Question:
Omkar is creating a mosaic using colored square tiles, which he places in an n × n grid. When the mosaic is complete, each cell in the grid will have either a glaucous or sinoper tile. However, currently he has only placed tiles in some cells.

A completed mosaic will be a mastapeece if and only if each tile is adjacent to exactly 2 tiles of the same color (2 tiles are adjacent if they share a side.) Omkar wants to fill the rest of the tiles so that the mosaic becomes a mastapeece. Now he is wondering, is the way to do this unique, and if it is, what is it?

Input

The first line contains a single integer n (1 ≤ n ≤ 2000).

Then follow n lines with n characters in each line. The i-th character in the j-th line corresponds to the cell in row i and column j of the grid, and will be S if Omkar has placed a sinoper tile in this cell, G if Omkar has placed a glaucous tile, . if it's empty.

Output

On the first line, print UNIQUE if there is a unique way to get a mastapeece, NONE if Omkar cannot create any, and MULTIPLE if there is more than one way to do so. All letters must be uppercase.

If you print UNIQUE, then print n additional lines with n characters in each line, such that the i-th character in the j^{th} line is S if the tile in row i and column j of the mastapeece is sinoper, and G if it is glaucous.

Examples

Input

4
S...
..G.
....
...S

Output

MULTIPLE

Input

6
S.....
....G.
..S...
.....S
....G.
G.....

Output

NONE

Input

10
.S....S...
..........
...SSS....
..........
..........
...GS.....
....G...G.
..........
......G...
..........

Output

UNIQUE
SSSSSSSSSS
SGGGGGGGGS
SGSSSSSSGS
SGSGGGGSGS
SGSGSSGSGS
SGSGSSGSGS
SGSGGGGSGS
SGSSSSSSGS
SGGGGGGGGS
SSSSSSSSSS

Input

1
.

Output

NONE

Note

For the first test case, Omkar can make the mastapeeces

SSSS

SGGS

SGGS

SSSS

and

SSGG

SSGG

GGSS

GGSS.

For the second test case, it can be proven that it is impossible for Omkar to add tiles to create a mastapeece.

For the third case, it can be proven that the given mastapeece is the only mastapeece Omkar can create by adding tiles.

For the fourth test case, it's clearly impossible for the only tile in any mosaic Omkar creates to be adjacent to two tiles of the same color, as it will be adjacent to 0 tiles total.


Question:
Petya has got an interesting flower. Petya is a busy person, so he sometimes forgets to water it. You are given n days from Petya's live and you have to determine what happened with his flower in the end.

The flower grows as follows:

  * If the flower isn't watered for two days in a row, it dies.
  * If the flower is watered in the i-th day, it grows by 1 centimeter.
  * If the flower is watered in the i-th and in the (i-1)-th day (i > 1), then it grows by 5 centimeters instead of 1.
  * If the flower is not watered in the i-th day, it does not grow.

At the beginning of the 1-st day the flower is 1 centimeter tall. What is its height after n days?

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains the only integer n (1 ≤ n ≤ 100).

The second line of each test case contains n integers a_1, a_2, ..., a_n (a_i = 0 or a_i = 1). If a_i = 1, the flower is watered in the i-th day, otherwise it is not watered.

Output

For each test case print a single integer k — the flower's height after n days, or -1, if the flower dies.

Example

Input

4
3
1 0 1
3
0 1 1
4
1 0 0 1
1
0

Output

3
7
-1
1


Question:
You are given an array a of length n.

Let's define the eversion operation. Let x = a_n. Then array a is partitioned into two parts: left and right. The left part contains the elements of a that are not greater than x (≤ x). The right part contains the elements of a that are strictly greater than x (> x). The order of elements in each part is kept the same as before the operation, i. e. the partition is stable. Then the array is replaced with the concatenation of the left and the right parts.

For example, if the array a is [2, 4, 1, 5, 3], the eversion goes like this: [2, 4, 1, 5, 3] → [2, 1, 3], [4, 5] → [2, 1, 3, 4, 5].

We start with the array a and perform eversions on this array. We can prove that after several eversions the array a stops changing. Output the minimum number k such that the array stops changing after k eversions.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print a single integer k — the number of eversions after which the array stops changing.

Example

Input

3
5
2 4 1 5 3
5
5 3 2 4 1
4
1 1 1 1

Output

1
2
0

Note

Consider the fist example.

  * The first eversion: a = [1, 4, 2, 5, 3], x = 3. [2, 4, 1, 5, 3] → [2, 1, 3], [4, 5] → [2, 1, 3, 4, 5].
  * The second and following eversions: a = [2, 1, 3, 4, 5], x = 5. [2, 1, 3, 4, 5] → [2, 1, 3, 4, 5], [] → [2, 1, 3, 4, 5]. This eversion does not change the array, so the answer is 1.

Consider the second example.

  * The first eversion: a = [5, 3, 2, 4, 1], x = 1. [5, 3, 2, 4, 1] → [1], [5, 3, 2, 4] → [1, 5, 3, 2, 4].
  * The second eversion: a = [1, 5, 3, 2, 4], x = 4. [1, 5, 3, 2, 4] → [1, 3, 2, 4], [5] → [1, 3, 2, 4, 5].
  * The third and following eversions: a = [1, 3, 2, 4, 5], x = 5. [1, 3, 2, 4, 5] → [1, 3, 2, 4, 5], [] → [1, 3, 2, 4, 5]. This eversion does not change the array, so the answer is 2.


Question:
A total of n depots are located on a number line. Depot i lies at the point x_i for 1 ≤ i ≤ n.

You are a salesman with n bags of goods, attempting to deliver one bag to each of the n depots. You and the n bags are initially at the origin 0. You can carry up to k bags at a time. You must collect the required number of goods from the origin, deliver them to the respective depots, and then return to the origin to collect your next batch of goods.

Calculate the minimum distance you need to cover to deliver all the bags of goods to the depots. You do not have to return to the origin after you have delivered all the bags.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10 500). Description of the test cases follows.

The first line of each test case contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5).

The second line of each test case contains n integers x_1, x_2, …, x_n (-10^9 ≤ x_i ≤ 10^9). It is possible that some depots share the same position.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output a single integer denoting the minimum distance you need to cover to deliver all the bags of goods to the depots.

Example

Input

4
5 1
1 2 3 4 5
9 3
-5 -10 -15 6 5 8 3 7 4
5 3
2 2 3 3 3
4 2
1000000000 1000000000 1000000000 1000000000

Output

25
41
7
3000000000

Note

In the first test case, you can carry only one bag at a time. Thus, the following is a solution sequence that gives a minimum travel distance: 0 → 2 → 0 → 4 → 0 → 3 → 0 → 1 → 0 → 5, where each 0 means you go the origin and grab one bag, and each positive integer means you deliver the bag to a depot at this coordinate, giving a total distance of 25 units. It must be noted that there are other sequences that give the same distance.

In the second test case, you can follow the following sequence, among multiple such sequences, to travel minimum distance: 0 → 6 → 8 → 7 → 0 → 5 → 4 → 3 → 0 → (-5) → (-10) → (-15), with distance 41. It can be shown that 41 is the optimal distance for this test case.


Question:
Petya has an array of integers a_1, a_2, …, a_n. He only likes sorted arrays. Unfortunately, the given array could be arbitrary, so Petya wants to sort it.

Petya likes to challenge himself, so he wants to sort array using only 3-cycles. More formally, in one operation he can pick 3 pairwise distinct indices i, j, and k (1 ≤ i, j, k ≤ n) and apply i → j → k → i cycle to the array a. It simultaneously places a_i on position j, a_j on position k, and a_k on position i, without changing any other element.

For example, if a is [10, 50, 20, 30, 40, 60] and he chooses i = 2, j = 1, k = 5, then the array becomes [\underline{50}, \underline{40}, 20, 30, \underline{10}, 60].

Petya can apply arbitrary number of 3-cycles (possibly, zero). You are to determine if Petya can sort his array a, i. e. make it non-decreasing.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 5 ⋅ 10^5). Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if Petya can sort the array a using 3-cycles, and "NO" (without quotes) otherwise. You can print each letter in any case (upper or lower).

Example

Input

7
1
1
2
2 2
2
2 1
3
1 2 3
3
2 1 3
3
3 1 2
4
2 1 4 3

Output

YES
YES
NO
YES
NO
YES
YES

Note

In the 6-th test case Petya can use the 3-cycle 1 → 3 → 2 → 1 to sort the array.

In the 7-th test case Petya can apply 1 → 3 → 2 → 1 and make a = [1, 4, 2, 3]. Then he can apply 2 → 4 → 3 → 2 and finally sort the array.


Question:
Petya has a rooted tree with an integer written on each vertex. The vertex 1 is the root. You are to answer some questions about the tree.

A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. The parent of a node v is the next vertex on the shortest path from v to the root.

Each question is defined by three integers v, l, and k. To get the answer to the question, you need to perform the following steps:

  * First, write down the sequence of all integers written on the shortest path from the vertex v to the root (including those written in the v and the root).
  * Count the number of times each integer occurs. Remove all integers with less than l occurrences.
  * Replace the sequence, removing all duplicates and ordering the elements by the number of occurrences in the original list in increasing order. In case of a tie, you can choose the order of these elements arbitrary.
  * The answer to the question is the k-th number in the remaining sequence. Note that the answer is not always uniquely determined, because there could be several orderings. Also, it is possible that the length of the sequence on this step is less than k, in this case the answer is -1.

For example, if the sequence of integers on the path from v to the root is [2, 2, 1, 7, 1, 1, 4, 4, 4, 4], l = 2 and k = 2, then the answer is 1.

Please answer all questions about the tree.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^6). Description of the test cases follows.

The first line of each test case contains two integers n, q (1 ≤ n, q ≤ 10^6) — the number of vertices in the tree and the number of questions.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n), where a_i is the number written on the i-th vertex.

The third line contains n-1 integers p_2, p_3, …, p_n (1 ≤ p_i ≤ n), where p_i is the parent of node i. It's guaranteed that the values p define a correct tree.

Each of the next q lines contains three integers v, l, k (1 ≤ v, l, k ≤ n) — descriptions of questions.

It is guaranteed that the sum of n and the sum of q over all test cases do not exceed 10^6.

Output

For each question of each test case print the answer to the question. In case of multiple answers, print any.

Example

Input

2
3 3
1 1 1
1 2
3 1 1
3 1 2
3 2 1
5 5
1 2 1 1 2
1 1 2 2
3 1 1
2 1 2
4 1 1
4 2 1
4 2 2

Output

1 -1 1
1 1 2 1 -1


Question:
You are given an array of n positive integers a_1, a_2, …, a_n. Your task is to calculate the number of arrays of n positive integers b_1, b_2, …, b_n such that:

  * 1 ≤ b_i ≤ a_i for every i (1 ≤ i ≤ n), and
  * b_i ≠ b_{i+1} for every i (1 ≤ i ≤ n - 1).

The number of such arrays can be very large, so print it modulo 998 244 353.

Input

The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

Output

Print the answer modulo 998 244 353 in a single line.

Examples

Input

3
2 2 2

Output

2

Input

2
2 3

Output

4

Input

3
1 1 1

Output

0

Note

In the first test case possible arrays are [1, 2, 1] and [2, 1, 2].

In the second test case possible arrays are [1, 2], [1, 3], [2, 1] and [2, 3].


Question:
Theofanis has a riddle for you and if you manage to solve it, he will give you a Cypriot snack halloumi for free (Cypriot cheese).

You are given an integer n. You need to find two integers l and r such that -10^{18} ≤ l < r ≤ 10^{18} and l + (l + 1) + … + (r - 1) + r = n.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first and only line of each test case contains a single integer n (1 ≤ n ≤ 10^{18}).

Output

For each test case, print the two integers l and r such that -10^{18} ≤ l < r ≤ 10^{18} and l + (l + 1) + … + (r - 1) + r = n.

It can be proven that an answer always exists. If there are multiple answers, print any.

Example

Input

7
1
2
3
6
100
25
3000000000000

Output

0 1
-1 2
1 2
1 3
18 22
-2 7
999999999999 1000000000001

Note

In the first test case, 0 + 1 = 1.

In the second test case, (-1) + 0 + 1 + 2 = 2.

In the fourth test case, 1 + 2 + 3 = 6.

In the fifth test case, 18 + 19 + 20 + 21 + 22 = 100.

In the sixth test case, (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 25.


Question:
Theofanis really likes sequences of positive integers, thus his teacher (Yeltsa Kcir) gave him a problem about a sequence that consists of only special numbers.

Let's call a positive number special if it can be written as a sum of different non-negative powers of n. For example, for n = 4 number 17 is special, because it can be written as 4^0 + 4^2 = 1 + 16 = 17, but 9 is not.

Theofanis asks you to help him find the k-th special number if they are sorted in increasing order. Since this number may be too large, output it modulo 10^9+7.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first and only line of each test case contains two integers n and k (2 ≤ n ≤ 10^9; 1 ≤ k ≤ 10^9).

Output

For each test case, print one integer — the k-th special number in increasing order modulo 10^9+7.

Example

Input

3
3 4
2 12
105 564

Output

9
12
3595374

Note

For n = 3 the sequence is [1,3,4,9...]


Question:
Theofanis has a string s_1 s_2 ... s_n and a character c. He wants to make all characters of the string equal to c using the minimum number of operations.

In one operation he can choose a number x (1 ≤ x ≤ n) and for every position i, where i is not divisible by x, replace s_i with c.

Find the minimum number of operations required to make all the characters equal to c and the x-s that he should use in his operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains the integer n (3 ≤ n ≤ 3 ⋅ 10^5) and a lowercase Latin letter c — the length of the string s and the character the resulting string should consist of.

The second line of each test case contains a string s of lowercase Latin letters — the initial string.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, firstly print one integer m — the minimum number of operations required to make all the characters equal to c.

Next, print m integers x_1, x_2, ..., x_m (1 ≤ x_j ≤ n) — the x-s that should be used in the order they are given.

It can be proved that under given constraints, an answer always exists. If there are multiple answers, print any.

Example

Input

3
4 a
aaaa
4 a
baaa
4 b
bzyx

Output

0
1
2
2
2 3

Note

Let's describe what happens in the third test case:

  1. x_1 = 2: we choose all positions that are not divisible by 2 and replace them, i. e. bzyx → bzbx;
  2. x_2 = 3: we choose all positions that are not divisible by 3 and replace them, i. e. bzbx → bbbb.

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"3\n4 a\naaba\n4 a\naaaa\n4 d\nxyzb\n", "3\n4 a\naaaa\n4 a\naaab\n4 c\nbzyx\n", "1\n3 _\naba\n", "3\n4 a\naaaa\n4 b\naaaa\n4 c\ny{bx\n", "3\n4 a\naaaa\n4 a\ncaaa\n4 c\nz{bx\n", "1\n3 a\naa`\n", "3\n4 `\naaaa\n4 a\ncaaa\n4 c\nx{bx\n", "3\n4 b\naaaa\n4 a\nbaaa\n4 b\nazyx\n", "3\n4 `\naaba\n4 a\naaab\n4 d\nxyzb\n", "1\n3 a\nab`\n", "3\n4 `\naaaa\n4 b\nbaaa\n4 a\nbzyx\n", "3\n4 b\naaaa\n4 a\naaab\n4 c\nbzyx\n", "1\n3 _\n`ba\n", "1\n3 a\na`a\n", "3\n4 `\naaaa\n4 a\ncaab\n4 c\nx{bx\n", "3\n4 a\n`aaa\n4 b\nbaaa\n4 c\nx{bx\n", "3\n4 b\naaba\n4 a\naaaa\n4 d\nxyzb\n", "1\n3 a\nbb`\n", "3\n4 `\naaaa\n4 b\naaaa\n4 a\nbzyx\n", "3\n4 b\naaaa\n4 b\naaab\n4 c\nbzyx\n", "1\n3 _\n`ab\n", "3\n4 `\naaaa\n4 a\ncaab\n4 c\nxb{x\n", "1\n3 `\nbb`\n", "1\n3 _\nba`\n", "3\n4 `\naaaa\n4 a\ncaab\n4 d\nxb{x\n", "1\n3 `\nba`\n", "1\n3 _\nbaa\n", "3\n4 `\naaaa\n4 a\ncaab\n4 e\nxb{x\n", "1\n3 `\naa`\n", "3\n4 `\naaaa\n4 a\ncaab\n4 f\nxb{x\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 a\nxyzb\n", "1\n3 `\n`ba\n", "3\n4 `\naaaa\n4 a\nbaaa\n4 b\nbzzx\n", "3\n4 a\naaaa\n4 a\naaab\n4 c\nyzbx\n", "3\n4 `\naaaa\n4 a\nbbaa\n4 b\nbyyx\n", "3\n4 a\naaaa\n4 `\naaab\n4 b\nbzyx\n", "3\n4 `\naaaa\n4 a\nbaaa\n4 a\nbzyx\n", "3\n4 a\naaaa\n4 b\nbaaa\n4 d\nbzyx\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 b\ny{bx\n", "1\n3 `\nbaa\n", "3\n4 b\naaaa\n4 a\ncaaa\n4 c\nx{bx\n", "1\n3 a\nbab\n", "3\n4 a\naaba\n4 a\naaaa\n4 c\nbzyx\n", "3\n4 `\naaaa\n4 b\nbaaa\n4 c\nbzyx\n", "3\n4 a\naaa`\n4 a\ncaaa\n4 c\nz{bx\n", "1\n3 _\naa`\n", "3\n4 `\naaaa\n4 a\naaca\n4 c\nx{bx\n", "3\n4 b\naaaa\n4 b\nbaaa\n4 b\nazyx\n", "3\n4 a\n`aaa\n4 b\nbaaa\n4 c\ny{ax\n", "3\n4 a\naaaa\n4 a\ncaaa\n4 b\n{xbx\n", "3\n4 b\naaba\n4 a\naaaa\n4 e\nbzyx\n", "3\n4 `\naaba\n4 `\naaab\n4 d\nxyzb\n", "1\n3 `\nab`\n", "3\n4 `\naaa`\n4 b\nbaaa\n4 a\nbzyx\n", "3\n4 b\naaaa\n4 `\naaab\n4 c\nbzyx\n", "3\n4 `\naaaa\n4 b\ncaab\n4 c\nx{bx\n", "3\n4 c\naaaa\n4 b\naaab\n4 c\nbzyx\n", "1\n3 ^\n`ab\n", "3\n4 `\naaaa\n4 a\nbaac\n4 c\nxb{x\n", "3\n4 a\n`aaa\n4 c\nbaaa\n4 c\nx{cx\n", "1\n3 `\nb`b\n", "1\n3 _\nb`a\n", "3\n4 `\naaaa\n4 a\ncaab\n4 f\nx{bx\n", "3\n4 `\naaaa\n4 b\ncaab\n4 e\nxb{x\n", "1\n3 `\nb`a\n", "3\n4 `\naaaa\n4 a\nbaaa\n4 b\nczzx\n", "3\n4 a\naaaa\n4 `\naaab\n4 c\nbzyx\n", "3\n4 `\naaba\n4 a\nbaaa\n4 a\nbzyx\n", "3\n4 a\naaaa\n4 b\nbaaa\n4 d\nxyzb\n", "1\n3 `\ncaa\n", "1\n3 a\nbac\n", "3\n4 a\naaba\n4 a\naaaa\n4 c\nxyzb\n", "3\n4 a\naaa`\n4 b\ncaaa\n4 c\nz{bx\n", "1\n3 ^\naa`\n", "3\n4 `\naaaa\n4 a\naaca\n4 c\nb{xx\n", "3\n4 b\naaaa\n4 b\nbaaa\n4 b\nazzx\n", "3\n4 `\n`aaa\n4 b\nbaaa\n4 c\ny{ax\n", "3\n4 `\naaca\n4 `\naaab\n4 d\nxyzb\n", "3\n4 `\naaa`\n4 b\nbaaa\n4 `\nbzyx\n", "3\n4 `\naaaa\n4 b\ncaab\n4 b\nx{bx\n", "3\n4 `\naaaa\n4 b\ncaab\n4 d\nxb{x\n", "1\n3 _\nb`b\n", "3\n4 `\nbaaa\n4 a\nbaaa\n4 b\nczzx\n", "3\n4 `\naaaa\n4 a\nbbaa\n4 c\nxyyb\n", "1\n3 _\ncaa\n", "1\n3 a\nbbc\n", "3\n4 a\naaa`\n4 b\naaac\n4 c\nz{bx\n", "1\n3 ^\n`aa\n", "3\n4 `\naac`\n4 `\naaab\n4 d\nxyzb\n", "1\n3 ^\nb`b\n", "3\n4 `\nbaaa\n4 a\naaab\n4 b\nczzx\n", "3\n4 `\naaaa\n4 a\nbbaa\n4 c\nyyyb\n", "1\n3 ]\nb`b\n", "3\n4 `\nbaaa\n4 a\naaab\n4 b\ncz{x\n", "1\n3 ]\nb_b\n", "1\n3 \\\nb_b\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 `\nbzyx\n", "1\n3 b\naba\n", "3\n4 a\naaaa\n4 a\naaba\n4 b\nbzyx\n", "3\n4 `\naaaa\n4 a\nbaaa\n4 b\nxyzb\n", "3\n4 `\naaaa\n4 a\nbbaa\n4 b\nczyx\n", "3\n4 a\naaaa\n4 a\nbaca\n4 c\nbzyx\n", "3\n4 a\naaaa\n4 a\nabab\n4 b\nbzyx\n", "1\n3 a\nbba\n", "3\n4 a\naaaa\n4 b\nbaaa\n4 e\nbzyx\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 c\nxb{y\n", "1\n3 _\naaa\n", "3\n4 b\naaaa\n4 a\nbaaa\n4 a\nbzyx\n", "1\n3 a\na`b\n", "3\n4 `\naaaa\n4 a\nbba`\n4 c\nbzyx\n", "3\n4 a\naaba\n4 a\nbaaa\n4 d\nbyyx\n", "3\n4 a\naaaa\n4 b\nbaaa\n4 d\ny{bx\n", "3\n4 a\naaba\n4 b\naaaa\n4 d\nbzyx\n", "3\n4 a\naaba\n4 a\naaa`\n4 d\nxyzb\n", "3\n4 `\nabaa\n4 a\naaaa\n4 d\nxyzb\n", "3\n4 `\naaaa\n4 b\naaaa\n4 c\ny{bx\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 c\nz{bx\n", "3\n4 `\naaaa\n4 a\ncaaa\n4 b\nx{bx\n", "3\n4 a\naaaa\n4 a\nabab\n4 c\nbzyx\n", "3\n4 a\n`aaa\n4 b\nb`aa\n4 c\ny{bx\n", "3\n4 a\naaaa\n4 a\ncaaa\n4 a\nx{bx\n", "3\n4 b\nbaaa\n4 a\naaaa\n4 d\nbzyx\n", "3\n4 `\nabaa\n4 a\naaab\n4 d\nxyzb\n", "1\n3 b\nab`\n", "3\n4 b\naaaa\n4 a\naaab\n4 c\nbyzx\n", "1\n3 `\na`a\n", "3\n4 `\naaaa\n4 a\ncaab\n4 c\nxzbx\n", "3\n4 a\n`aaa\n4 b\nbaaa\n4 c\nb{xx\n", "1\n3 `\nbba\n", "3\n4 b\naaaa\n4 b\naaab\n4 c\nbzxx\n", "1\n3 ^\nba`\n", "3\n4 `\naaba\n4 a\ncaab\n4 d\nxb{x\n", "1\n3 b\naca\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 `\nxyzb\n", "3\n4 `\naaaa\n4 a\ncbaa\n4 b\nbyyx\n", "3\n4 a\naaaa\n4 `\nbaaa\n4 c\nbzyx\n", "3\n4 a\naaaa\n4 a\nbaba\n4 b\nbzyx\n", "3\n4 a\n`aaa\n4 b\nbaaa\n4 d\nbzyx\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 b\nyzbx\n", "3\n4 `\naaaa\n4 b\nbaaa\n4 c\nxyzb\n", "1\n3 _\na``\n", "3\n4 `\naaba\n4 `\naaba\n4 d\nxyzb\n", "1\n3 _\nab`\n", "3\n4 b\naaaa\n4 `\naaab\n4 c\nbxyz\n", "3\n4 a\naaaa\n4 a\nbaac\n4 c\nxb{x\n", "3\n4 `\naaaa\n4 b\ncaab\n4 f\nx{bx\n", "3\n4 a\naaaa\n4 `\naaab\n4 a\nbzyx\n", "3\n4 `\naaba\n4 a\nbaaa\n4 a\nbzxx\n", "3\n4 a\naaaa\n4 a\nbaaa\n4 d\nxyzb\n", "3\n4 b\naaaa\n4 a\nbaaa\n4 c\ny{bx\n"], "outputs": ["0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "1\n3\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n3\n2\n3 4\n", "2\n2 3\n", "0\n", "1\n2\n", "1\n4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "1\n4\n0\n2\n3 4\n", "1\n3\n2\n3 4\n2\n3 4\n", "2\n3 4\n0\n2\n3 4\n", "1\n3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "1\n3\n1\n4\n2\n3 4\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "0\n1\n4\n1\n3\n", "1\n3\n0\n2\n3 4\n", "1\n4\n2\n3 4\n1\n3\n", "2\n3 4\n1\n4\n1\n4\n", "2\n3 4\n1\n4\n1\n3\n", "0\n1\n3\n1\n3\n", "1\n4\n1\n3\n2\n3 4\n", "1\n3\n1\n3\n2\n3 4\n", "0\n0\n2\n3 4\n", "1\n3\n1\n4\n1\n3\n", "2\n3 4\n2\n3 4\n1\n3\n", "1\n3\n1\n4\n1\n4\n", "2\n3 4\n1\n3\n1\n3\n", "0\n2\n3 4\n1\n3\n", "1\n3\n1\n3\n1\n3\n", "1\n4\n2\n3 4\n1\n4\n", "2\n3 4\n1\n3\n1\n4\n", "0\n1\n4\n1\n4\n", "1\n3\n1\n3\n1\n4\n", "1\n3\n2\n3 4\n1\n3\n", "0\n2\n3 4\n1\n4\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n2 3\n", "0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "1\n4\n0\n2\n3 4\n", "0\n1\n3\n2\n3 4\n", "2\n2 3\n", "0\n2\n3 4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "1\n2\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n2 3\n", "1\n3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "1\n3\n0\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n3\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n3\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n3\n", "2\n3 4\n1\n3\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n3\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "0\n1\n4\n1\n3\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "1\n2\n", "1\n4\n0\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "1\n3\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "0\n1\n4\n1\n3\n", "1\n3\n0\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "1\n3\n", "1\n4\n2\n3 4\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n4\n2\n3 4\n1\n3\n", "1\n2\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "1\n2\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "1\n2\n", "1\n4\n0\n2\n3 4\n", "1\n3\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n1\n3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n2 3\n", "1\n3\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "1\n4\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n2 3\n", "2\n2 3\n", "0\n1\n4\n2\n3 4\n", "1\n2\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n1\n4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "0\n1\n3\n2\n3 4\n", "1\n3\n", "0\n2\n3 4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "1\n4\n1\n3\n2\n3 4\n", "2\n3 4\n0\n2\n3 4\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n1\n3\n", "0\n1\n3\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n0\n2\n3 4\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n2\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n2\n", "2\n3 4\n1\n3\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n1\n3\n2\n3 4\n", "2\n2 3\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "1\n4\n2\n3 4\n2\n3 4\n", "0\n1\n4\n1\n3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "2\n2 3\n", "2\n3 4\n2\n3 4\n2\n3 4\n", "0\n1\n3\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n2\n3 4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n", "0\n1\n4\n2\n3 4\n", "2\n3 4\n1\n4\n2\n3 4\n"]}


Question:
Theofanis started playing the new online game called "Among them". However, he always plays with Cypriot players, and they all have the same name: "Andreas" (the most common name in Cyprus).

In each game, Theofanis plays with n other players. Since they all have the same name, they are numbered from 1 to n.

The players write m comments in the chat. A comment has the structure of "i j c" where i and j are two distinct integers and c is a string (1 ≤ i, j ≤ n; i ≠ j; c is either imposter or crewmate). The comment means that player i said that player j has the role c.

An imposter always lies, and a crewmate always tells the truth.

Help Theofanis find the maximum possible number of imposters among all the other Cypriot players, or determine that the comments contradict each other (see the notes for further explanation).

Note that each player has exactly one role: either imposter or crewmate.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of each test case follows.

The first line of each test case contains two integers n and m (1 ≤ n ≤ 2 ⋅ 10^5; 0 ≤ m ≤ 5 ⋅ 10^5) — the number of players except Theofanis and the number of comments.

Each of the next m lines contains a comment made by the players of the structure "i j c" where i and j are two distinct integers and c is a string (1 ≤ i, j ≤ n; i ≠ j; c is either imposter or crewmate).

There can be multiple comments for the same pair of (i, j).

It is guaranteed that the sum of all n does not exceed 2 ⋅ 10^5 and the sum of all m does not exceed 5 ⋅ 10^5.

Output

For each test case, print one integer — the maximum possible number of imposters. If the comments contradict each other, print -1.

Example

Input

5
3 2
1 2 imposter
2 3 crewmate
5 4
1 3 crewmate
2 5 crewmate
2 4 imposter
3 4 imposter
2 2
1 2 imposter
2 1 crewmate
3 5
1 2 imposter
1 2 imposter
3 2 crewmate
3 2 crewmate
1 3 imposter
5 0

Output

2
4
-1
2
5

Note

In the first test case, imposters can be Andreas 2 and 3.

In the second test case, imposters can be Andreas 1, 2, 3 and 5.

In the third test case, comments contradict each other. This is because player 1 says that player 2 is an imposter, and player 2 says that player 1 is a crewmate. If player 1 is a crewmate, then he must be telling the truth, so player 2 must be an imposter. But if player 2 is an imposter then he must be lying, so player 1 can't be a crewmate. Contradiction.

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"5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n8 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n3 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n2 0\n", "5\n6 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n13 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 4 imposter\n2 1 crewmate\n6 5\n1 1 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n4 5 crewmate\n1 4 imposter\n2 1 imposter\n4 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n4 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n3 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n6 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n2 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n3 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n10 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n6 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 3 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n2 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n2 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n1 3 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n2 2 crewmate\n1 2 imposter\n2 0\n", "5\n5 2\n1 2 imposter\n4 2 crewmate\n10 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n10 2\n1 2 imposter\n4 2 crewmate\n10 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n6 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n1 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n3 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 1 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 4 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n2 0\n", "5\n5 2\n1 2 imposter\n2 4 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 5 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 2 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n4 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n4 2\n1 2 imposter\n2 2 crewmate\n5 4\n4 3 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 1 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n3 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n8 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n2 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n1 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n3 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 5 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 5 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 4 crewmate\n2 5 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n3 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n2 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 1 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 3 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n1 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 3 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n4 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 3 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 3 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 1 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 1 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 3 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n1 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 1 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n1 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n1 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 4 crewmate\n3 5 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 4 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n10 5\n1 2 imposter\n1 1 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n6 4\n1 3 crewmate\n2 5 crewmate\n3 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n2 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n2 1 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n4 5 crewmate\n3 4 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n4 5 crewmate\n3 5 imposter\n3 1 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 4 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 1 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 1 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 3 imposter\n3 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 1 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 1 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n8 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n1 4 imposter\n2 1 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n3 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n4 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 4 crewmate\n2 1 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n2 5 crewmate\n2 5 crewmate\n3 4 imposter\n3 1 imposter\n3 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n4 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 4 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 1 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n3 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n4 3 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 1 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n3 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n3 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n2 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n3 4 imposter\n4 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 3 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n9 0\n", "5\n3 2\n1 2 imposter\n3 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n2 2 imposter\n3 1 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 1 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n1 4 imposter\n3 4 imposter\n4 2\n1 4 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 1 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 4 crewmate\n3 5 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n6 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n7 2\n1 2 imposter\n2 1 crewmate\n10 5\n1 2 imposter\n1 1 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n1 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 2 crewmate\n2 5 crewmate\n2 1 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n1 1 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n6 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 5 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 1 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 1 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n4 5 crewmate\n1 4 imposter\n2 1 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n2 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n4 3 crewmate\n2 3 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 1 imposter\n1 2 imposter\n1 2 crewmate\n1 2 crewmate\n1 3 imposter\n3 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n3 4 imposter\n3 4 imposter\n3 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n2 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 1 crewmate\n5 4\n1 2 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 3 imposter\n2 2 imposter\n3 1 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 1 crewmate\n2 4 imposter\n3 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 5 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n6 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n2 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n1 1 crewmate\n2 4 imposter\n1 4 imposter\n5 2\n1 2 imposter\n2 1 crewmate\n6 5\n1 2 imposter\n1 2 imposter\n3 1 crewmate\n3 2 crewmate\n1 5 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n3 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n6 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n2 2 crewmate\n1 3 imposter\n7 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n2 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 3 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n2 2 crewmate\n3 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 1 crewmate\n2 5 crewmate\n2 5 imposter\n3 5 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n2 2 crewmate\n1 2 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 3 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n4 0\n", "5\n5 2\n1 2 imposter\n2 2 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n1 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 2 imposter\n4 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n6 4\n1 3 crewmate\n2 5 crewmate\n2 2 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n4 5\n1 3 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n6 4\n1 3 crewmate\n2 5 crewmate\n2 3 imposter\n1 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n1 2 crewmate\n3 2 crewmate\n2 3 imposter\n2 0\n", "5\n5 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n4 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 3 crewmate\n1 3 imposter\n5 0\n", "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n1 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n2 2 crewmate\n1 3 imposter\n13 0\n"], "outputs": ["2\n4\n-1\n2\n5\n", "2\n4\n1\n2\n5\n", "2\n4\n-1\n2\n5\n", "2\n3\n-1\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n2\n2\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n-1\n2\n4\n", "2\n4\n-1\n-1\n5\n", "-1\n4\n1\n-1\n5\n", "2\n-1\n1\n-1\n5\n", "4\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n7\n", "2\n-1\n1\n-1\n7\n", "4\n4\n1\n-1\n2\n", "2\n4\n-1\n2\n9\n", "4\n3\n-1\n2\n5\n", "2\n4\n-1\n9\n5\n", "2\n9\n1\n-1\n5\n", "2\n4\n-1\n-1\n4\n", "2\n3\n-1\n-1\n4\n", "2\n4\n4\n2\n5\n", "4\n5\n1\n-1\n2\n", "2\n4\n-1\n2\n13\n", "2\n4\n3\n-1\n5\n", "4\n3\n-1\n2\n10\n", "2\n4\n1\n2\n4\n", "2\n3\n1\n-1\n5\n", "2\n-1\n3\n-1\n7\n", "2\n4\n1\n-1\n8\n", "2\n-1\n-1\n-1\n7\n", "2\n4\n2\n2\n4\n", "2\n4\n-1\n5\n2\n", "-1\n4\n1\n-1\n7\n", "2\n4\n2\n-1\n5\n", "4\n-1\n1\n-1\n7\n", "2\n-1\n-1\n2\n9\n", "4\n3\n1\n2\n5\n", "2\n4\n1\n-1\n7\n", "2\n-1\n1\n-1\n4\n", "2\n-1\n-1\n2\n5\n", "-1\n4\n1\n-1\n3\n", "2\n4\n1\n-1\n15\n", "2\n4\n1\n-1\n3\n", "2\n3\n1\n-1\n6\n", "2\n-1\n1\n-1\n3\n", "2\n3\n1\n-1\n3\n", "2\n6\n-1\n2\n7\n", "4\n4\n2\n-1\n2\n", "2\n4\n-1\n4\n5\n", "2\n3\n-1\n2\n7\n", "2\n4\n1\n2\n13\n", "2\n3\n1\n2\n5\n", "2\n4\n-1\n-1\n7\n", "2\n6\n3\n-1\n5\n", "2\n-1\n1\n2\n5\n", "2\n4\n-1\n2\n2\n", "2\n4\n2\n2\n10\n", "2\n-1\n1\n-1\n9\n", "2\n4\n1\n-1\n10\n", "2\n-1\n-1\n-1\n4\n", "5\n4\n-1\n-1\n5\n", "4\n3\n1\n-1\n5\n", "-1\n-1\n1\n-1\n7\n", "3\n3\n1\n-1\n3\n", "-1\n-1\n1\n-1\n5\n", "7\n4\n2\n-1\n2\n", "5\n4\n1\n2\n13\n", "2\n4\n4\n-1\n5\n", "2\n3\n3\n-1\n5\n", "3\n4\n1\n-1\n7\n", "2\n4\n2\n-1\n10\n", "2\n5\n-1\n2\n4\n", "2\n4\n-1\n-1\n2\n", "-1\n3\n1\n-1\n5\n", "2\n4\n1\n2\n2\n", "4\n8\n-1\n2\n5\n", "9\n8\n-1\n2\n5\n", "2\n4\n3\n2\n5\n", "5\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n3\n", "2\n3\n-1\n5\n5\n", "2\n-1\n-1\n2\n4\n", "4\n-1\n1\n-1\n2\n", "4\n-1\n-1\n2\n5\n", "-1\n4\n-1\n5\n5\n", "4\n-1\n1\n2\n5\n", "3\n-1\n1\n-1\n3\n", "2\n4\n1\n2\n8\n", "2\n4\n-1\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n3\n-1\n2\n5\n", "2\n4\n2\n2\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "-1\n4\n1\n-1\n5\n", "2\n3\n-1\n2\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n-1\n2\n4\n", "2\n3\n-1\n2\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n-1\n2\n7\n", "2\n4\n1\n-1\n5\n", "2\n-1\n1\n-1\n7\n", "2\n-1\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n3\n-1\n2\n5\n", "2\n4\n-1\n2\n4\n", "-1\n4\n1\n-1\n5\n", "2\n4\n4\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n3\n-1\n2\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "4\n3\n-1\n2\n5\n", "2\n-1\n1\n-1\n7\n", "2\n-1\n1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "4\n3\n-1\n2\n5\n", "2\n4\n-1\n-1\n5\n", "4\n5\n1\n-1\n2\n", "2\n3\n1\n-1\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n-1\n5\n5\n", "2\n4\n3\n-1\n5\n", "-1\n4\n1\n-1\n5\n", "2\n3\n1\n-1\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "2\n-1\n1\n-1\n7\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n8\n", "2\n3\n1\n-1\n5\n", "2\n4\n-1\n5\n5\n", "-1\n4\n1\n-1\n7\n", "2\n3\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n-1\n5\n5\n", "-1\n4\n1\n-1\n7\n", "2\n4\n1\n-1\n3\n", "2\n-1\n1\n-1\n3\n", "2\n4\n2\n-1\n5\n", "2\n-1\n-1\n2\n5\n", "-1\n4\n1\n-1\n5\n", "2\n3\n1\n-1\n5\n", "2\n4\n-1\n2\n9\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n-1\n4\n", "2\n4\n4\n2\n5\n", "2\n4\n-1\n-1\n5\n", "2\n4\n3\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n-1\n5\n", "-1\n4\n1\n-1\n7\n", "2\n-1\n1\n-1\n5\n", "4\n-1\n1\n-1\n7\n", "2\n4\n1\n-1\n7\n", "2\n4\n-1\n-1\n5\n", "2\n3\n1\n-1\n5\n", "2\n-1\n1\n-1\n3\n", "2\n4\n2\n-1\n5\n", "-1\n4\n1\n-1\n5\n", "2\n4\n-1\n-1\n4\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n7\n", "2\n4\n-1\n-1\n5\n", "2\n4\n1\n-1\n7\n", "2\n4\n-1\n2\n5\n", "2\n-1\n-1\n2\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n5\n", "2\n-1\n1\n-1\n5\n", "2\n4\n1\n-1\n5\n", "2\n4\n-1\n2\n4\n", "4\n3\n-1\n2\n5\n", "2\n4\n-1\n2\n4\n", "2\n-1\n1\n-1\n5\n", "4\n4\n1\n-1\n2\n", "4\n3\n-1\n2\n5\n", "2\n4\n-1\n2\n13\n"]}


Question:
It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.

Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?

You have a perfect binary tree of 2^k - 1 nodes — a binary tree where all vertices i from 1 to 2^{k - 1} - 1 have exactly two children: vertices 2i and 2i + 1. Vertices from 2^{k - 1} to 2^k - 1 don't have any children. You want to color its vertices with the 6 Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).

Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.

<image>| <image>
---|---
A picture of Rubik's cube and its 2D map.

More formally:

  * a white node can not be neighboring with white and yellow nodes;
  * a yellow node can not be neighboring with white and yellow nodes;
  * a green node can not be neighboring with green and blue nodes;
  * a blue node can not be neighboring with green and blue nodes;
  * a red node can not be neighboring with red and orange nodes;
  * an orange node can not be neighboring with red and orange nodes;

You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.

The answer may be too large, so output the answer modulo 10^9+7.

Input

The first and only line contains the integers k (1 ≤ k ≤ 60) — the number of levels in the perfect binary tree you need to color.

Output

Print one integer — the number of the different colorings modulo 10^9+7.

Examples

Input

3

Output

24576

Input

14

Output

934234

Note

In the picture below, you can see one of the correct colorings of the first example.

<image>


Question:
It is the hard version of the problem. The difference is that in this version, there are nodes with already chosen colors.

Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?

You have a perfect binary tree of 2^k - 1 nodes — a binary tree where all vertices i from 1 to 2^{k - 1} - 1 have exactly two children: vertices 2i and 2i + 1. Vertices from 2^{k - 1} to 2^k - 1 don't have any children. You want to color its vertices with the 6 Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).

Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.

<image>| <image>
---|---
A picture of Rubik's cube and its 2D map.

More formally:

  * a white node can not be neighboring with white and yellow nodes;
  * a yellow node can not be neighboring with white and yellow nodes;
  * a green node can not be neighboring with green and blue nodes;
  * a blue node can not be neighboring with green and blue nodes;
  * a red node can not be neighboring with red and orange nodes;
  * an orange node can not be neighboring with red and orange nodes;

However, there are n special nodes in the tree, colors of which are already chosen.

You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.

The answer may be too large, so output the answer modulo 10^9+7.

Input

The first line contains the integers k (1 ≤ k ≤ 60) — the number of levels in the perfect binary tree you need to color.

The second line contains the integer n (1 ≤ n ≤ min(2^k - 1, 2000)) — the number of nodes, colors of which are already chosen.

The next n lines contains integer v (1 ≤ v ≤ 2^k - 1) and string s — the index of the node and the color of the node (s is one of the white, yellow, green, blue, red and orange).

It is guaranteed that each node v appears in the input at most once.

Output

Print one integer — the number of the different colorings modulo 10^9+7.

Examples

Input

3
2
5 orange
2 white

Output

1024

Input

2
2
1 white
2 white

Output

0

Input

10
3
1 blue
4 red
5 orange

Output

328925088

Note

In the picture below, you can see one of the correct colorings of the first test example.

<image>

{"inputs": ["10\n3\n1 blue\n4 red\n5 orange\n", "3\n2\n5 orange\n2 white\n", "2\n2\n1 white\n2 white\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n12 red\n6 orange\n29 blue\n", "3\n1\n7 yellow\n", "2\n2\n1 green\n3 red\n", "1\n1\n1 yellow\n", "1\n1\n1 white\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n3 red\n6 orange\n29 blue\n", "3\n2\n3 orange\n2 white\n", "3\n2\n3 orange\n4 white\n", "10\n1\n1 blue\n4 red\n5 orange\n", "2\n1\n1 white\n2 white\n", "3\n2\n3 orange\n7 white\n", "10\n2\n2 blue\n1 red\n7 dgo`ro\n", "10\n2\n4 blue\n3 red\n7 or`nge\n", "5\n9\n31 yellow\n30 green\n26 yellow\n25 red\n2 red\n22 white\n12 red\n6 orange\n29 blue\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n3 red\n1 orange\n29 blue\n", "3\n2\n3 orange\n5 white\n", "10\n1\n1 blue\n4 red\n5 or`nge\n", "2\n1\n1 white\n2 wiite\n", "5\n9\n31 yellow\n30 green\n26 yellow\n15 red\n2 red\n22 white\n3 red\n1 orange\n29 blue\n", "10\n1\n2 blue\n4 red\n5 or`nge\n", "10\n1\n2 blue\n4 red\n8 or`nge\n", "10\n1\n2 blue\n6 red\n8 or`nge\n", "2\n1\n1 green\n3 red\n", "5\n8\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n3 red\n6 orange\n29 blue\n", "10\n1\n1 blue\n4 red\n6 orange\n", "2\n1\n1 white\n1 white\n", "10\n1\n1 blue\n4 red\n9 or`nge\n", "10\n1\n2 blue\n1 red\n8 or`nge\n", "2\n1\n1 green\n3 sed\n", "5\n8\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n4 red\n6 orange\n29 blue\n", "10\n1\n1 blue\n4 red\n3 orange\n", "10\n1\n1 blue\n4 rdd\n9 or`nge\n", "10\n1\n1 blue\n0 red\n3 orange\n", "3\n2\n1 orange\n2 white\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n1 red\n6 orange\n29 blue\n", "10\n1\n1 blue\n4 red\n5 oranhe\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n1 red\n1 orange\n29 blue\n", "10\n1\n1 blue\n4 der\n5 or`nge\n", "10\n1\n2 blue\n4 red\n6 or`nge\n", "10\n1\n2 blue\n9 red\n8 or`nge\n", "10\n1\n1 blue\n4 red\n6 oraneg\n", "2\n1\n1 white\n0 white\n", "10\n1\n1 blue\n4 red\n11 or`nge\n", "10\n1\n2 blue\n1 red\n8 or`oge\n", "10\n1\n1 blue\n4 der\n3 orange\n", "10\n1\n1 blue\n0 rdd\n9 or`nge\n", "10\n1\n1 blue\n-1 red\n3 orange\n", "3\n2\n1 orange\n3 white\n", "10\n1\n1 blue\n4 der\n5 oranhe\n", "10\n1\n2 blue\n5 red\n6 or`nge\n", "10\n1\n2 blue\n9 der\n8 or`nge\n", "10\n1\n1 blue\n4 qed\n6 oraneg\n", "10\n1\n1 blue\n4 der\n11 or`nge\n", "10\n1\n2 blue\n1 red\n8 or`ogd\n", "10\n1\n1 blue\n0 rdd\n9 egn`ro\n", "10\n1\n1 blue\n4 der\n3 oranhe\n", "10\n1\n2 blue\n4 red\n6 oreng`\n", "10\n1\n2 blue\n9 der\n8 or_nge\n", "10\n1\n1 blue\n4 qed\n6 orbneg\n", "10\n1\n2 blue\n4 der\n11 or`nge\n", "10\n1\n2 blue\n1 red\n8 dgo`ro\n", "10\n1\n1 blue\n1 rdd\n9 egn`ro\n", "10\n1\n1 blue\n4 eer\n3 oranhe\n", "10\n1\n2 blue\n2 red\n6 oreng`\n", "10\n1\n2 blue\n9 der\n8 gr_noe\n", "10\n1\n2 blue\n4 cer\n11 or`nge\n", "10\n1\n2 blue\n1 red\n7 dgo`ro\n", "10\n1\n1 blue\n1 ddr\n9 egn`ro\n", "10\n1\n2 blue\n6 der\n8 gr_noe\n", "10\n1\n2 blue\n4 rec\n11 or`nge\n", "10\n1\n2 blue\n0 red\n7 dgo`ro\n", "10\n1\n1 blue\n1 ddr\n0 egn`ro\n", "10\n1\n2 blue\n6 der\n8 eon_rg\n", "10\n1\n2 blue\n4 rec\n11 oreng`\n", "10\n1\n1 blue\n1 ddr\n0 ogn`re\n", "10\n1\n2 blue\n4 cer\n11 oreng`\n", "10\n1\n1 blue\n1 ddr\n0 pgn`re\n", "10\n1\n2 blue\n4 ber\n11 oreng`\n", "10\n1\n2 blue\n4 bdr\n11 oreng`\n", "10\n1\n2 blue\n4 bdr\n4 oreng`\n", "10\n1\n2 blue\n4 bdr\n5 oreng`\n", "10\n1\n2 blue\n2 bdr\n5 oreng`\n", "10\n1\n2 blue\n2 cdr\n5 oreng`\n", "10\n1\n2 blue\n2 cdr\n5 oregn`\n", "10\n1\n2 blue\n2 rdc\n5 oregn`\n", "5\n9\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n3 red\n5 orange\n29 blue\n", "2\n1\n1 white\n2 wgite\n", "3\n2\n3 orange\n1 white\n", "2\n1\n1 white\n2 etiiw\n", "10\n1\n4 blue\n4 red\n8 or`nge\n", "10\n1\n2 blue\n5 red\n8 or`nge\n", "10\n1\n2 blue\n1 qed\n8 or`nge\n", "5\n8\n31 yellow\n30 green\n26 yellow\n13 red\n2 red\n24 white\n4 red\n6 orange\n29 blue\n", "10\n1\n1 blue\n4 red\n5 egnaro\n", "5\n9\n29 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n1 red\n6 orange\n29 blue\n", "10\n1\n2 blue\n3 red\n6 or`nge\n", "10\n1\n2 blue\n9 red\n8 egn`ro\n", "10\n1\n1 blue\n0 red\n11 or`nge\n", "10\n1\n2 blue\n1 red\n8 ego`ro\n", "10\n1\n1 blue\n0 rcd\n9 or`nge\n", "10\n1\n1 blue\n6 der\n5 oranhe\n", "10\n1\n2 blue\n5 sed\n6 or`nge\n", "10\n1\n1 blue\n4 der\n12 or`nge\n", "10\n1\n2 blue\n1 der\n8 or`ogd\n", "10\n1\n1 blue\n0 rdd\n14 egn`ro\n", "10\n1\n1 blue\n4 der\n6 oranhe\n", "10\n1\n2 blue\n0 red\n6 oreng`\n", "10\n1\n2 blue\n9 der\n8 or_nhe\n", "10\n1\n2 blue\n18 der\n8 gr_noe\n", "10\n1\n1 blue\n1 ddr\n9 egn`so\n", "10\n1\n2 blue\n0 rec\n11 or`nge\n", "10\n1\n2 blue\n0 red\n4 dgo`ro\n", "10\n1\n1 blue\n1 cdr\n0 egn`ro\n", "10\n1\n3 blue\n6 der\n8 eon_rg\n", "10\n1\n2 blue\n5 rec\n11 oreng`\n", "10\n1\n1 blue\n0 ddr\n0 ogn`re\n", "10\n1\n2 blue\n4 bre\n11 oreng`\n", "10\n1\n2 blue\n3 bdr\n11 oreng`\n", "10\n1\n2 blue\n2 bdr\n4 oreng`\n", "10\n1\n2 blue\n4 bdr\n9 oreng`\n", "10\n1\n2 blue\n2 adr\n5 oreng`\n", "10\n1\n2 blue\n2 cdr\n9 oreng`\n", "10\n1\n2 blue\n2 rdc\n5 `ngero\n", "5\n9\n22 yellow\n30 green\n26 yellow\n13 red\n2 red\n22 white\n3 red\n5 orange\n29 blue\n", "10\n1\n2 blue\n5 red\n8 os`nge\n", "5\n8\n31 yellow\n30 green\n26 yellow\n16 red\n2 red\n24 white\n4 red\n6 orange\n29 blue\n", "10\n1\n1 blue\n4 red\n5 egoarn\n", "10\n1\n2 blue\n3 red\n6 egn`ro\n", "10\n1\n2 blue\n9 der\n8 egn`ro\n", "10\n1\n1 blue\n0 der\n11 or`nge\n", "10\n1\n2 blue\n1 red\n8 egn`ro\n", "10\n1\n1 blue\n0 dcr\n9 or`nge\n", "10\n1\n1 blue\n4 der\n12 nr`nge\n", "10\n1\n2 blue\n0 ree\n6 oreng`\n", "10\n1\n2 blue\n16 der\n8 or_nhe\n", "10\n2\n2 blue\n1 red\n7 ego`ro\n", "10\n1\n1 blue\n18 der\n8 gr_noe\n", "10\n1\n1 blue\n0 ddr\n9 egn`so\n", "10\n1\n2 blue\n-1 rec\n11 or`nge\n", "10\n1\n1 blue\n1 cdr\n0 or`nge\n", "10\n1\n3 blue\n6 der\n8 fon_rg\n", "10\n1\n2 blue\n0 ddr\n0 ogn`re\n", "10\n1\n2 blue\n4 erb\n11 oreng`\n", "10\n1\n2 blue\n3 bdr\n14 oreng`\n", "10\n1\n2 blue\n2 rdb\n4 oreng`\n", "10\n1\n2 blue\n4 bdr\n9 orfng`\n", "10\n1\n2 blue\n2 rda\n5 oreng`\n", "10\n1\n2 blue\n2 cdr\n9 nreog`\n", "10\n1\n3 blue\n2 rdc\n5 `ngero\n", "10\n1\n2 blue\n3 red\n8 os`nge\n", "10\n1\n2 blue\n3 red\n5 egn`ro\n", "10\n1\n2 blue\n9 eer\n8 egn`ro\n", "10\n1\n1 blue\n1 der\n11 or`nge\n", "10\n1\n2 blue\n1 rde\n8 egn`ro\n", "10\n1\n1 blue\n4 der\n12 rn`nge\n", "10\n1\n1 blue\n0 ree\n6 oreng`\n", "10\n1\n2 blue\n21 der\n8 or_nhe\n", "10\n1\n1 blue\n18 der\n4 gr_noe\n", "10\n1\n1 blue\n0 dds\n9 egn`so\n", "10\n1\n2 blue\n-1 erc\n11 or`nge\n", "10\n1\n4 blue\n4 erb\n11 oreng`\n", "10\n1\n2 blue\n1 bdr\n14 oreng`\n", "10\n1\n1 blue\n2 rdb\n4 oreng`\n", "10\n1\n2 blue\n1 bdr\n9 orfng`\n", "10\n1\n2 blue\n2 rda\n6 oreng`\n", "10\n1\n2 blue\n0 cdr\n9 nreog`\n", "10\n1\n3 blue\n2 rdc\n3 `ngero\n", "10\n1\n2 blue\n3 sed\n8 os`nge\n", "10\n1\n4 blue\n3 red\n5 egn`ro\n", "10\n1\n1 blue\n1 red\n11 or`nge\n", "10\n1\n2 blue\n1 rde\n8 nge`ro\n", "10\n1\n1 blue\n0 ree\n6 orgne`\n", "10\n1\n4 blue\n4 erb\n11 oremg`\n", "10\n1\n2 blue\n1 ber\n14 oreng`\n", "10\n1\n1 blue\n1 rdb\n4 oreng`\n", "10\n1\n2 blue\n2 rda\n6 `gnero\n", "10\n1\n2 blue\n1 cdr\n9 nreog`\n", "10\n1\n2 blue\n3 sed\n12 os`nge\n", "10\n1\n4 blue\n3 red\n5 or`nge\n", "10\n1\n1 blue\n-1 red\n11 or`nge\n", "10\n1\n2 blue\n1 edr\n8 nge`ro\n", "10\n1\n1 blue\n0 red\n6 orgne`\n", "10\n1\n4 blue\n4 erb\n11 `gnero\n", "10\n1\n2 blue\n1 beq\n14 oreng`\n", "10\n1\n1 blue\n1 rbd\n4 oreng`\n", "10\n1\n2 blue\n1 rdc\n9 nreog`\n", "10\n1\n2 blue\n3 des\n12 os`nge\n", "10\n1\n4 blue\n3 red\n7 or`nge\n", "10\n1\n2 blue\n1 edr\n8 nge`or\n", "10\n1\n1 blue\n0 sed\n6 orgne`\n", "10\n1\n4 blue\n4 bre\n11 `gnero\n", "10\n1\n1 blue\n1 rbd\n4 nreng`\n", "10\n1\n2 blue\n2 rdc\n9 nreog`\n", "10\n1\n2 blue\n3 des\n12 os`mge\n", "10\n1\n1 blue\n0 sde\n6 orgne`\n", "10\n1\n2 blue\n2 rdc\n9 noerg`\n", "10\n1\n4 blue\n3 des\n12 os`mge\n", "10\n1\n2 blue\n2 rdc\n6 noerg`\n", "10\n1\n4 blue\n3 des\n12 om`sge\n", "10\n1\n2 blue\n2 rdc\n0 noerg`\n", "10\n1\n4 blue\n3 des\n1 om`sge\n", "10\n1\n2 blue\n2 rdc\n0 ooerg`\n", "10\n1\n4 blue\n3 des\n1 om`egs\n", "10\n1\n2 blue\n2 rdc\n0 ooegr`\n", "10\n1\n4 blue\n2 des\n1 om`egs\n"], "outputs": ["328925088\n", "1024\n", "0\n", "0\n", "4096\n", "4\n", "1\n", "1\n", "0\n", "512\n", "768\n", "525602746\n", "16\n", "1024\n", "631400690\n", "973550521\n", "0\n", "0\n", "768\n", "525602746\n", "16\n", "0\n", "525602746\n", "525602746\n", "525602746\n", "16\n", "0\n", "525602746\n", "16\n", "525602746\n", "525602746\n", "16\n", "0\n", "525602746\n", "525602746\n", "525602746\n", "1024\n", "0\n", "525602746\n", "0\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "16\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "1024\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "0\n", "16\n", "1024\n", "16\n", "525602746\n", "525602746\n", "525602746\n", "0\n", "525602746\n", "0\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "0\n", "525602746\n", "0\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "631400690\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n", "525602746\n"]}


Question:
Theofanis decided to visit his uncle's farm. There are s animals and n animal pens on the farm. For utility purpose, animal pens are constructed in one row.

Uncle told Theofanis that a farm is lucky if you can distribute all animals in all pens in such a way that there are no empty pens and there is at least one continuous segment of pens that has exactly k animals in total.

Moreover, a farm is ideal if it's lucky for any distribution without empty pens.

Neither Theofanis nor his uncle knows if their farm is ideal or not. Can you help them to figure it out?

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

The first and only line of each test case contains three integers s, n, and k (1 ≤ s, n, k ≤ 10^{18}; n ≤ s).

Output

For each test case, print YES (case-insensitive), if the farm is ideal, or NO (case-insensitive) otherwise.

Example

Input

4
1 1 1
1 1 2
100 50 200
56220 47258 14497

Output

YES
NO
NO
YES

Note

For the first and the second test case, the only possible combination is [1] so there always will be a subsegment with 1 animal but not with 2 animals.


Question:
Monocarp is playing a computer game. Now he wants to complete the first level of this game.

A level is a rectangular grid of 2 rows and n columns. Monocarp controls a character, which starts in cell (1, 1) — at the intersection of the 1-st row and the 1-st column.

Monocarp's character can move from one cell to another in one step if the cells are adjacent by side and/or corner. Formally, it is possible to move from cell (x_1, y_1) to cell (x_2, y_2) in one step if |x_1 - x_2| ≤ 1 and |y_1 - y_2| ≤ 1. Obviously, it is prohibited to go outside the grid.

There are traps in some cells. If Monocarp's character finds himself in such a cell, he dies, and the game ends.

To complete a level, Monocarp's character should reach cell (2, n) — at the intersection of row 2 and column n.

Help Monocarp determine if it is possible to complete the level.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Then the test cases follow. Each test case consists of three lines.

The first line contains a single integer n (3 ≤ n ≤ 100) — the number of columns.

The next two lines describe the level. The i-th of these lines describes the i-th line of the level — the line consists of the characters '0' and '1'. The character '0' corresponds to a safe cell, the character '1' corresponds to a trap cell.

Additional constraint on the input: cells (1, 1) and (2, n) are safe.

Output

For each test case, output YES if it is possible to complete the level, and NO otherwise.

Example

Input

4
3
000
000
4
0011
1100
4
0111
1110
6
010101
101010

Output

YES
YES
NO
YES

Note

Consider the example from the statement.

In the first test case, one of the possible paths is (1, 1) → (2, 2) → (2, 3).

In the second test case, one of the possible paths is (1, 1) → (1, 2) → (2, 3) → (2, 4).

In the fourth test case, one of the possible paths is (1, 1) → (2, 2) → (1, 3) → (2, 4) → (1, 5) → (2, 6).


Question:
n students attended the first meeting of the Berland SU programming course (n is even). All students will be divided into two groups. Each group will be attending exactly one lesson each week during one of the five working days (Monday, Tuesday, Wednesday, Thursday and Friday), and the days chosen for the groups must be different. Furthermore, both groups should contain the same number of students.

Each student has filled a survey in which they told which days of the week are convenient for them to attend a lesson, and which are not.

Your task is to determine if it is possible to choose two different week days to schedule the lessons for the group (the first group will attend the lesson on the first chosen day, the second group will attend the lesson on the second chosen day), and divide the students into two groups, so the groups have equal sizes, and for each student, the chosen lesson day for their group is convenient.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.

Then the descriptions of t testcases follow.

The first line of each testcase contains one integer n (2 ≤ n ≤ 1 000) — the number of students.

The i-th of the next n lines contains 5 integers, each of them is 0 or 1. If the j-th integer is 1, then the i-th student can attend the lessons on the j-th day of the week. If the j-th integer is 0, then the i-th student cannot attend the lessons on the j-th day of the week.

Additional constraints on the input: for each student, at least one of the days of the week is convenient, the total number of students over all testcases doesn't exceed 10^5.

Output

For each testcase print an answer. If it's possible to divide the students into two groups of equal sizes and choose different days for the groups so each student can attend the lesson in the chosen day of their group, print "YES" (without quotes). Otherwise, print "NO" (without quotes).

Example

Input

2
4
1 0 0 1 0
0 1 0 0 1
0 0 0 1 0
0 1 0 1 0
2
0 0 0 1 0
0 0 0 1 0

Output

YES
NO

Note

In the first testcase, there is a way to meet all the constraints. For example, the first group can consist of the first and the third students, they will attend the lessons on Thursday (the fourth day); the second group can consist of the second and the fourth students, and they will attend the lessons on Tuesday (the second day).

In the second testcase, it is impossible to divide the students into groups so they attend the lessons on different days.