't get durable immunity.You need to help special programming forces to calculate the number of suspicious people for a given person (number of people who had contact with a given person).There are 3 given inputs on beginning $$$n$$$ where $$$n$$$ is population, $$$q$$$ number of queries, $$$k$$$ virus incubation time in days. Each query is one of three types:    ($$$x$$$, $$$y$$$) person $$$x$$$ and person $$$y$$$ met that day ($$$x \neq y$$$).   ($$$z$$$) return the number of people in contact with $$$z$$$, counting himself.   The end of the current day moves on to the next day.

The first line of input contains three integers $$$n$$$ ($$$1 \le n\le 10^5$$$) the number of people in the state, $$$q$$$ ($$$1 \le q\le 5×10^5$$$) number of queries and $$$k$$$ ($$$1 \le k\le 10^5$$$) virus incubation time in days. Each of the next $$$q$$$ lines starts with an integer $$$t$$$ ($$$1 \le t\le 3$$$) the type of the query. A pair of integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le n$$$) follows in the query of the first type ($$$x \neq y$$$). An integer $$$i$$$ ($$$1 \le i\le n$$$) follows in the query of the second type.  Query of third type does not have the following number.

For the queries of the second type print on a separate line the current number of people in contact with a given person.

NotePay attention if persons $$$1$$$ and $$$2$$$ had contact first day and next day persons $$$1$$$ and $$$3$$$ had contact, for $$$k$$$>$$$1$$$ number of contacts of person $$$3$$$ is $$$3$$$(persons:1,2,3).


So, the New Year holidays are over. Santa Claus and his colleagues can take a rest and have guests at last. When two "New Year and Christmas Men" meet, thear assistants cut out of cardboard the letters from the guest's name and the host's name in honor of this event. Then the hung the letters above the main entrance. One night, when everyone went to bed, someone took all the letters of our characters' names. Then he may have shuffled the letters and put them in one pile in front of the door.The next morning it was impossible to find the culprit who had made the disorder. But everybody wondered whether it is possible to restore the names of the host and his guests from the letters lying at the door? That is, we need to verify that there are no extra letters, and that nobody will need to cut more letters.Help the "New Year and Christmas Men" and their friends to cope with this problem. You are given both inscriptions that hung over the front door the previous night, and a pile of letters that were found at the front door next morning.

The input file consists of three lines: the first line contains the guest's name, the second line contains the name of the residence host and the third line contains letters in a pile that were found at the door in the morning. All lines are not empty and contain only uppercase Latin letters. The length of each line does not exceed 100.

Print "YES" without the quotes, if the letters in the pile could be permuted to make the names of the "New Year and Christmas Men". Otherwise, print "NO" without the quotes.

NoteIn the first sample the letters written in the last line can be used to write the names and there won't be any extra letters left.In the second sample letter "P" is missing from the pile and there's an extra letter "L".In the third sample there's an extra letter "L".


The only difference between easy and hard versions is constraints.Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly $$$T$$$ minutes.In the player, Polycarp stores $$$n$$$ songs, each of which is characterized by two parameters: $$$t_i$$$ and $$$g_i$$$, where $$$t_i$$$ is the length of the song in minutes ($$$1 \le t_i \le 50$$$), $$$g_i$$$ is its genre ($$$1 \le g_i \le 3$$$).Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the $$$i$$$-th song, he would spend exactly $$$t_i$$$ minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.

The first line of the input contains two integers $$$n$$$ and $$$T$$$ ($$$1 \le n \le 50, 1 \le T \le 2500$$$) — the number of songs in the player and the required total duration, respectively. Next, the $$$n$$$ lines contain descriptions of songs: the $$$i$$$-th line contains two integers $$$t_i$$$ and $$$g_i$$$ ($$$1 \le t_i \le 50, 1 \le g_i \le 3$$$) — the duration of the $$$i$$$-th song and its genre, respectively.

Output one integer — the number of different sequences of songs, the total length of exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo $$$10^9 + 7$$$ (that is, the remainder when dividing the quantity by $$$10^9 + 7$$$).

NoteIn the first example, Polycarp can make any of the $$$6$$$ possible playlist by rearranging the available songs: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$ and $$$[3, 2, 1]$$$ (indices of the songs are given).In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of $$$2$$$ possible ways: $$$[1, 3, 2]$$$ and $$$[2, 3, 1]$$$ (indices of the songs are given).In the third example, Polycarp can make the following playlists: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$, $$$[3, 2, 1]$$$, $$$[1, 4]$$$, $$$[4, 1]$$$, $$$[2, 3, 4]$$$ and $$$[4, 3, 2]$$$ (indices of the songs are given).


One very experienced problem writer decided to prepare a problem for April Fools Day contest. The task was very simple - given an arithmetic expression, return the result of evaluating this expression. However, looks like there is a bug in the reference solution...

The only line of input data contains the arithmetic expression. The expression will contain between 2 and 10 operands, separated with arithmetic signs plus and/or minus. Each operand will be an integer between 0 and 255, inclusive.

Reproduce the output of the reference solution, including the bug.


Vadim is really keen on travelling. Recently he heard about kayaking activity near his town and became very excited about it, so he joined a party of kayakers.Now the party is ready to start its journey, but firstly they have to choose kayaks. There are 2·n people in the group (including Vadim), and they have exactly n - 1 tandem kayaks (each of which, obviously, can carry two people) and 2 single kayaks. i-th person's weight is wi, and weight is an important matter in kayaking — if the difference between the weights of two people that sit in the same tandem kayak is too large, then it can crash. And, of course, people want to distribute their seats in kayaks in order to minimize the chances that kayaks will crash.Formally, the instability of a single kayak is always 0, and the instability of a tandem kayak is the absolute difference between weights of the people that are in this kayak. Instability of the whole journey is the total instability of all kayaks.Help the party to determine minimum possible total instability!

The first line contains one number n (2 ≤ n ≤ 50). The second line contains 2·n integer numbers w1, w2, ..., w2n, where wi is weight of person i (1 ≤ wi ≤ 1000).

Print minimum possible total instability.


Vus the Cossack holds a programming competition, in which $$$n$$$ people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly $$$m$$$ pens and $$$k$$$ notebooks.Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.

The first line contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$1 \leq n, m, k \leq 100$$$) — the number of participants, the number of pens, and the number of notebooks respectively.

Print "Yes" if it possible to reward all the participants. Otherwise, print "No". You can print each letter in any case (upper or lower).

NoteIn the first example, there are $$$5$$$ participants. The Cossack has $$$8$$$ pens and $$$6$$$ notebooks. Therefore, he has enough pens and notebooks.In the second example, there are $$$3$$$ participants. The Cossack has $$$9$$$ pens and $$$3$$$ notebooks. He has more than enough pens but only the minimum needed number of notebooks.In the third example, there are $$$8$$$ participants but only $$$5$$$ pens. Since the Cossack does not have enough pens, the answer is "No".


You stumbled upon a new kind of chess puzzles. The chessboard you are given is not necesserily $$$8 \times 8$$$, but it still is $$$N \times N$$$. Each square has some number written on it, all the numbers are from $$$1$$$ to $$$N^2$$$ and all the numbers are pairwise distinct. The $$$j$$$-th square in the $$$i$$$-th row has a number $$$A_{ij}$$$ written on it.In your chess set you have only three pieces: a knight, a bishop and a rook. At first, you put one of them on the square with the number $$$1$$$ (you can choose which one). Then you want to reach square $$$2$$$ (possibly passing through some other squares in process), then square $$$3$$$ and so on until you reach square $$$N^2$$$. In one step you are allowed to either make a valid move with the current piece or replace it with some other piece. Each square can be visited arbitrary number of times.A knight can move to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally. A bishop moves diagonally. A rook moves horizontally or vertically. The move should be performed to a different square from the one a piece is currently standing on.You want to minimize the number of steps of the whole traversal. Among all the paths to have the same number of steps you want to choose the one with the lowest number of piece replacements.What is the path you should take to satisfy all conditions?

The first line contains a single integer $$$N$$$ ($$$3 \le N \le 10$$$) — the size of the chessboard. Each of the next $$$N$$$ lines contains $$$N$$$ integers $$$A_{i1}, A_{i2}, \dots, A_{iN}$$$ ($$$1 \le A_{ij} \le N^2$$$) — the numbers written on the squares of the $$$i$$$-th row of the board. It is guaranteed that all $$$A_{ij}$$$ are pairwise distinct.

The only line should contain two integers — the number of steps in the best answer and the number of replacement moves in it.

NoteHere are the steps for the first example (the starting piece is a knight):  Move to $$$(3, 2)$$$  Move to $$$(1, 3)$$$  Move to $$$(3, 2)$$$  Replace the knight with a rook  Move to $$$(3, 1)$$$  Move to $$$(3, 3)$$$  Move to $$$(3, 2)$$$  Move to $$$(2, 2)$$$  Move to $$$(2, 3)$$$  Move to $$$(2, 1)$$$  Move to $$$(1, 1)$$$  Move to $$$(1, 2)$$$


wHAT DO WE NEED cAPS LOCK FOR?Caps lock is a computer keyboard key. Pressing it sets an input mode in which typed letters are capital by default. If it is pressed by accident, it leads to accidents like the one we had in the first passage. Let's consider that a word has been typed with the Caps lock key accidentally switched on, if:   either it only contains uppercase letters;  or all letters except for the first one are uppercase. In this case we should automatically change the case of all letters. For example, the case of the letters that form words "hELLO", "HTTP", "z" should be changed.Write a program that applies the rule mentioned above. If the rule cannot be applied, the program should leave the word unchanged.

The first line of the input data contains a word consisting of uppercase and lowercase Latin letters. The word's length is from 1 to 100 characters, inclusive.

Print the result of the given word's processing.


The final round of Bayan Programming Contest will be held in Tehran, and the participants will be carried around with a yellow bus. The bus has 34 passenger seats: 4 seats in the last row and 3 seats in remaining rows.   The event coordinator has a list of k participants who should be picked up at the airport. When a participant gets on the bus, he will sit in the last row with an empty seat. If there is more than one empty seat in that row, he will take the leftmost one. In order to keep track of the people who are on the bus, the event coordinator needs a figure showing which seats are going to be taken by k participants. Your task is to draw the figure representing occupied seats.

The only line of input contains integer k, (0 ≤ k ≤ 34), denoting the number of participants.

Print the figure of a bus with k passengers as described in sample tests. Character '#' denotes an empty seat, while 'O' denotes a taken seat. 'D' is the bus driver and other characters in the output are for the purpose of beautifying the figure. Strictly follow the sample test cases output format. Print exactly six lines. Do not output extra space or other characters.


A large banner with word CODEFORCES was ordered for the 1000-th onsite round of Codeforcesω that takes place on the Miami beach. Unfortunately, the company that made the banner mixed up two orders and delivered somebody else's banner that contains someone else's word. The word on the banner consists only of upper-case English letters.There is very little time to correct the mistake. All that we can manage to do is to cut out some substring from the banner, i.e. several consecutive letters. After that all the resulting parts of the banner will be glued into a single piece (if the beginning or the end of the original banner was cut out, only one part remains); it is not allowed change the relative order of parts of the banner (i.e. after a substring is cut, several first and last letters are left, it is allowed only to glue the last letters to the right of the first letters). Thus, for example, for example, you can cut a substring out from string 'TEMPLATE' and get string 'TEMPLE' (if you cut out string AT), 'PLATE' (if you cut out TEM), 'T' (if you cut out EMPLATE), etc.Help the organizers of the round determine whether it is possible to cut out of the banner some substring in such a way that the remaining parts formed word CODEFORCES.

The single line of the input contains the word written on the banner. The word only consists of upper-case English letters. The word is non-empty and its length doesn't exceed 100 characters. It is guaranteed that the word isn't word CODEFORCES.

Print 'YES', if there exists a way to cut out the substring, and 'NO' otherwise (without the quotes).

CODEWAITFORITFORCES BOTTOMCODER DECODEFORCES DOGEFORCES


Vasily the bear has a favorite rectangle, it has one vertex at point (0, 0), and the opposite vertex at point (x, y). Of course, the sides of Vasya's favorite rectangle are parallel to the coordinate axes. Vasya also loves triangles, if the triangles have one vertex at point B = (0, 0). That's why today he asks you to find two points A = (x1, y1) and C = (x2, y2), such that the following conditions hold:  the coordinates of points: x1, x2, y1, y2 are integers. Besides, the following inequation holds: x1 < x2;  the triangle formed by point A, B and C is rectangular and isosceles ( is right);  all points of the favorite rectangle are located inside or on the border of triangle ABC;  the area of triangle ABC is as small as possible. Help the bear, find the required points. It is not so hard to proof that these points are unique.

The first line contains two integers x, y ( - 109 ≤ x, y ≤ 109, x ≠ 0, y ≠ 0).

Print in the single line four integers x1, y1, x2, y2 — the coordinates of the required points.


Amr is a young coder who likes music a lot. He always wanted to learn how to play music but he was busy coding so he got an idea.Amr has n instruments, it takes ai days to learn i-th instrument. Being busy, Amr dedicated k days to learn how to play the maximum possible number of instruments.Amr asked for your help to distribute his free days between instruments so that he can achieve his goal.

The first line contains two numbers n, k (1 ≤ n ≤ 100, 0 ≤ k ≤ 10 000), the number of instruments and number of days respectively. The second line contains n integers ai (1 ≤ ai ≤ 100), representing number of days required to learn the i-th instrument.

In the first line output one integer m representing the maximum number of instruments Amr can learn. In the second line output m space-separated integers: the indices of instruments to be learnt. You may output indices in any order. if there are multiple optimal solutions output any. It is not necessary to use all days for studying.

NoteIn the first test Amr can learn all 4 instruments.In the second test other possible solutions are: {2, 3, 5} or {3, 4, 5}.In the third test Amr doesn't have enough time to learn the only presented instrument.


When preparing a tournament, Codeforces coordinators try treir best to make the first problem as easy as possible. This time the coordinator had chosen some problem and asked $$$n$$$ people about their opinions. Each person answered whether this problem is easy or hard.If at least one of these $$$n$$$ people has answered that the problem is hard, the coordinator decides to change the problem. For the given responses, check if the problem is easy enough.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of people who were asked to give their opinions. The second line contains $$$n$$$ integers, each integer is either $$$0$$$ or $$$1$$$. If $$$i$$$-th integer is $$$0$$$, then $$$i$$$-th person thinks that the problem is easy; if it is $$$1$$$, then $$$i$$$-th person thinks that the problem is hard.

Print one word: "EASY" if the problem is easy according to all responses, or "HARD" if there is at least one person who thinks the problem is hard.  You may print every letter in any register: "EASY", "easy", "EaSY" and "eAsY" all will be processed correctly.

NoteIn the first example the third person says it's a hard problem, so it should be replaced.In the second example the problem easy for the only person, so it doesn't have to be replaced.


Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?

The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.

Print a single integer — the minimum sum in rubles that Ann will need to spend.

NoteIn the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.


Students Vasya and Petya are studying at the BSU (Byteland State University). At one of the breaks they decided to order a pizza. In this problem pizza is a circle of some radius. The pizza was delivered already cut into n pieces. The i-th piece is a sector of angle equal to ai. Vasya and Petya want to divide all pieces of pizza into two continuous sectors in such way that the difference between angles of these sectors is minimal. Sector angle is sum of angles of all pieces in it. Pay attention, that one of sectors can be empty.

The first line contains one integer n (1 ≤ n ≤ 360)  — the number of pieces into which the delivered pizza was cut. The second line contains n integers ai (1 ≤ ai ≤ 360)  — the angles of the sectors into which the pizza was cut. The sum of all ai is 360.

Print one integer  — the minimal difference between angles of sectors that will go to Vasya and Petya.

NoteIn first sample Vasya can take 1 and 2 pieces, Petya can take 3 and 4 pieces. Then the answer is |(90 + 90) - (90 + 90)| = 0.In third sample there is only one piece of pizza that can be taken by only one from Vasya and Petya. So the answer is |360 - 0| = 360.In fourth sample Vasya can take 1 and 4 pieces, then Petya will take 2 and 3 pieces. So the answer is |(170 + 10) - (30 + 150)| = 0.Picture explaning fourth sample:Both red and green sectors consist of two adjacent pieces of pizza. So Vasya can take green sector, then Petya will take red sector.


Roman is a young mathematician, very famous in Uzhland. Unfortunately, Sereja doesn't think so. To make Sereja change his mind, Roman is ready to solve any mathematical problem. After some thought, Sereja asked Roma to find, how many numbers are close to number n, modulo m.Number x is considered close to number n modulo m, if:  it can be obtained by rearranging the digits of number n,  it doesn't have any leading zeroes,  the remainder after dividing number x by m equals 0. Roman is a good mathematician, but the number of such numbers is too huge for him. So he asks you to help him.

The first line contains two integers: n (1 ≤ n < 1018) and m (1 ≤ m ≤ 100).

In a single line print a single integer — the number of numbers close to number n modulo m.

NoteIn the first sample the required numbers are: 104, 140, 410.In the second sample the required number is 232.


It seems like the year of 2013 came only yesterday. Do you know a curious fact? The year of 2013 is the first year after the old 1987 with only distinct digits.Now you are suggested to solve the following problem: given a year number, find the minimum year number which is strictly larger than the given one and has only distinct digits.

The single line contains integer y (1000 ≤ y ≤ 9000) — the year number.

Print a single integer — the minimum year number that is strictly larger than y and all it's digits are distinct. It is guaranteed that the answer exists.


There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:  Red-green tower is consisting of some number of levels;  Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level — of n - 1 blocks, the third one — of n - 2 blocks, and so on — the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;  Each level of the red-green tower should contain blocks of the same color.  Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.You are to write a program that will find the number of different red-green towers of height h modulo 109 + 7.

The only line of input contains two integers r and g, separated by a single space — the number of available red and green blocks respectively (0 ≤ r, g ≤ 2·105, r + g ≥ 1).

Output the only integer — the number of different possible red-green towers of height h modulo 109 + 7.

NoteThe image in the problem statement shows all possible red-green towers for the first sample.


A never-ending, fast-changing and dream-like world unfolds, as the secret door opens.A world is an unordered graph G, in whose vertex set V(G) there are two special vertices s(G) and t(G). An initial world has vertex set {s(G), t(G)} and an edge between them.A total of n changes took place in an initial world. In each change, a new vertex w is added into V(G), an existing edge (u, v) is chosen, and two edges (u, w) and (v, w) are added into E(G). Note that it's possible that some edges are chosen in more than one change.It's known that the capacity of the minimum s-t cut of the resulting graph is m, that is, at least m edges need to be removed in order to make s(G) and t(G) disconnected.Count the number of non-similar worlds that can be built under the constraints, modulo 109 + 7. We define two worlds similar, if they are isomorphic and there is isomorphism in which the s and t vertices are not relabelled. Formally, two worlds G and H are considered similar, if there is a bijection between their vertex sets , such that:   f(s(G)) = s(H);  f(t(G)) = t(H);  Two vertices u and v of G are adjacent in G if and only if f(u) and f(v) are adjacent in H.

The first and only line of input contains two space-separated integers n, m (1 ≤ n, m ≤ 50) — the number of operations performed and the minimum cut, respectively.

Output one integer — the number of non-similar worlds that can be built, modulo 109 + 7.

NoteIn the first example, the following 6 worlds are pairwise non-similar and satisfy the constraints, with s(G) marked in green, t(G) marked in blue, and one of their minimum cuts in light blue.  In the second example, the following 3 worlds satisfy the constraints.


There is the faculty of Computer Science in Berland. In the social net "TheContact!" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university. Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than x from the year of university entrance of this student, where x — some non-negative integer. A value x is not given, but it can be uniquely determined from the available data. Note that students don't join other groups. You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance.

The first line contains the positive odd integer n (1 ≤ n ≤ 5) — the number of groups which Igor joined.  The next line contains n distinct integers a1, a2, ..., an (2010 ≤ ai ≤ 2100) — years of student's university entrance for each group in which Igor is the member. It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly.

Print the year of Igor's university entrance.

NoteIn the first test the value x = 1. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.In the second test the value x = 0. Igor entered only the group which corresponds to the year of his university entrance.


You are given two lists of non-zero digits.Let's call an integer pretty if its (base 10) representation has at least one digit from the first list and at least one digit from the second list. What is the smallest positive pretty integer?

The first line contains two integers n and m (1 ≤ n, m ≤ 9) — the lengths of the first and the second lists, respectively. The second line contains n distinct digits a1, a2, ..., an (1 ≤ ai ≤ 9) — the elements of the first list. The third line contains m distinct digits b1, b2, ..., bm (1 ≤ bi ≤ 9) — the elements of the second list.

NoteIn the first example 25, 46, 24567 are pretty, as well as many other integers. The smallest among them is 25. 42 and 24 are not pretty because they don't have digits from the second list.In the second example all integers that have at least one digit different from 9 are pretty. It's obvious that the smallest among them is 1, because it's the smallest positive integer.


One beautiful July morning a terrible thing happened in Mainframe: a mean virus Megabyte somehow got access to the memory of his not less mean sister Hexadecimal. He loaded there a huge amount of n different natural numbers from 1 to n to obtain total control over her energy.But his plan failed. The reason for this was very simple: Hexadecimal didn't perceive any information, apart from numbers written in binary format. This means that if a number in a decimal representation contained characters apart from 0 and 1, it was not stored in the memory. Now Megabyte wants to know, how many numbers were loaded successfully.

Input data contains the only number n (1 ≤ n ≤ 109).

Output the only number — answer to the problem.

NoteFor n = 10 the answer includes numbers 1 and 10.


Ted has a pineapple. This pineapple is able to bark like a bulldog! At time t (in seconds) it barks for the first time. Then every s seconds after it, it barks twice with 1 second interval. Thus it barks at times t, t + s, t + s + 1, t + 2s, t + 2s + 1, etc.  Barney woke up in the morning and wants to eat the pineapple, but he can't eat it when it's barking. Barney plans to eat it at time x (in seconds), so he asked you to tell him if it's gonna bark at that time.

The first and only line of input contains three integers t, s and x (0 ≤ t, x ≤ 109, 2 ≤ s ≤ 109) — the time the pineapple barks for the first time, the pineapple barking interval, and the time Barney wants to eat the pineapple respectively.

Print a single "YES" (without quotes) if the pineapple will bark at time x or a single "NO" (without quotes) otherwise in the only line of output.

NoteIn the first and the second sample cases pineapple will bark at moments 3, 13, 14, ..., so it won't bark at the moment 4 and will bark at the moment 3.In the third and fourth sample cases pineapple will bark at moments 3, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, ..., so it will bark at both moments 51 and 52.


Harry Potter lost his Invisibility Cloak, running from the school caretaker Filch. Finding an invisible object is not an easy task. Fortunately, Harry has friends who are willing to help. Hermione Granger had read "The Invisibility Cloaks, and Everything about Them", as well as six volumes of "The Encyclopedia of Quick Search of Shortest Paths in Graphs, Network Flows, the Maximal Increasing Subsequences and Other Magical Objects". She has already developed a search algorithm for the invisibility cloak in complex dynamic systems (Hogwarts is one of them).Hogwarts consists of n floors, numbered by integers from 1 to n. Some pairs of floors are connected by staircases. The staircases may change its position, moving exactly one end. Formally the situation is like this: if a staircase connects the floors a and b, then in one move it may modify its position so as to connect the floors a and c or b and c, where c is any floor different from a and b. Under no circumstances the staircase can connect a floor with itself. At the same time there can be multiple stairs between a pair of floors.Initially, Harry is on the floor with the number 1. He does not remember on what floor he has lost the cloak and wants to look for it on each of the floors. Therefore, his goal is to visit each of n floors at least once. Harry can visit the floors in any order and finish the searching at any floor.Nowadays the staircases move quite rarely. However, Ron and Hermione are willing to put a spell on any of them to help Harry find the cloak. To cause less suspicion, the three friends plan to move the staircases one by one, and no more than once for each staircase. In between shifting the staircases Harry will be able to move about the floors, reachable at the moment from the staircases, and look for his Invisibility Cloak. It is assumed that during all this time the staircases will not move spontaneously.Help the three friends to compose a searching plan. If there are several variants to solve the problem, any valid option (not necessarily the optimal one) will be accepted.

The first line contains integers n and m (1 ≤ n ≤ 100000, 0 ≤ m ≤ 200000), which are the number of floors and staircases in Hogwarts, respectively. The following m lines contain pairs of floors connected by staircases at the initial moment of time.

In the first line print "YES" (without the quotes) if Harry is able to search all the floors, and "NO" otherwise. If the answer is positive, then print on the second line the number of staircases that Ron and Hermione will have to shift. Further output should look like this: Harry's moves  a staircase's move  Harry's moves a staircase's move ... a staircase's move Harry's moves Each "Harry's move" should be represented as a list of floors in the order in which they have been visited. The total amount of elements of these lists must not exceed 106. When you print each list, first print the number of elements in it, and then in the same line print the actual space-separated elements. The first number in the first list should be the number 1 (the floor, from which Harry begins to search). Any list except the first one might contain the zero number of elements. Note that Harry can visit some floors again, but must visit all n floors at least once. Two consecutively visited floors must be directly connected by a staircase (at the time Harry goes from one of them to the other one). No two floors that are visited consequtively can be equal. In the description of a "staircase's move" indicate the number of staircase (the staircases are numbered from 1 to m in the order in which they are given in the input data) and its new location (two numbers of the connected floors in any order). Any staircase can be moved at most once. If there are several solutions, output any.


Kolya loves putting gnomes at the circle table and giving them coins, and Tanya loves studying triplets of gnomes, sitting in the vertexes of an equilateral triangle.More formally, there are 3n gnomes sitting in a circle. Each gnome can have from 1 to 3 coins. Let's number the places in the order they occur in the circle by numbers from 0 to 3n - 1, let the gnome sitting on the i-th place have ai coins. If there is an integer i (0 ≤ i < n) such that ai + ai + n + ai + 2n ≠ 6, then Tanya is satisfied. Count the number of ways to choose ai so that Tanya is satisfied. As there can be many ways of distributing coins, print the remainder of this number modulo 109 + 7. Two ways, a and b, are considered distinct if there is index i (0 ≤ i < 3n), such that ai ≠ bi (that is, some gnome got different number of coins in these two ways).

A single line contains number n (1 ≤ n ≤ 105) — the number of the gnomes divided by three.

Print a single number — the remainder of the number of variants of distributing coins that satisfy Tanya modulo 109 + 7.

Note20 ways for n = 1 (gnome with index 0 sits on the top of the triangle, gnome 1 on the right vertex, gnome 2 on the left vertex):


It's the end of July – the time when a festive evening is held at Jelly Castle! Guests from all over the kingdom gather here to discuss new trends in the world of confectionery. Yet some of the things discussed here are not supposed to be disclosed to the general public: the information can cause discord in the kingdom of Sweetland in case it turns out to reach the wrong hands. So it's a necessity to not let any uninvited guests in.There are 26 entrances in Jelly Castle, enumerated with uppercase English letters from A to Z. Because of security measures, each guest is known to be assigned an entrance he should enter the castle through. The door of each entrance is opened right before the first guest's arrival and closed right after the arrival of the last guest that should enter the castle through this entrance. No two guests can enter the castle simultaneously.For an entrance to be protected from possible intrusion, a candy guard should be assigned to it. There are k such guards in the castle, so if there are more than k opened doors, one of them is going to be left unguarded! Notice that a guard can't leave his post until the door he is assigned to is closed.Slastyona had a suspicion that there could be uninvited guests at the evening. She knows the order in which the invited guests entered the castle, and wants you to help her check whether there was a moment when more than k doors were opened.

Two integers are given in the first string: the number of guests n and the number of guards k (1 ≤ n ≤ 106, 1 ≤ k ≤ 26). In the second string, n uppercase English letters s1s2... sn are given, where si is the entrance used by the i-th guest.

Output «YES» if at least one door was unguarded during some time, and «NO» otherwise. You can output each letter in arbitrary case (upper or lower).

NoteIn the first sample case, the door A is opened right before the first guest's arrival and closed when the second guest enters the castle. The door B is opened right before the arrival of the third guest, and closed after the fifth one arrives. One guard can handle both doors, as the first one is closed before the second one is opened.In the second sample case, the door B is opened before the second guest's arrival, but the only guard can't leave the door A unattended, as there is still one more guest that should enter the castle through this door.


A little girl loves problems on bitwise operations very much. Here's one of them.You are given two integers l and r. Let's consider the values of  for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.Expression  means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".

The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

In a single line print a single integer — the maximum value of  for all pairs of integers a, b (l ≤ a ≤ b ≤ r).


Two boys decided to compete in text typing on the site "Key races". During the competition, they have to type a text consisting of s characters. The first participant types one character in v1 milliseconds and has ping t1 milliseconds. The second participant types one character in v2 milliseconds and has ping t2 milliseconds.If connection ping (delay) is t milliseconds, the competition passes for a participant as follows:   Exactly after t milliseconds after the start of the competition the participant receives the text to be entered.  Right after that he starts to type it.  Exactly t milliseconds after he ends typing all the text, the site receives information about it. The winner is the participant whose information on the success comes earlier. If the information comes from both participants at the same time, it is considered that there is a draw.Given the length of the text and the information about participants, determine the result of the game.

The first line contains five integers s, v1, v2, t1, t2 (1 ≤ s, v1, v2, t1, t2 ≤ 1000) — the number of characters in the text, the time of typing one character for the first participant, the time of typing one character for the the second participant, the ping of the first participant and the ping of the second participant.

If the first participant wins, print "First". If the second participant wins, print "Second". In case of a draw print "Friendship".

NoteIn the first example, information on the success of the first participant comes in 7 milliseconds, of the second participant — in 14 milliseconds. So, the first wins.In the second example, information on the success of the first participant comes in 11 milliseconds, of the second participant — in 5 milliseconds. So, the second wins.In the third example, information on the success of the first participant comes in 22 milliseconds, of the second participant — in 22 milliseconds. So, it is be a draw.


Meg the Rabbit decided to do something nice, specifically — to determine the shortest distance between two points on the surface of our planet. But Meg... what can you say, she wants everything simple. So, she already regards our planet as a two-dimensional circle. No, wait, it's even worse — as a square of side n. Thus, the task has been reduced to finding the shortest path between two dots on a square (the path should go through the square sides). To simplify the task let us consider the vertices of the square to lie at points whose coordinates are: (0, 0), (n, 0), (0, n) and (n, n).

The single line contains 5 space-separated integers: n, x1, y1, x2, y2 (1 ≤ n ≤ 1000, 0 ≤ x1, y1, x2, y2 ≤ n) which correspondingly represent a side of the square, the coordinates of the first point and the coordinates of the second point. It is guaranteed that the points lie on the sides of the square.

You must print on a single line the shortest distance between the points.


Nauuo is a girl who loves traveling.One day she went to a tree, Old Driver Tree, literally, a tree with an old driver on it.The tree is a connected graph consisting of $$$n$$$ nodes and $$$n-1$$$ edges. Each node has a color, and Nauuo will visit the ODT through a simple path on the tree in the old driver's car.Nauuo wants to visit see more different colors in her journey, but she doesn't know which simple path she will be traveling on. So, she wants to calculate the sum of the numbers of different colors on all different paths. Can you help her?What's more, the ODT is being redecorated, so there will be $$$m$$$ modifications, each modification will change a single node's color. Nauuo wants to know the answer after each modification too.Note that in this problem, we consider the simple path from $$$u$$$ to $$$v$$$ and the simple path from $$$v$$$ to $$$u$$$ as two different simple paths if and only if $$$u\ne v$$$.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2\le n\le 4\cdot 10^5$$$, $$$1\le m\le 4\cdot 10^5$$$) — the number of nodes and the number of modifications. The second line contains $$$n$$$ integers $$$c_1,c_2,\ldots,c_n$$$ ($$$1\le c_i\le n$$$), where $$$c_i$$$ is the initial color of node $$$i$$$. Each of the next $$$n-1$$$ lines contains two integers $$$u$$$ and $$$v$$$ ($$$1\le u,v\le n$$$), denoting there is an edge between $$$u$$$ and $$$v$$$. It is guaranteed that the given edges form a tree. Each of the next $$$m$$$ lines contains two integers $$$u$$$ and $$$x$$$ ($$$1\le u,x\le n$$$), which means a modification that changes the color of node $$$u$$$ into $$$x$$$.

The output contains $$$m+1$$$ integers — the first integer is the answer at the beginning, the rest integers are the answers after every modification in the given order.

NoteExample 1The number of colors on each simple path at the beginning:


You are given a rectangular board of M × N squares. Also you are given an unlimited number of standard domino pieces of 2 × 1 squares. You are allowed to rotate the pieces. You are asked to place as many dominoes as possible on the board so as to meet the following conditions:1. Each domino completely covers two squares.2. No two dominoes overlap.3. Each domino lies entirely inside the board. It is allowed to touch the edges of the board.Find the maximum number of dominoes, which can be placed under these restrictions.

In a single line you are given two integers M and N — board sizes in squares (1 ≤ M ≤ N ≤ 16).

Output one number — the maximal number of dominoes, which can be placed.


One day Vasya was lying in bed watching his electronic clock to fall asleep quicker.Vasya lives in a strange country, where days have h hours, and every hour has m minutes. Clock shows time in decimal number system, in format H:M, where the string H always has a fixed length equal to the number of digits in the decimal representation of number h - 1. To achieve this, leading zeros are added if necessary. The string M has a similar format, and its length is always equal to the number of digits in the decimal representation of number m - 1. For example, if h = 17, m = 1000, then time equal to 13 hours and 75 minutes will be displayed as "13:075".Vasya had been watching the clock from h1 hours m1 minutes to h2 hours m2 minutes inclusive, and then he fell asleep. Now he asks you to count how many times he saw the moment at which at least k digits changed on the clock simultaneously.For example, when switching 04:19  →  04:20 two digits change. When switching 23:59  →  00:00, four digits change.Consider that Vasya has been watching the clock for strictly less than one day. Note that the last time Vasya saw on the clock before falling asleep was "h2:m2". That is, Vasya didn't see the moment at which time "h2:m2" switched to the next value.

The first line of the input file contains three space-separated integers h, m and k (2 ≤ h, m ≤ 109, 1 ≤ k ≤ 20). The second line contains space-separated integers h1, m1 (0 ≤ h1 < h, 0 ≤ m1 < m). The third line contains space-separated integers h2, m2 (0 ≤ h2 < h, 0 ≤ m2 < m).

Print a single number — the number of times Vasya saw the moment of changing at least k digits simultaneously. Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin stream (also you may use the %I64d specificator).

NoteIn the first example Vasya will see the following moments of time: 4:4  0:0  →  0:1  →  0:2  →  0:3  →  0:4  1:0  →  1:1  →  1:2  →  1:3  →  1:4  2:0  →  2:1  →  2:2  →  2:3  →  2:4. Double arrow () marks the sought moments of time (in this example — when Vasya sees two numbers changing simultaneously).In the second example k = 1. Any switching time can be accepted, since during switching of the clock at least one digit is changed. Total switching equals to 24·60 = 1440, but Vasya have not seen one of them — the switching of 23:59  00:00.In the third example Vasya fell asleep immediately after he began to look at the clock, so he did not see any change.


Tokitsukaze is one of the characters in the game "Kantai Collection". In this game, every character has a common attribute — health points, shortened to HP.In general, different values of HP are grouped into $$$4$$$ categories:  Category $$$A$$$ if HP is in the form of $$$(4 n + 1)$$$, that is, when divided by $$$4$$$, the remainder is $$$1$$$;  Category $$$B$$$ if HP is in the form of $$$(4 n + 3)$$$, that is, when divided by $$$4$$$, the remainder is $$$3$$$;  Category $$$C$$$ if HP is in the form of $$$(4 n + 2)$$$, that is, when divided by $$$4$$$, the remainder is $$$2$$$;  Category $$$D$$$ if HP is in the form of $$$4 n$$$, that is, when divided by $$$4$$$, the remainder is $$$0$$$. The above-mentioned $$$n$$$ can be any integer.These $$$4$$$ categories ordered from highest to lowest as $$$A > B > C > D$$$, which means category $$$A$$$ is the highest and category $$$D$$$ is the lowest.While playing the game, players can increase the HP of the character. Now, Tokitsukaze wants you to increase her HP by at most $$$2$$$ (that is, either by $$$0$$$, $$$1$$$ or $$$2$$$). How much should she increase her HP so that it has the highest possible category?

The only line contains a single integer $$$x$$$ ($$$30 \leq x \leq 100$$$) — the value Tokitsukaze's HP currently.

Print an integer $$$a$$$ ($$$0 \leq a \leq 2$$$) and an uppercase letter $$$b$$$ ($$$b \in \lbrace A, B, C, D \rbrace$$$), representing that the best way is to increase her HP by $$$a$$$, and then the category becomes $$$b$$$. Note that the output characters are case-sensitive.

NoteFor the first example, the category of Tokitsukaze's HP is already $$$A$$$, so you don't need to enhance her ability.For the second example:  If you don't increase her HP, its value is still $$$98$$$, which equals to $$$(4 \times 24 + 2)$$$, and its category is $$$C$$$.  If you increase her HP by $$$1$$$, its value becomes $$$99$$$, which equals to $$$(4 \times 24 + 3)$$$, and its category becomes $$$B$$$.  If you increase her HP by $$$2$$$, its value becomes $$$100$$$, which equals to $$$(4 \times 25)$$$, and its category becomes $$$D$$$. Therefore, the best way is to increase her HP by $$$1$$$ so that the category of her HP becomes $$$B$$$.


Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.In his pocket Polycarp has an unlimited number of "10-burle coins" and exactly one coin of r burles (1 ≤ r ≤ 9).What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.

The single line of input contains two integers k and r (1 ≤ k ≤ 1000, 1 ≤ r ≤ 9) — the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from "10-burle coins".  Remember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.

Print the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change.

NoteIn the first example Polycarp can buy 9 shovels and pay 9·117 = 1053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.In the second example it is enough for Polycarp to buy one shovel.In the third example Polycarp should buy two shovels and pay 2·15 = 30 burles. It is obvious that he can pay this sum without any change.


n hobbits are planning to spend the night at Frodo's house. Frodo has n beds standing in a row and m pillows (n ≤ m). Each hobbit needs a bed and at least one pillow to sleep, however, everyone wants as many pillows as possible. Of course, it's not always possible to share pillows equally, but any hobbit gets hurt if he has at least two pillows less than some of his neighbors have. Frodo will sleep on the k-th bed in the row. What is the maximum number of pillows he can have so that every hobbit has at least one pillow, every pillow is given to some hobbit and no one is hurt?

The only line contain three integers n, m and k (1 ≤ n ≤ m ≤ 109, 1 ≤ k ≤ n) — the number of hobbits, the number of pillows and the number of Frodo's bed.

Print single integer — the maximum number of pillows Frodo can have so that no one is hurt.

NoteIn the first example Frodo can have at most two pillows. In this case, he can give two pillows to the hobbit on the first bed, and one pillow to each of the hobbits on the third and the fourth beds.In the second example Frodo can take at most four pillows, giving three pillows to each of the others.In the third example Frodo can take three pillows, giving two pillows to the hobbit in the middle and one pillow to the hobbit on the third bed.


You have $$$n \times n$$$ square grid and an integer $$$k$$$. Put an integer in each cell while satisfying the conditions below.  All numbers in the grid should be between $$$1$$$ and $$$k$$$ inclusive.  Minimum number of the $$$i$$$-th row is $$$1$$$ ($$$1 \le i \le n$$$).  Minimum number of the $$$j$$$-th column is $$$1$$$ ($$$1 \le j \le n$$$). Find the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo $$$(10^{9} + 7)$$$.  These are the examples of valid and invalid grid when $$$n=k=2$$$.

The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 250$$$, $$$1 \le k \le 10^{9}$$$).

Print the answer modulo $$$(10^{9} + 7)$$$.

NoteIn the first example, following $$$7$$$ cases are possible.  In the second example, make sure you print the answer modulo $$$(10^{9} + 7)$$$.


There are n people, sitting in a line at the table. For each person we know that he always tells either the truth or lies.Little Serge asked them: how many of you always tell the truth? Each of the people at the table knows everything (who is an honest person and who is a liar) about all the people at the table. The honest people are going to say the correct answer, the liars are going to say any integer from 1 to n, which is not the correct answer. Every liar chooses his answer, regardless of the other liars, so two distinct liars may give distinct answer.Serge does not know any information about the people besides their answers to his question. He took a piece of paper and wrote n integers a1, a2, ..., an, where ai is the answer of the i-th person in the row. Given this sequence, Serge determined that exactly k people sitting at the table apparently lie.Serge wonders, how many variants of people's answers (sequences of answers a of length n) there are where one can say that exactly k people sitting at the table apparently lie. As there can be rather many described variants of answers, count the remainder of dividing the number of the variants by 777777777.

The first line contains two integers n, k, (1 ≤ k ≤ n ≤ 28). It is guaranteed that n — is the power of number 2.

Print a single integer — the answer to the problem modulo 777777777.


We all know that GukiZ often plays with arrays. Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition: ? Here operation  means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation  means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |). Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him!

First and the only line of input contains four integers n, k, l, m (2 ≤ n ≤ 1018, 0 ≤ k ≤ 1018, 0 ≤ l ≤ 64, 1 ≤ m ≤ 109 + 7).

In the single line print the number of arrays satisfying the condition above modulo m.

NoteIn the first sample, satisfying arrays are {1, 1}, {3, 1}, {1, 3}.In the second sample, only satisfying array is {1, 1}.In the third sample, satisfying arrays are {0, 3, 3}, {1, 3, 2}, {1, 3, 3}, {2, 3, 1}, {2, 3, 3}, {3, 3, 0}, {3, 3, 1}, {3, 3, 2}, {3, 3, 3}.


A boy named Vasya wants to play an old Russian solitaire called "Accordion". In this solitaire, the player must observe the following rules:  A deck of n cards is carefully shuffled, then all n cards are put on the table in a line from left to right;  Before each move the table has several piles of cards lying in a line (initially there are n piles, each pile has one card). Let's number the piles from left to right, from 1 to x. During one move, a player can take the whole pile with the maximum number x (that is the rightmost of remaining) and put it on the top of pile x - 1 (if it exists) or on the top of pile x - 3 (if it exists). The player can put one pile on top of another one only if the piles' top cards have the same suits or values. Please note that if pile x goes on top of pile y, then the top card of pile x becomes the top card of the resulting pile. Also note that each move decreases the total number of piles by 1;  The solitaire is considered completed if all cards are in the same pile. Vasya has already shuffled the cards and put them on the table, help him understand whether completing this solitaire is possible or not.

The first input line contains a single integer n (1 ≤ n ≤ 52) — the number of cards in Vasya's deck. The next line contains n space-separated strings c1, c2, ..., cn, where string ci describes the i-th card on the table. Each string ci consists of exactly two characters, the first one represents the card's value, the second one represents its suit. Cards on the table are numbered from left to right.  A card's value is specified by one of these characters: "2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K", "A". A card's suit is specified by one of these characters: "S", "D", "H", "C". It is not guaranteed that the deck has all possible cards. Also, the cards in Vasya's deck can repeat.

On a single line print the answer to the problem: string "YES" (without the quotes) if completing the solitaire is possible, string "NO" (without the quotes) otherwise.

NoteIn the first sample you can act like that:   put the 4-th pile on the 1-st one;  put the 3-rd pile on the 2-nd one;  put the 2-nd pile on the 1-st one. In the second sample there is no way to complete the solitaire.