import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.function.BiConsumer;
import java.util.function.Consumer;
import java.util.function.Function;
import java.util.function.Supplier;
import java.util.stream.Stream;

public class E_440
{
	public static final long[] POWER2 = generatePOWER2();
	public static final IteratorBuffer<Long> ITERATOR_BUFFER_PRIME = new IteratorBuffer<>(streamPrime(1000000).iterator());
	private static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
	private static StringTokenizer stringTokenizer = null;
	private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

	public static void add(int delta, int[] result)
	{
		for (int index = 0; index < result.length; index++)
		{
			result[index] += delta;
		}
	}

	public static void add(int delta, int[]... result)
	{
		for (int index = 0; index < result.length; index++)
		{
			add(delta, result[index]);
		}
	}

	public static int binarySearchMaximum(Function<Integer, Boolean> filter, int start, int end)
	{
		return -binarySearchMinimum(x -> filter.apply(-x), -end, -start);
	}

	public static int binarySearchMinimum(Function<Integer, Boolean> filter, int start, int end)
	{
		int result;
		if (start == end)
		{
			result = end;
		}
		else
		{
			int middle = start + (end - start) / 2;
			if (filter.apply(middle))
			{
				result = binarySearchMinimum(filter, start, middle);
			}
			else
			{
				result = binarySearchMinimum(filter, middle + 1, end);
			}
		}
		return result;
	}

	public static void close()
	{
		out.close();
	}

	public static List<List<Integer>> combinations(int n, int k)
	{
		List<List<Integer>> result = new ArrayList<>();
		if (k == 0)
		{
		}
		else
		{
			if (k == 1)
			{
				List<Integer> combination = new ArrayList<>();
				combination.add(n);
				result.add(combination);
			}
			else
			{
				for (int index = 0; index <= n; index++)
				{
					for (List<Integer> combination : combinations(n - index, k - 1))
					{
						combination.add(index);
						result.add(combination);
					}
				}
			}
		}
		return result;
	}

	public static <Type> int compare(Iterator<Type> iterator0, Iterator<Type> iterator1, Comparator<Type> comparator)
	{
		int result = 0;
		while (result == 0 && iterator0.hasNext() && iterator1.hasNext())
		{
			result = comparator.compare(iterator0.next(), iterator1.next());
		}
		if (result == 0)
		{
			if (iterator1.hasNext())
			{
				result = -1;
			}
			else
			{
				if (iterator0.hasNext())
				{
					result = 1;
				}
			}
		}
		return result;
	}

	public static <Type> int compare(Iterable<Type> iterable0, Iterable<Type> iterable1, Comparator<Type> comparator)
	{
		return compare(iterable0.iterator(), iterable1.iterator(), comparator);
	}

	public static long divideCeil(long x, long y)
	{
		return (x + y - 1) / y;
	}

	public static Set<Long> divisors(long n)
	{
		SortedSetAVL<Long> result = new SortedSetAVL<>(Comparator.naturalOrder());
		result.add(1L);
		for (Long factor : factors(n))
		{
			SortedSetAVL<Long> divisors = new SortedSetAVL<>(result);
			for (Long divisor : result)
			{
				divisors.add(divisor * factor);
			}
			result = divisors;
		}
		return result;
	}

	public static LinkedList<Long> factors(long n)
	{
		LinkedList<Long> result = new LinkedList<>();
		Iterator<Long> primes = ITERATOR_BUFFER_PRIME.iterator();
		Long prime;
		while (n > 1 && (prime = primes.next()) * prime <= n)
		{
			while (n % prime == 0)
			{
				result.add(prime);
				n /= prime;
			}
		}
		if (n > 1)
		{
			result.add(n);
		}
		return result;
	}

	public static long faculty(int n)
	{
		long result = 1;
		for (int index = 2; index <= n; index++)
		{
			result *= index;
		}
		return result;
	}

	public static long gcd(long a, long b)
	{
		while (a != 0 && b != 0)
		{
			if (a > b)
			{
				a %= b;
			}
			else
			{
				b %= a;
			}
		}
		return a + b;
	}

	public static long[] generatePOWER2()
	{
		long[] result = new long[63];
		for (int x = 0; x < result.length; x++)
		{
			result[x] = 1L << x;
		}
		return result;
	}

	public static boolean isPrime(long x)
	{
		boolean result = x > 1;
		Iterator<Long> iterator = ITERATOR_BUFFER_PRIME.iterator();
		Long prime;
		while ((prime = iterator.next()) * prime <= x)
		{
			result &= x % prime > 0;
		}
		return result;
	}

	public static long knapsack(List<Tuple3<Long, Integer, Integer>> itemsValueWeightCount, int weightMaximum)
	{
		long[] valuesMaximum = new long[weightMaximum + 1];
		for (Tuple3<Long, Integer, Integer> itemValueWeightCount : itemsValueWeightCount)
		{
			long itemValue = itemValueWeightCount.v0;
			int itemWeight = itemValueWeightCount.v1;
			int itemCount = itemValueWeightCount.v2;
			for (int weight = weightMaximum; 0 <= weight; weight--)
			{
				for (int index = 1; index <= itemCount && 0 <= weight - index * itemWeight; index++)
				{
					valuesMaximum[weight] = Math.max(valuesMaximum[weight], valuesMaximum[weight - index * itemWeight] + index * itemValue);
				}
			}
		}
		long result = 0;
		for (long valueMaximum : valuesMaximum)
		{
			result = Math.max(result, valueMaximum);
		}
		return result;
	}

	public static boolean knapsackPossible(List<Tuple2<Integer, Integer>> itemsWeightCount, int weightMaximum)
	{
		boolean[] weightPossible = new boolean[weightMaximum + 1];
		weightPossible[0] = true;
		int weightLargest = 0;
		for (Tuple2<Integer, Integer> itemWeightCount : itemsWeightCount)
		{
			int itemWeight = itemWeightCount.v0;
			int itemCount = itemWeightCount.v1;
			for (int weightStart = 0; weightStart < itemWeight; weightStart++)
			{
				int count = 0;
				for (int weight = weightStart; weight <= weightMaximum && (0 < count || weight <= weightLargest); weight += itemWeight)
				{
					if (weightPossible[weight])
					{
						count = itemCount;
					}
					else
					{
						if (0 < count)
						{
							weightPossible[weight] = true;
							weightLargest = weight;
							count -= 1;
						}
					}
				}
			}
		}
		return weightPossible[weightMaximum];
	}

	public static long lcm(int a, int b)
	{
		return a * b / gcd(a, b);
	}

	public static void main(String[] args)
	{
		try
		{
			solve();
		}
		catch (IOException exception)
		{
			exception.printStackTrace();
		}
		close();
	}

	public static double nextDouble() throws IOException
	{
		return Double.parseDouble(nextString());
	}

	public static int nextInt() throws IOException
	{
		return Integer.parseInt(nextString());
	}

	public static void nextInts(int n, int[]... result) throws IOException
	{
		for (int index = 0; index < n; index++)
		{
			for (int value = 0; value < result.length; value++)
			{
				result[value][index] = nextInt();
			}
		}
	}

	public static int[] nextInts(int n) throws IOException
	{
		int[] result = new int[n];
		nextInts(n, result);
		return result;
	}

	public static String nextLine() throws IOException
	{
		return bufferedReader.readLine();
	}

	public static long nextLong() throws IOException
	{
		return Long.parseLong(nextString());
	}

	public static void nextLongs(int n, long[]... result) throws IOException
	{
		for (int index = 0; index < n; index++)
		{
			for (int value = 0; value < result.length; value++)
			{
				result[value][index] = nextLong();
			}
		}
	}

	public static long[] nextLongs(int n) throws IOException
	{
		long[] result = new long[n];
		nextLongs(n, result);
		return result;
	}

	public static String nextString() throws IOException
	{
		while ((stringTokenizer == null) || (!stringTokenizer.hasMoreTokens()))
		{
			stringTokenizer = new StringTokenizer(bufferedReader.readLine());
		}
		return stringTokenizer.nextToken();
	}

	public static String[] nextStrings(int n) throws IOException
	{
		String[] result = new String[n];
		{
			for (int index = 0; index < n; index++)
			{
				result[index] = nextString();
			}
		}
		return result;
	}

	public static <T> List<T> permutation(long p, List<T> x)
	{
		List<T> copy = new ArrayList<>();
		for (int index = 0; index < x.size(); index++)
		{
			copy.add(x.get(index));
		}
		List<T> result = new ArrayList<>();
		for (int indexTo = 0; indexTo < x.size(); indexTo++)
		{
			int indexFrom = (int) p % copy.size();
			p = p / copy.size();
			result.add(copy.remove(indexFrom));
		}
		return result;
	}

	public static <Type> List<List<Type>> permutations(List<Type> list)
	{
		List<List<Type>> result = new ArrayList<>();
		result.add(new ArrayList<>());
		for (Type element : list)
		{
			List<List<Type>> permutations = result;
			result = new ArrayList<>();
			for (List<Type> permutation : permutations)
			{
				for (int index = 0; index <= permutation.size(); index++)
				{
					List<Type> permutationNew = new ArrayList<>(permutation);
					permutationNew.add(index, element);
					result.add(permutationNew);
				}
			}
		}
		return result;
	}

	public static Stream<BigInteger> streamFibonacci()
	{
		return Stream.generate(new Supplier<BigInteger>()
		{
			private BigInteger n0 = BigInteger.ZERO;
			private BigInteger n1 = BigInteger.ONE;

			@Override
			public BigInteger get()
			{
				BigInteger result = n0;
				n0 = n1;
				n1 = result.add(n0);
				return result;
			}
		});
	}

	public static Stream<Long> streamPrime(int sieveSize)
	{
		return Stream.generate(new Supplier<Long>()
		{
			private boolean[] isPrime = new boolean[sieveSize];
			private long sieveOffset = 2;
			private List<Long> primes = new ArrayList<>();
			private int index = 0;

			public void filter(long prime, boolean[] result)
			{
				if (prime * prime < this.sieveOffset + sieveSize)
				{
					long remainingStart = this.sieveOffset % prime;
					long start = remainingStart == 0 ? 0 : prime - remainingStart;
					for (long index = start; index < sieveSize; index += prime)
					{
						result[(int) index] = false;
					}
				}
			}

			public void generatePrimes()
			{
				Arrays.fill(this.isPrime, true);
				this.primes.forEach(prime -> filter(prime, isPrime));
				for (int index = 0; index < sieveSize; index++)
				{
					if (isPrime[index])
					{
						this.primes.add(this.sieveOffset + index);
						filter(this.sieveOffset + index, isPrime);
					}
				}
				this.sieveOffset += sieveSize;
			}

			@Override
			public Long get()
			{
				while (this.primes.size() <= this.index)
				{
					generatePrimes();
				}
				Long result = this.primes.get(this.index);
				this.index += 1;
				return result;
			}
		});
	}

	public static <Type> String toString(Iterator<Type> iterator, String separator)
	{
		StringBuilder stringBuilder = new StringBuilder();
		if (iterator.hasNext())
		{
			stringBuilder.append(iterator.next());
		}
		while (iterator.hasNext())
		{
			stringBuilder.append(separator);
			stringBuilder.append(iterator.next());
		}
		return stringBuilder.toString();
	}

	public static <Type> String toString(Iterator<Type> iterator)
	{
		return toString(iterator, " ");
	}

	public static <Type> String toString(Iterable<Type> iterable, String separator)
	{
		return toString(iterable.iterator(), separator);
	}

	public static <Type> String toString(Iterable<Type> iterable)
	{
		return toString(iterable, " ");
	}

	public static long totient(long n)
	{
		Set<Long> factors = new SortedSetAVL<>(factors(n), Comparator.naturalOrder());
		long result = n;
		for (long p : factors)
		{
			result -= result / p;
		}
		return result;
	}

	interface BiFunctionResult<Type0, Type1, TypeResult>
	{
		TypeResult apply(Type0 x0, Type1 x1, TypeResult x2);
	}

	static class Array<Type> implements Iterable<Type>
	{
		private final Object[] array;

		public Array(int size)
		{
			this.array = new Object[size];
		}

		public Array(int size, Type element)
		{
			this(size);
			Arrays.fill(this.array, element);
		}

		public Array(Array<Type> array, Type element)
		{
			this(array.size() + 1);
			for (int index = 0; index < array.size(); index++)
			{
				set(index, array.get(index));
			}
			set(size() - 1, element);
		}

		public Array(List<Type> list)
		{
			this(list.size());
			int index = 0;
			for (Type element : list)
			{
				set(index, element);
				index += 1;
			}
		}

		public Type get(int index)
		{
			return (Type) this.array[index];
		}

		@Override
		public Iterator<Type> iterator()
		{
			return new Iterator<Type>()
			{
				int index = 0;

				@Override
				public boolean hasNext()
				{
					return this.index < size();
				}

				@Override
				public Type next()
				{
					Type result = Array.this.get(index);
					index += 1;
					return result;
				}
			};
		}

		public Array set(int index, Type value)
		{
			this.array[index] = value;
			return this;
		}

		public int size()
		{
			return this.array.length;
		}

		public List<Type> toList()
		{
			List<Type> result = new ArrayList<>();
			for (Type element : this)
			{
				result.add(element);
			}
			return result;
		}

		@Override
		public String toString()
		{
			return "[" + E_440.toString(this, ", ") + "]";
		}
	}

	static class BIT
	{
		private final long[] tree;

		public BIT(int size)
		{
			this.tree = new long[size];
		}

		private static int lastBit(int index)
		{
			return index & -index;
		}

		public void add(int index, long delta)
		{
			index += 1;
			while (index <= this.tree.length)
			{
				tree[index - 1] += delta;
				index += lastBit(index);
			}
		}

		private long prefix(int end)
		{
			long result = 0;
			while (end > 0)
			{
				result += this.tree[end - 1];
				end -= lastBit(end);
			}
			return result;
		}

		public int size()
		{
			return this.tree.length;
		}

		public long sum(int start, int end)
		{
			return prefix(end) - prefix(start);
		}
	}

	static abstract class Edge<TypeVertex extends Vertex<TypeVertex, TypeEdge>, TypeEdge extends Edge<TypeVertex, TypeEdge>>
	{
		public final TypeVertex vertex0;
		public final TypeVertex vertex1;
		public final boolean bidirectional;

		public Edge(TypeVertex vertex0, TypeVertex vertex1, boolean bidirectional)
		{
			this.vertex0 = vertex0;
			this.vertex1 = vertex1;
			this.bidirectional = bidirectional;
			this.vertex0.edges.add(getThis());
			if (this.bidirectional)
			{
				this.vertex1.edges.add(getThis());
			}
		}

		public abstract TypeEdge getThis();

		public TypeVertex other(Vertex<TypeVertex, TypeEdge> vertex)
		{
			TypeVertex result;
			if (vertex0 == vertex)
			{
				result = vertex1;
			}
			else
			{
				result = vertex0;
			}
			return result;
		}

		public void remove()
		{
			this.vertex0.edges.remove(getThis());
			if (this.bidirectional)
			{
				this.vertex1.edges.remove(getThis());
			}
		}

		@Override
		public String toString()
		{
			return this.vertex0 + "->" + this.vertex1;
		}
	}

	public static class EdgeDefault<TypeVertex extends Vertex<TypeVertex, EdgeDefault<TypeVertex>>> extends Edge<TypeVertex, EdgeDefault<TypeVertex>>
	{
		public EdgeDefault(TypeVertex vertex0, TypeVertex vertex1, boolean bidirectional)
		{
			super(vertex0, vertex1, bidirectional);
		}

		@Override
		public EdgeDefault<TypeVertex> getThis()
		{
			return this;
		}
	}

	public static class EdgeDefaultDefault extends Edge<VertexDefaultDefault, EdgeDefaultDefault>
	{
		public EdgeDefaultDefault(VertexDefaultDefault vertex0, VertexDefaultDefault vertex1, boolean bidirectional)
		{
			super(vertex0, vertex1, bidirectional);
		}

		@Override
		public EdgeDefaultDefault getThis()
		{
			return this;
		}
	}

	public static class FIFO<Type>
	{
		public SingleLinkedList<Type> start;
		public SingleLinkedList<Type> end;

		public FIFO()
		{
			this.start = null;
			this.end = null;
		}

		public boolean isEmpty()
		{
			return this.start == null;
		}

		public Type peek()
		{
			return this.start.element;
		}

		public Type pop()
		{
			Type result = this.start.element;
			this.start = this.start.next;
			return result;
		}

		public void push(Type element)
		{
			SingleLinkedList<Type> list = new SingleLinkedList<>(element, null);
			if (this.start == null)
			{
				this.start = list;
				this.end = list;
			}
			else
			{
				this.end.next = list;
				this.end = list;
			}
		}
	}

	static class Fraction implements Comparable<Fraction>
	{
		public static final Fraction ZERO = new Fraction(0, 1);
		public final long numerator;
		public final long denominator;

		private Fraction(long numerator, long denominator)
		{
			this.numerator = numerator;
			this.denominator = denominator;
		}

		public static Fraction fraction(long whole)
		{
			return fraction(whole, 1);
		}

		public static Fraction fraction(long numerator, long denominator)
		{
			Fraction result;
			if (denominator == 0)
			{
				throw new ArithmeticException();
			}
			if (numerator == 0)
			{
				result = Fraction.ZERO;
			}
			else
			{
				int sign;
				if (numerator < 0 ^ denominator < 0)
				{
					sign = -1;
					numerator = Math.abs(numerator);
					denominator = Math.abs(denominator);
				}
				else
				{
					sign = 1;
				}
				long gcd = gcd(numerator, denominator);
				result = new Fraction(sign * numerator / gcd, denominator / gcd);
			}
			return result;
		}

		public Fraction add(Fraction fraction)
		{
			return fraction(this.numerator * fraction.denominator + fraction.numerator * this.denominator, this.denominator * fraction.denominator);
		}

		@Override
		public int compareTo(Fraction that)
		{
			return Long.compare(this.numerator * that.denominator, that.numerator * this.denominator);
		}

		public Fraction divide(Fraction fraction)
		{
			return multiply(fraction.inverse());
		}

		public boolean equals(Fraction that)
		{
			return this.compareTo(that) == 0;
		}

		public boolean equals(Object that)
		{
			return this.compareTo((Fraction) that) == 0;
		}

		public Fraction getRemainder()
		{
			return fraction(this.numerator - getWholePart() * denominator, denominator);
		}

		public long getWholePart()
		{
			return this.numerator / this.denominator;
		}

		public Fraction inverse()
		{
			return fraction(this.denominator, this.numerator);
		}

		public Fraction multiply(Fraction fraction)
		{
			return fraction(this.numerator * fraction.numerator, this.denominator * fraction.denominator);
		}

		public Fraction neg()
		{
			return fraction(-this.numerator, this.denominator);
		}

		public Fraction sub(Fraction fraction)
		{
			return add(fraction.neg());
		}

		@Override
		public String toString()
		{
			String result;
			if (getRemainder().equals(Fraction.ZERO))
			{
				result = "" + this.numerator;
			}
			else
			{
				result = this.numerator + "/" + this.denominator;
			}
			return result;
		}
	}

	static class IteratorBuffer<Type>
	{
		private Iterator<Type> iterator;
		private List<Type> list;

		public IteratorBuffer(Iterator<Type> iterator)
		{
			this.iterator = iterator;
			this.list = new ArrayList<Type>();
		}

		public Iterator<Type> iterator()
		{
			return new Iterator<Type>()
			{
				int index = 0;

				@Override
				public boolean hasNext()
				{
					return this.index < list.size() || IteratorBuffer.this.iterator.hasNext();
				}

				@Override
				public Type next()
				{
					if (list.size() <= this.index)
					{
						list.add(iterator.next());
					}
					Type result = list.get(index);
					index += 1;
					return result;
				}
			};
		}
	}

	public static class MapCount<Type> extends SortedMapAVL<Type, Long>
	{
		private int count;

		public MapCount(Comparator<? super Type> comparator)
		{
			super(comparator);
			this.count = 0;
		}

		public long add(Type key, Long delta)
		{
			long result;
			if (delta > 0)
			{
				Long value = get(key);
				if (value == null)
				{
					value = delta;
				}
				else
				{
					value += delta;
				}
				put(key, value);
				result = delta;
			}
			else
			{
				result = 0;
			}
			this.count += result;
			return result;
		}

		public int count()
		{
			return this.count;
		}

		public List<Type> flatten()
		{
			List<Type> result = new ArrayList<>();
			for (Entry<Type, Long> entry : entrySet())
			{
				for (long index = 0; index < entry.getValue(); index++)
				{
					result.add(entry.getKey());
				}
			}
			return result;
		}

		@Override
		public SortedMapAVL<Type, Long> headMap(Type keyEnd)
		{
			throw new UnsupportedOperationException();
		}

		@Override
		public void putAll(Map<? extends Type, ? extends Long> map)
		{
			throw new UnsupportedOperationException();
		}

		public long remove(Type key, Long delta)
		{
			long result;
			if (delta > 0)
			{
				Long value = get(key) - delta;
				if (value <= 0)
				{
					result = delta + value;
					remove(key);
				}
				else
				{
					result = delta;
					put(key, value);
				}
			}
			else
			{
				result = 0;
			}
			this.count -= result;
			return result;
		}

		@Override
		public Long remove(Object key)
		{
			Long result = super.remove(key);
			this.count -= result;
			return result;
		}

		@Override
		public SortedMapAVL<Type, Long> subMap(Type keyStart, Type keyEnd)
		{
			throw new UnsupportedOperationException();
		}

		@Override
		public SortedMapAVL<Type, Long> tailMap(Type keyStart)
		{
			throw new UnsupportedOperationException();
		}
	}

	public static class MapSet<TypeKey, TypeValue> extends SortedMapAVL<TypeKey, SortedSetAVL<TypeValue>> implements Iterable<TypeValue>
	{
		private Comparator<? super TypeValue> comparatorValue;

		public MapSet(Comparator<? super TypeKey> comparatorKey, Comparator<? super TypeValue> comparatorValue)
		{
			super(comparatorKey);
			this.comparatorValue = comparatorValue;
		}

		public MapSet(Comparator<? super TypeKey> comparatorKey, SortedSetAVL<Entry<TypeKey, SortedSetAVL<TypeValue>>> entrySet, Comparator<? super TypeValue> comparatorValue)
		{
			super(comparatorKey, entrySet);
			this.comparatorValue = comparatorValue;
		}

		public boolean add(TypeKey key, TypeValue value)
		{
			SortedSetAVL<TypeValue> set = computeIfAbsent(key, k -> new SortedSetAVL<>(comparatorValue));
			return set.add(value);
		}

		public TypeValue firstValue()
		{
			TypeValue result;
			Entry<TypeKey, SortedSetAVL<TypeValue>> firstEntry = firstEntry();
			if (firstEntry == null)
			{
				result = null;
			}
			else
			{
				result = firstEntry.getValue().first();
			}
			return result;
		}

		@Override
		public MapSet<TypeKey, TypeValue> headMap(TypeKey keyEnd)
		{
			return new MapSet<>(this.comparator, this.entrySet.headSet(new AbstractMap.SimpleEntry<>(keyEnd, null)), this.comparatorValue);
		}

		public Iterator<TypeValue> iterator()
		{
			return new Iterator<TypeValue>()
			{
				Iterator<SortedSetAVL<TypeValue>> iteratorValues = values().iterator();
				Iterator<TypeValue> iteratorValue = null;

				@Override
				public boolean hasNext()
				{
					return iteratorValues.hasNext() || (iteratorValue != null && iteratorValue.hasNext());
				}

				@Override
				public TypeValue next()
				{
					if (iteratorValue == null || !iteratorValue.hasNext())
					{
						iteratorValue = iteratorValues.next().iterator();
					}
					return iteratorValue.next();
				}
			};
		}

		public TypeValue lastValue()
		{
			TypeValue result;
			Entry<TypeKey, SortedSetAVL<TypeValue>> lastEntry = lastEntry();
			if (lastEntry == null)
			{
				result = null;
			}
			else
			{
				result = lastEntry.getValue().last();
			}
			return result;
		}

		public boolean removeSet(TypeKey key, TypeValue value)
		{
			boolean result;
			SortedSetAVL<TypeValue> set = get(key);
			if (set == null)
			{
				result = false;
			}
			else
			{
				result = set.remove(value);
				if (set.size() == 0)
				{
					remove(key);
				}
			}
			return result;
		}

		@Override
		public MapSet<TypeKey, TypeValue> tailMap(TypeKey keyStart)
		{
			return new MapSet<>(this.comparator, this.entrySet.tailSet(new AbstractMap.SimpleEntry<>(keyStart, null)), this.comparatorValue);
		}
	}

	public static class Matrix
	{
		public final int rows;
		public final int columns;
		public final Fraction[][] cells;

		public Matrix(int rows, int columns)
		{
			this.rows = rows;
			this.columns = columns;
			this.cells = new Fraction[rows][columns];
			for (int row = 0; row < rows; row++)
			{
				for (int column = 0; column < columns; column++)
				{
					set(row, column, Fraction.ZERO);
				}
			}
		}

		public void add(int rowSource, int rowTarget, Fraction fraction)
		{
			for (int column = 0; column < columns; column++)
			{
				this.cells[rowTarget][column] = this.cells[rowTarget][column].add(this.cells[rowSource][column].multiply(fraction));
			}
		}

		private int columnPivot(int row)
		{
			int result = this.columns;
			for (int column = this.columns - 1; 0 <= column; column--)
			{
				if (this.cells[row][column].compareTo(Fraction.ZERO) != 0)
				{
					result = column;
				}
			}
			return result;
		}

		public void reduce()
		{
			for (int rowMinimum = 0; rowMinimum < this.rows; rowMinimum++)
			{
				int rowPivot = rowPivot(rowMinimum);
				if (rowPivot != -1)
				{
					int columnPivot = columnPivot(rowPivot);
					Fraction current = this.cells[rowMinimum][columnPivot];
					Fraction pivot = this.cells[rowPivot][columnPivot];
					Fraction fraction = pivot.inverse().sub(current.divide(pivot));
					add(rowPivot, rowMinimum, fraction);
					for (int row = rowMinimum + 1; row < this.rows; row++)
					{
						if (columnPivot(row) == columnPivot)
						{
							add(rowMinimum, row, this.cells[row][columnPivot(row)].neg());
						}
					}
				}
			}
		}

		private int rowPivot(int rowMinimum)
		{
			int result = -1;
			int pivotColumnMinimum = this.columns;
			for (int row = rowMinimum; row < this.rows; row++)
			{
				int pivotColumn = columnPivot(row);
				if (pivotColumn < pivotColumnMinimum)
				{
					result = row;
					pivotColumnMinimum = pivotColumn;
				}
			}
			return result;
		}

		public void set(int row, int column, Fraction value)
		{
			this.cells[row][column] = value;
		}

		public String toString()
		{
			String result = "";
			for (int row = 0; row < rows; row++)
			{
				for (int column = 0; column < columns; column++)
				{
					result += this.cells[row][column] + "\t";
				}
				result += "\n";
			}
			return result;
		}
	}

	public static class Node<Type>
	{
		public final Type value;
		public final Node<Type> left;
		public final Node<Type> right;
		public final int size;
		private final int height;

		public Node(Type value, Node<Type> left, Node<Type> right)
		{
			this.value = value;
			this.left = left;
			this.right = right;
			this.size = 1 + size(left) + size(right);
			this.height = 1 + Math.max(height(left), height(right));
		}

		public static <Type> Node<Type> balance(Node<Type> result)
		{
			while (result != null && 1 < Math.abs(height(result.left) - height(result.right)))
			{
				if (height(result.left) < height(result.right))
				{
					Node<Type> right = result.right;
					if (height(right.right) < height(right.left))
					{
						result = new Node<>(result.value, result.left, right.rotateRight());
					}
					result = result.rotateLeft();
				}
				else
				{
					Node<Type> left = result.left;
					if (height(left.left) < height(left.right))
					{
						result = new Node<>(result.value, left.rotateLeft(), result.right);
					}
					result = result.rotateRight();
				}
			}
			return result;
		}

		public static <Type> Node<Type> clone(Node<Type> result)
		{
			if (result != null)
			{
				result = new Node<>(result.value, clone(result.left), clone(result.right));
			}
			return result;
		}

		public static <Type> Node<Type> delete(Node<Type> node, Type value, Comparator<? super Type> comparator)
		{
			Node<Type> result;
			if (node == null)
			{
				result = null;
			}
			else
			{
				int compare = comparator.compare(value, node.value);
				if (compare == 0)
				{
					if (node.left == null)
					{
						result = node.right;
					}
					else
					{
						if (node.right == null)
						{
							result = node.left;
						}
						else
						{
							Node<Type> first = first(node.right);
							result = new Node<>(first.value, node.left, delete(node.right, first.value, comparator));
						}
					}
				}
				else
				{
					if (compare < 0)
					{
						result = new Node<>(node.value, delete(node.left, value, comparator), node.right);
					}
					else
					{
						result = new Node<>(node.value, node.left, delete(node.right, value, comparator));
					}
				}
				result = balance(result);
			}
			return result;
		}

		public static <Type> Node<Type> first(Node<Type> result)
		{
			while (result.left != null)
			{
				result = result.left;
			}
			return result;
		}

		public static <Type> Node<Type> get(Node<Type> node, Type value, Comparator<? super Type> comparator)
		{
			Node<Type> result;
			if (node == null)
			{
				result = null;
			}
			else
			{
				int compare = comparator.compare(value, node.value);
				if (compare == 0)
				{
					result = node;
				}
				else
				{
					if (compare < 0)
					{
						result = get(node.left, value, comparator);
					}
					else
					{
						result = get(node.right, value, comparator);
					}
				}
			}
			return result;
		}

		public static <Type> Node<Type> head(Node<Type> node, Type value, Comparator<? super Type> comparator)
		{
			Node<Type> result;
			if (node == null)
			{
				result = null;
			}
			else
			{
				int compare = comparator.compare(value, node.value);
				if (compare == 0)
				{
					result = node.left;
				}
				else
				{
					if (compare < 0)
					{
						result = head(node.left, value, comparator);
					}
					else
					{
						result = new Node<>(node.value, node.left, head(node.right, value, comparator));
					}
				}
				result = balance(result);
			}
			return result;
		}

		public static int height(Node node)
		{
			return node == null ? 0 : node.height;
		}

		public static <Type> Node<Type> insert(Node<Type> node, Type value, Comparator<? super Type> comparator)
		{
			Node<Type> result;
			if (node == null)
			{
				result = new Node<>(value, null, null);
			}
			else
			{
				int compare = comparator.compare(value, node.value);
				if (compare == 0)
				{
					result = new Node<>(value, node.left, node.right);
					;
				}
				else
				{
					if (compare < 0)
					{
						result = new Node<>(node.value, insert(node.left, value, comparator), node.right);
					}
					else
					{
						result = new Node<>(node.value, node.left, insert(node.right, value, comparator));
					}
				}
				result = balance(result);
			}
			return result;
		}

		public static <Type> Node<Type> last(Node<Type> result)
		{
			while (result.right != null)
			{
				result = result.right;
			}
			return result;
		}

		public static int size(Node node)
		{
			return node == null ? 0 : node.size;
		}

		public static <Type> Node<Type> tail(Node<Type> node, Type value, Comparator<? super Type> comparator)
		{
			Node<Type> result;
			if (node == null)
			{
				result = null;
			}
			else
			{
				int compare = comparator.compare(value, node.value);
				if (compare == 0)
				{
					result = new Node<>(node.value, null, node.right);
				}
				else
				{
					if (compare < 0)
					{
						result = new Node<>(node.value, tail(node.left, value, comparator), node.right);
					}
					else
					{
						result = tail(node.right, value, comparator);
					}
				}
				result = balance(result);
			}
			return result;
		}

		public static <Type> void traverseOrderIn(Node<Type> node, Consumer<Type> consumer)
		{
			if (node != null)
			{
				traverseOrderIn(node.left, consumer);
				consumer.accept(node.value);
				traverseOrderIn(node.right, consumer);
			}
		}

		public Node<Type> rotateLeft()
		{
			Node<Type> left = new Node<>(this.value, this.left, this.right.left);
			return new Node<>(this.right.value, left, this.right.right);
		}

		public Node<Type> rotateRight()
		{
			Node<Type> right = new Node<>(this.value, this.left.right, this.right);
			return new Node<>(this.left.value, this.left.left, right);
		}
	}

	public static class SingleLinkedList<Type>
	{
		public final Type element;
		public SingleLinkedList<Type> next;

		public SingleLinkedList(Type element, SingleLinkedList<Type> next)
		{
			this.element = element;
			this.next = next;
		}

		public void toCollection(Collection<Type> collection)
		{
			if (this.next != null)
			{
				this.next.toCollection(collection);
			}
			collection.add(this.element);
		}
	}

	public static class SmallSetIntegers
	{
		public static final int SIZE = 20;
		public static final int[] SET = generateSet();
		public static final int[] COUNT = generateCount();
		public static final int[] INTEGER = generateInteger();

		private static int count(int set)
		{
			int result = 0;
			for (int integer = 0; integer < SIZE; integer++)
			{
				if (0 < (set & set(integer)))
				{
					result += 1;
				}
			}
			return result;
		}

		private static final int[] generateCount()
		{
			int[] result = new int[1 << SIZE];
			for (int set = 0; set < result.length; set++)
			{
				result[set] = count(set);
			}
			return result;
		}

		private static final int[] generateInteger()
		{
			int[] result = new int[1 << SIZE];
			Arrays.fill(result, -1);
			for (int integer = 0; integer < SIZE; integer++)
			{
				result[SET[integer]] = integer;
			}
			return result;
		}

		private static final int[] generateSet()
		{
			int[] result = new int[SIZE];
			for (int integer = 0; integer < result.length; integer++)
			{
				result[integer] = set(integer);
			}
			return result;
		}

		private static int set(int integer)
		{
			return 1 << integer;
		}
	}

	public static class SortedMapAVL<TypeKey, TypeValue> implements SortedMap<TypeKey, TypeValue>
	{
		public final Comparator<? super TypeKey> comparator;
		public final SortedSetAVL<Entry<TypeKey, TypeValue>> entrySet;

		public SortedMapAVL(Comparator<? super TypeKey> comparator)
		{
			this(comparator, new SortedSetAVL<>((entry0, entry1) -> comparator.compare(entry0.getKey(), entry1.getKey())));
		}

		private SortedMapAVL(Comparator<? super TypeKey> comparator, SortedSetAVL<Entry<TypeKey, TypeValue>> entrySet)
		{
			this.comparator = comparator;
			this.entrySet = entrySet;
		}

		@Override
		public void clear()
		{
			this.entrySet.clear();
		}

		@Override
		public Comparator<? super TypeKey> comparator()
		{
			return this.comparator;
		}

		@Override
		public boolean containsKey(Object key)
		{
			return this.entrySet().contains(new AbstractMap.SimpleEntry<>((TypeKey) key, null));
		}

		@Override
		public boolean containsValue(Object value)
		{
			throw new UnsupportedOperationException();
		}

		@Override
		public SortedSetAVL<Entry<TypeKey, TypeValue>> entrySet()
		{
			return this.entrySet;
		}

		public Entry<TypeKey, TypeValue> firstEntry()
		{
			return this.entrySet.first();
		}

		@Override
		public TypeKey firstKey()
		{
			return firstEntry().getKey();
		}

		@Override
		public TypeValue get(Object key)
		{
			Entry<TypeKey, TypeValue> entry = new AbstractMap.SimpleEntry<>((TypeKey) key, null);
			entry = this.entrySet.get(entry);
			return entry == null ? null : entry.getValue();
		}

		@Override
		public SortedMapAVL<TypeKey, TypeValue> headMap(TypeKey keyEnd)
		{
			return new SortedMapAVL<>(this.comparator, this.entrySet.headSet(new AbstractMap.SimpleEntry<>(keyEnd, null)));
		}

		@Override
		public boolean isEmpty()
		{
			return this.entrySet.isEmpty();
		}

		@Override
		public Set<TypeKey> keySet()
		{
			return new SortedSet<TypeKey>()
			{
				@Override
				public boolean add(TypeKey typeKey)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean addAll(Collection<? extends TypeKey> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public void clear()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public Comparator<? super TypeKey> comparator()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean contains(Object o)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean containsAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public TypeKey first()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public SortedSet<TypeKey> headSet(TypeKey typeKey)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean isEmpty()
				{
					return size() == 0;
				}

				@Override
				public Iterator<TypeKey> iterator()
				{
					final Iterator<Entry<TypeKey, TypeValue>> iterator = SortedMapAVL.this.entrySet.iterator();
					return new Iterator<TypeKey>()
					{
						@Override
						public boolean hasNext()
						{
							return iterator.hasNext();
						}

						@Override
						public TypeKey next()
						{
							return iterator.next().getKey();
						}
					};
				}

				@Override
				public TypeKey last()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean remove(Object o)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean removeAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean retainAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public int size()
				{
					return SortedMapAVL.this.entrySet.size();
				}

				@Override
				public SortedSet<TypeKey> subSet(TypeKey typeKey, TypeKey e1)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public SortedSet<TypeKey> tailSet(TypeKey typeKey)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public Object[] toArray()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public <T> T[] toArray(T[] ts)
				{
					throw new UnsupportedOperationException();
				}
			};
		}

		public Entry<TypeKey, TypeValue> lastEntry()
		{
			return this.entrySet.last();
		}

		@Override
		public TypeKey lastKey()
		{
			return lastEntry().getKey();
		}

		@Override
		public TypeValue put(TypeKey key, TypeValue value)
		{
			TypeValue result = get(key);
			Entry<TypeKey, TypeValue> entry = new AbstractMap.SimpleEntry<>(key, value);
			this.entrySet().add(entry);
			return result;
		}

		@Override
		public void putAll(Map<? extends TypeKey, ? extends TypeValue> map)
		{
			map.entrySet()
					.forEach(entry -> put(entry.getKey(), entry.getValue()));
		}

		@Override
		public TypeValue remove(Object key)
		{
			TypeValue result = get(key);
			Entry<TypeKey, TypeValue> entry = new AbstractMap.SimpleEntry<>((TypeKey) key, null);
			this.entrySet.remove(entry);
			return result;
		}

		@Override
		public int size()
		{
			return this.entrySet().size();
		}

		@Override
		public SortedMapAVL<TypeKey, TypeValue> subMap(TypeKey keyStart, TypeKey keyEnd)
		{
			return new SortedMapAVL<>(this.comparator, this.entrySet.subSet(new AbstractMap.SimpleEntry<>(keyStart, null), new AbstractMap.SimpleEntry<>(keyEnd, null)));
		}

		@Override
		public SortedMapAVL<TypeKey, TypeValue> tailMap(TypeKey keyStart)
		{
			return new SortedMapAVL<>(this.comparator, this.entrySet.tailSet(new AbstractMap.SimpleEntry<>(keyStart, null)));
		}

		@Override
		public String toString()
		{
			return this.entrySet().toString();
		}

		@Override
		public Collection<TypeValue> values()
		{
			return new Collection<TypeValue>()
			{
				@Override
				public boolean add(TypeValue typeValue)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean addAll(Collection<? extends TypeValue> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public void clear()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean contains(Object value)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean containsAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean isEmpty()
				{
					return SortedMapAVL.this.entrySet.isEmpty();
				}

				@Override
				public Iterator<TypeValue> iterator()
				{
					return new Iterator<TypeValue>()
					{
						Iterator<Entry<TypeKey, TypeValue>> iterator = SortedMapAVL.this.entrySet.iterator();

						@Override
						public boolean hasNext()
						{
							return this.iterator.hasNext();
						}

						@Override
						public TypeValue next()
						{
							return this.iterator.next().getValue();
						}
					};
				}

				@Override
				public boolean remove(Object o)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean removeAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public boolean retainAll(Collection<?> collection)
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public int size()
				{
					return SortedMapAVL.this.entrySet.size();
				}

				@Override
				public Object[] toArray()
				{
					throw new UnsupportedOperationException();
				}

				@Override
				public <T> T[] toArray(T[] ts)
				{
					throw new UnsupportedOperationException();
				}
			};
		}
	}

	public static class SortedSetAVL<Type> implements SortedSet<Type>
	{
		public Comparator<? super Type> comparator;
		public Node<Type> root;

		private SortedSetAVL(Comparator<? super Type> comparator, Node<Type> root)
		{
			this.comparator = comparator;
			this.root = root;
		}

		public SortedSetAVL(Comparator<? super Type> comparator)
		{
			this(comparator, null);
		}

		public SortedSetAVL(Collection<? extends Type> collection, Comparator<? super Type> comparator)
		{
			this(comparator, null);
			this.addAll(collection);
		}

		public SortedSetAVL(SortedSetAVL<Type> sortedSetAVL)
		{
			this(sortedSetAVL.comparator, Node.clone(sortedSetAVL.root));
		}

		@Override
		public boolean add(Type value)
		{
			int sizeBefore = size();
			this.root = Node.insert(this.root, value, this.comparator);
			return sizeBefore != size();
		}

		@Override
		public boolean addAll(Collection<? extends Type> collection)
		{
			return collection.stream()
					.map(this::add)
					.reduce(true, (x, y) -> x | y);
		}

		@Override
		public void clear()
		{
			this.root = null;
		}

		@Override
		public Comparator<? super Type> comparator()
		{
			return this.comparator;
		}

		@Override
		public boolean contains(Object value)
		{
			return Node.get(this.root, (Type) value, this.comparator) != null;
		}

		@Override
		public boolean containsAll(Collection<?> collection)
		{
			return collection.stream()
					.allMatch(this::contains);
		}

		@Override
		public Type first()
		{
			return Node.first(this.root).value;
		}

		public Type get(Type value)
		{
			Node<Type> node = Node.get(this.root, value, this.comparator);
			return node == null ? null : node.value;
		}

		@Override
		public SortedSetAVL<Type> headSet(Type valueEnd)
		{
			return new SortedSetAVL<>(this.comparator, Node.head(this.root, valueEnd, this.comparator));
		}

		@Override
		public boolean isEmpty()
		{
			return this.root == null;
		}

		@Override
		public Iterator<Type> iterator()
		{
			Stack<Node<Type>> path = new Stack<>();
			return new Iterator<Type>()
			{
				{
					push(SortedSetAVL.this.root);
				}

				@Override
				public boolean hasNext()
				{
					return !path.isEmpty();
				}

				@Override
				public Type next()
				{
					if (path.isEmpty())
					{
						throw new NoSuchElementException();
					}
					else
					{
						Node<Type> node = path.peek();
						Type result = node.value;
						if (node.right != null)
						{
							push(node.right);
						}
						else
						{
							do
							{
								node = path.pop();
							}
							while (!path.isEmpty() && path.peek().right == node);
						}
						return result;
					}
				}

				public void push(Node<Type> node)
				{
					while (node != null)
					{
						path.push(node);
						node = node.left;
					}
				}
			};
		}

		@Override
		public Type last()
		{
			return Node.last(this.root).value;
		}

		@Override
		public boolean remove(Object value)
		{
			int sizeBefore = size();
			this.root = Node.delete(this.root, (Type) value, this.comparator);
			return sizeBefore != size();
		}

		@Override
		public boolean removeAll(Collection<?> collection)
		{
			return collection.stream()
					.map(this::remove)
					.reduce(true, (x, y) -> x | y);
		}

		@Override
		public boolean retainAll(Collection<?> collection)
		{
			SortedSetAVL<Type> set = new SortedSetAVL<>(this.comparator);
			collection.stream()
					.map(element -> (Type) element)
					.filter(this::contains)
					.forEach(set::add);
			boolean result = size() != set.size();
			this.root = set.root;
			return result;
		}

		@Override
		public int size()
		{
			return this.root == null ? 0 : this.root.size;
		}

		@Override
		public SortedSetAVL<Type> subSet(Type valueStart, Type valueEnd)
		{
			return tailSet(valueStart).headSet(valueEnd);
		}

		@Override
		public SortedSetAVL<Type> tailSet(Type valueStart)
		{
			return new SortedSetAVL<>(this.comparator, Node.tail(this.root, valueStart, this.comparator));
		}

		@Override
		public Object[] toArray()
		{
			return toArray(new Object[0]);
		}

		@Override
		public <T> T[] toArray(T[] ts)
		{
			List<Object> list = new ArrayList<>();
			Node.traverseOrderIn(this.root, list::add);
			return list.toArray(ts);
		}

		@Override
		public String toString()
		{
			return "{" + E_440.toString(this, ", ") + "}";
		}
	}

	public static class Tree2D
	{
		public static final int SIZE = 1 << 30;
		public static final Tree2D[] TREES_NULL = new Tree2D[] { null, null, null, null };
		public final Tree2D[] trees;
		public final int count;

		private Tree2D(Tree2D[] trees, int count)
		{
			this.trees = trees;
			this.count = count;
		}

		public Tree2D(Tree2D[] trees)
		{
			this(trees, count(trees));
		}

		public Tree2D()
		{
			this(TREES_NULL);
		}

		public static boolean contains(int x, int y, int left, int bottom, int size)
		{
			return left <= x && x < left + size && bottom <= y && y < bottom + size;
		}

		public static int count(Tree2D[] trees)
		{
			int result = 0;
			for (int index = 0; index < 4; index++)
			{
				if (trees[index] != null)
				{
					result += trees[index].count;
				}
			}
			return result;
		}

		public static int count
				(
						int rectangleLeft,
						int rectangleBottom,
						int rectangleRight,
						int rectangleTop,
						Tree2D tree,
						int left,
						int bottom,
						int size
				)
		{
			int result;
			if (tree == null)
			{
				result = 0;
			}
			else
			{
				int right = left + size;
				int top = bottom + size;
				int intersectionLeft = Math.max(rectangleLeft, left);
				int intersectionBottom = Math.max(rectangleBottom, bottom);
				int intersectionRight = Math.min(rectangleRight, right);
				int intersectionTop = Math.min(rectangleTop, top);
				if (intersectionRight <= intersectionLeft || intersectionTop <= intersectionBottom)
				{
					result = 0;
				}
				else
				{
					if (intersectionLeft == left && intersectionBottom == bottom && intersectionRight == right && intersectionTop == top)
					{
						result = tree.count;
					}
					else
					{
						size = size >> 1;
						result = 0;
						for (int index = 0; index < 4; index++)
						{
							result += count
									(
											rectangleLeft,
											rectangleBottom,
											rectangleRight,
											rectangleTop,
											tree.trees[index],
											quadrantLeft(left, size, index),
											quadrantBottom(bottom, size, index),
											size
									);
						}
					}
				}
			}
			return result;
		}

		public static int quadrantBottom(int bottom, int size, int index)
		{
			return bottom + (index >> 1) * size;
		}

		public static int quadrantLeft(int left, int size, int index)
		{
			return left + (index & 1) * size;
		}

		public int count(int rectangleLeft, int rectangleBottom, int rectangleRight, int rectangleTop)
		{
			return count
					(
							rectangleLeft,
							rectangleBottom,
							rectangleRight,
							rectangleTop,
							this,
							0,
							0,
							SIZE
					);
		}

		public Tree2D setPoint
				(
						int x,
						int y,
						Tree2D tree,
						int left,
						int bottom,
						int size
				)
		{
			Tree2D result;
			if (contains(x, y, left, bottom, size))
			{
				if (size == 1)
				{
					result = new Tree2D(TREES_NULL, 1);
				}
				else
				{
					size = size >> 1;
					Tree2D[] trees = new Tree2D[4];
					for (int index = 0; index < 4; index++)
					{
						trees[index] = setPoint
								(
										x,
										y,
										tree == null ? null : tree.trees[index],
										quadrantLeft(left, size, index),
										quadrantBottom(bottom, size, index),
										size
								);
					}
					result = new Tree2D(trees);
				}
			}
			else
			{
				result = tree;
			}
			return result;
		}

		public Tree2D setPoint(int x, int y)
		{
			return setPoint
					(
							x,
							y,
							this,
							0,
							0,
							SIZE
					);
		}
	}

	public static class Tuple2<Type0, Type1>
	{
		public final Type0 v0;
		public final Type1 v1;

		public Tuple2(Type0 v0, Type1 v1)
		{
			this.v0 = v0;
			this.v1 = v1;
		}

		@Override
		public String toString()
		{
			return "(" + this.v0 + ", " + this.v1 + ")";
		}
	}

	public static class Tuple2Comparable<Type0 extends Comparable<? super Type0>, Type1 extends Comparable<? super Type1>> extends Tuple2<Type0, Type1> implements Comparable<Tuple2Comparable<Type0, Type1>>
	{
		public Tuple2Comparable(Type0 v0, Type1 v1)
		{
			super(v0, v1);
		}

		@Override
		public int compareTo(Tuple2Comparable<Type0, Type1> that)
		{
			int result = this.v0.compareTo(that.v0);
			if (result == 0)
			{
				result = this.v1.compareTo(that.v1);
			}
			return result;
		}
	}

	public static class Tuple3<Type0, Type1, Type2>
	{
		public final Type0 v0;
		public final Type1 v1;
		public final Type2 v2;

		public Tuple3(Type0 v0, Type1 v1, Type2 v2)
		{
			this.v0 = v0;
			this.v1 = v1;
			this.v2 = v2;
		}

		@Override
		public String toString()
		{
			return "(" + this.v0 + ", " + this.v1 + ", " + this.v2 + ")";
		}
	}

	public static class Vertex<TypeVertex extends Vertex<TypeVertex, TypeEdge>, TypeEdge extends Edge<TypeVertex, TypeEdge>> implements Comparable<Vertex<? super TypeVertex, ? super TypeEdge>>
	{
		public final int index;
		public final List<TypeEdge> edges;

		public Vertex(int index)
		{
			this.index = index;
			this.edges = new ArrayList<>();
		}

		public static <TypeVertex extends Vertex<TypeVertex, TypeEdge>, TypeEdge extends Edge<TypeVertex, TypeEdge>, TypeResult> TypeResult breadthFirstSearch(
				TypeVertex vertex,
				TypeEdge edge,
				BiFunctionResult<TypeVertex, TypeEdge, TypeResult> function,
				Array<Boolean> visited,
				FIFO<TypeVertex> verticesNext,
				FIFO<TypeEdge> edgesNext,
				TypeResult result
		)
		{
			if (!visited.get(vertex.index))
			{
				visited.set(vertex.index, true);
				result = function.apply(vertex, edge, result);
				for (TypeEdge edgeNext : vertex.edges)
				{
					TypeVertex vertexNext = edgeNext.other(vertex);
					if (!visited.get(vertexNext.index))
					{
						verticesNext.push(vertexNext);
						edgesNext.push(edgeNext);
					}
				}
			}
			return result;
		}

		public static <TypeVertex extends Vertex<TypeVertex, TypeEdge>, TypeEdge extends Edge<TypeVertex, TypeEdge>, TypeResult> TypeResult breadthFirstSearch
				(
						Array<TypeVertex> vertices,
						int indexVertexStart,
						BiFunctionResult<TypeVertex, TypeEdge, TypeResult> function,
						TypeResult result
				)
		{
			Array<Boolean> visited = new Array<>(vertices.size(), false);
			FIFO<TypeVertex> verticesNext = new FIFO<>();
			verticesNext.push(vertices.get(indexVertexStart));
			FIFO<TypeEdge> edgesNext = new FIFO<>();
			edgesNext.push(null);
			while (!verticesNext.isEmpty())
			{
				result = breadthFirstSearch(verticesNext.pop(), edgesNext.pop(), function, visited, verticesNext, edgesNext, result);
			}
			return result;
		}

		public static <
				TypeVertex extends Vertex<TypeVertex, TypeEdge>,
				TypeEdge extends Edge<TypeVertex, TypeEdge>
				>
		SortedSet<TypeVertex>
		depthFirstSearch
				(
						TypeVertex start,
						BiConsumer<TypeVertex, TypeEdge> functionVisitPre,
						BiConsumer<TypeVertex, TypeEdge> functionVisitPost
				)
		{
			SortedSet<TypeVertex> result = new SortedSetAVL<>(Comparator.naturalOrder());
			Stack<TypeVertex> stackVertex = new Stack<>();
			Stack<TypeEdge> stackEdge = new Stack<>();
			stackVertex.push(start);
			stackEdge.push(null);
			while (!stackVertex.isEmpty())
			{
				TypeVertex vertex = stackVertex.pop();
				TypeEdge edge = stackEdge.pop();
				if (result.contains(vertex))
				{
					functionVisitPost.accept(vertex, edge);
				}
				else
				{
					result.add(vertex);
					stackVertex.push(vertex);
					stackEdge.push(edge);
					functionVisitPre.accept(vertex, edge);
					for (TypeEdge otherEdge : vertex.edges)
					{
						TypeVertex otherVertex = otherEdge.other(vertex);
						if (!result.contains(otherVertex))
						{
							stackVertex.push(otherVertex);
							stackEdge.push(otherEdge);
						}
					}
				}
			}
			return result;
		}

		public static <
				TypeVertex extends Vertex<TypeVertex, TypeEdge>,
				TypeEdge extends Edge<TypeVertex, TypeEdge>
				>
		boolean
		cycle
				(
						TypeVertex start,
						SortedSet<TypeVertex> result
				)
		{
			boolean cycle = false;
			Stack<TypeVertex> stackVertex = new Stack<>();
			Stack<TypeEdge> stackEdge = new Stack<>();
			stackVertex.push(start);
			stackEdge.push(null);
			while (!stackVertex.isEmpty())
			{
				TypeVertex vertex = stackVertex.pop();
				TypeEdge edge = stackEdge.pop();
				if (!result.contains(vertex))
				{
					result.add(vertex);
					for (TypeEdge otherEdge : vertex.edges)
					{
						if (otherEdge != edge)
						{
							TypeVertex otherVertex = otherEdge.other(vertex);
							if (result.contains(otherVertex))
							{
								cycle = true;
							}
							else
							{
								stackVertex.push(otherVertex);
								stackEdge.push(otherEdge);
							}
						}
					}
				}
			}
			return cycle;
		}

		@Override
		public int compareTo(Vertex<? super TypeVertex, ? super TypeEdge> that)
		{
			return Integer.compare(this.index, that.index);
		}

		@Override
		public String toString()
		{
			return "" + this.index;
		}
	}

	public static class VertexDefault<TypeEdge extends Edge<VertexDefault<TypeEdge>, TypeEdge>> extends Vertex<VertexDefault<TypeEdge>, TypeEdge>
	{
		public VertexDefault(int index)
		{
			super(index);
		}
	}

	public static class VertexDefaultDefault extends Vertex<VertexDefaultDefault, EdgeDefaultDefault>
	{
		public VertexDefaultDefault(int index)
		{
			super(index);
		}

		public static Array<VertexDefaultDefault> vertices(int n)
		{
			Array<VertexDefaultDefault> result = new Array<>(n);
			for (int index = 0; index < n; index++)
			{
				result.set(index, new VertexDefaultDefault(index));
			}
			return result;
		}
	}

	public static class Wrapper<Type>
	{
		public Type value;

		public Wrapper(Type value)
		{
			this.value = value;
		}

		public Type get()
		{
			return this.value;
		}

		public void set(Type value)
		{
			this.value = value;
		}

		@Override
		public String toString()
		{
			return this.value.toString();
		}
	}

	static class Point extends Vertex<Point, EdgeDefault<Point>>
	{
		public static final Comparator<Point> COMPARATOR_X = Comparator.comparing(Point::getX);
		public static final Comparator<Point> COMPARATOR_Y = Comparator.comparing(Point::getX);
		public final int x;
		public final int y;

		public Point(int index, int x, int y)
		{
			super(index);
			this.x = x;
			this.y = y;
		}

		public int getX()
		{
			return x;
		}

		public int getY()
		{
			return y;
		}
	}

	public static long BIG = 1000000007;

	public static int countLines(Set<Point> points)
	{
		Set<Integer> xs = new SortedSetAVL<>(Comparator.naturalOrder());
		Set<Integer> ys = new SortedSetAVL<>(Comparator.naturalOrder());
		for (Point point : points)
		{
			xs.add(point.getX());
			ys.add(point.getY());
		}
		return xs.size() + ys.size();
	}

	public static long modMultiply(long a, long b)
	{
		return (a * b) % BIG;
	}

	public static long modAdd(long a, long b)
	{
		return (a + b) % BIG;
	}

	public static long modSubtract(long a, long b)
	{
		return (a - b + BIG) % BIG;
	}

	public static long modPower2(int a)
	{
		long result = 1;
		for (int index = 0; index < a; index++)
		{
			result = modMultiply(result, 2);
		}
		return result;
	}

	public static void solve() throws IOException
	{
		int n = nextInt();
		Array<Point> points = new Array<>(n);
		MapSet<Integer, Point> y2Points = new MapSet<>(Comparator.naturalOrder(), Point.COMPARATOR_X);
		for (int index = 0; index < n; index++)
		{
			Point point = new Point(index, nextInt(), nextInt());
			points.set(index, point);
			y2Points.add(point.getY(), point);
		}
		Map<Integer, Point> x2LastY = new SortedMapAVL<>(Comparator.naturalOrder());
		for (Set<Point> set : y2Points.values())
		{
			Point lastX = null;
			for (Point point : set)
			{
				if (lastX != null)
				{
					new EdgeDefault<>(point, lastX, true);
				}
				lastX = point;
				Point lastY = x2LastY.get(point.getX());
				if (lastY != null)
				{
					new EdgeDefault<>(point, lastY, true);
				}
				x2LastY.put(point.getX(), point);
			}
		}
		Map<Point, Set<Point>> pointsCycleFalse = new SortedMapAVL<>(Comparator.naturalOrder());
		Map<Point, Set<Point>> pointsCycleTrue = new SortedMapAVL<>(Comparator.naturalOrder());
		Set<Point> pointsProcessed = new SortedSetAVL<>(Comparator.naturalOrder());
		for (Point point : points)
		{
			if (!pointsProcessed.contains(point))
			{
				SortedSet<Point> structure = new SortedSetAVL<>(Comparator.naturalOrder());
				if (Vertex.cycle(point, structure))
				{
					pointsCycleTrue.put(point, structure);
				}
				else
				{
					pointsCycleFalse.put(point, structure);
				}
				pointsProcessed.addAll(structure);
			}
		}
		long result = 1;
		for (Set<Point> set : pointsCycleFalse.values())
		{
			result = modMultiply(result, modSubtract(modPower2(countLines(set)), 1));
		}
		for (Set<Point> set : pointsCycleTrue.values())
		{
			result = modMultiply(result, modPower2(countLines(set)));
		}
		out.println(result);
	}
}


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

import static java.lang.Math.random;

/**
 * @author Don Li
 */
public class PointsLinesTitles {

    int N = (int) 1e5 + 10;
    int MOD = (int) 1e9 + 7;

    int n;
    int[][] p;
    List<Integer>[] G;

    boolean[] used = new boolean[N];
    Set<Integer> uniqueX = new HashSet<>(), uniqueY = new HashSet<>();
    long sumDegree = 0, numNode = 0;

    void solve() {
        n = in.nextInt();

        p = new int[n][2];
        for (int i = 0; i < n; i++) {
            p[i][0] = in.nextInt();
            p[i][1] = in.nextInt();
        }

        int[] x = new int[n], y = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = p[i][0];
            y[i] = p[i][1];
        }
        sort(x);
        sort(y);
        for (int i = 0; i < n; i++) {
            p[i][0] = lowerBound(x, p[i][0]);
            p[i][1] = lowerBound(y, p[i][1]);
        }

        G = new List[n];
        for (int i = 0; i < n; i++) G[i] = new ArrayList<>();

        List<Integer>[] ver = new List[n], hor = new List[n];
        for (int i = 0; i < n; i++) {
            ver[i] = new ArrayList<>();
            hor[i] = new ArrayList<>();
        }
        for (int i = 0; i < n; i++) {
            ver[p[i][0]].add(i);
            hor[p[i][1]].add(i);
        }
        for (int i = 0; i < n; i++) {
            ver[i].sort(Comparator.comparingInt(a -> p[a][1]));
            for (int j = 1; j < ver[i].size(); j++) {
                int u = ver[i].get(j - 1), v = ver[i].get(j);
                addNeighbors(u, v);
            }
            hor[i].sort(Comparator.comparingInt(a -> p[a][0]));
            for (int j = 1; j < hor[i].size(); j++) {
                int u = hor[i].get(j - 1), v = hor[i].get(j);
                addNeighbors(u, v);
            }
        }

        long ans = 1;
        for (int i = 0; i < n; i++) {
            if (!used[i]) {
                uniqueX.clear();
                uniqueY.clear();
                sumDegree = 0; numNode = 0;
                dfs(i);
                long ways = mpow(2, uniqueX.size() + uniqueY.size());
                if (sumDegree / 2 == numNode - 1) ways = (ways - 1 + MOD) % MOD;
                ans = ans * ways % MOD;
            }
        }
        out.println(ans);
    }

    void dfs(int u) {
        used[u] = true;
        uniqueX.add(p[u][0]);
        uniqueY.add(p[u][1]);
        numNode++;
        sumDegree += G[u].size();
        for (int v : G[u]) {
            if (!used[v]) dfs(v);
        }
    }

    long mpow(long a, long n) {
        long res = 1;
        while (n > 0) {
            if ((n & 1) > 0) res = res * a % MOD;
            a = a * a % MOD;
            n >>= 1;
        }
        return res;
    }

    void addNeighbors(int u, int v) {
        G[u].add(v);
        G[v].add(u);
    }

    void sort(int[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (i + random() * (n - i));
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
        Arrays.sort(a);
    }

    int lowerBound(int[] a, int k) {
        int lb = -1, ub = a.length;
        while (ub - lb > 1) {
            int m = (lb + ub) >> 1;
            if (a[m] >= k) ub = m;
            else lb = m;
        }
        return ub;
    }

    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new PointsLinesTitles().solve();
        out.close();
    }

    static FastScanner in;
    static PrintWriter out;

    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;

        public FastScanner(BufferedReader in) {
            this.in = in;
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}


import java.util.*;
import java.io.*;
import java.math.*;
import java.lang.*;
import java.awt.*;
import java.awt.geom.*;
import java.util.stream.*;

/**
 * @author Pradyumn
 */

public class Main implements Runnable{
	public int TC = 0;
	public static void main(String[] args) {
		new Thread(null, new Main(), ":)", 1L << 26).start();
	}
	static final int MODULO = (int)(1e9 + 7);
	@SuppressWarnings("Unchecked")
	public void solve() throws IOException {
	    int n = ni();
	    HashSet<Integer> x = new HashSet<>();
	    HashSet<Integer> y = new HashSet<>();
	    HashMap<Integer, Integer> mapX = new HashMap<>();
	    HashMap<Integer, Integer> mapY = new HashMap<>();
	    int[][] pp = new int[2][n];
	    for (int i = 0; i < n;  ++i) {
	    	for(int j = 0;j < 2; ++j) {
	    		pp[j][i] = ni();
	    		if(j == 0) x.add(pp[j][i]);
	    		else y.add(pp[j][i]);
	    	}
	    }

	    int mapIdx = 0;
	    for(int xx : x)
	    	if(!mapX.containsKey(xx))
	    		mapX.put(xx, mapIdx++);

	    for(int yy : y)
	    	if(!mapY.containsKey(yy))
	    		mapY.put(yy, mapIdx++);

	    DJSet ds = new DJSet(mapIdx);
	    for(int i = 0;i < n; ++i) {
	    	ds.union(mapX.get(pp[0][i]), mapY.get(pp[1][i]));
	    }

	    long res = 1;
	    factorial();
	    for (int i = 0; i < mapIdx; i++)
            if (ds.upper[i] < 0) {
                int numPoints = ds.pointsNum[i], lines = -ds.upper[i];
                long ways = 0;
                for (int j = 0; j <= Math.min(numPoints, lines); j++) {
                    ways += ncr(lines, j);
                    if (ways >= MODULO) ways -= MODULO;
                }
                res *= ways;
                res %= MODULO;
            }
	    out.println(res);
	}
	// O(1) nCr
    static int MAX = 5 * 100000 + 1;
    static int fact[] = new int[MAX];

    static int ncr(int n, int r) {
        return (int) ((long) fact[n] * ((inv(fact[r], MODULO) * inv(fact[n - r], MODULO)) % MODULO) % MODULO) % MODULO;
    }

    static long inv(long x, long mod) {
        long r, y;
        for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
            if ((y & 1) == 1)
                r = r * x % mod;
        return r;
    }

    static void factorial() {
        fact[0] = fact[1] = 1;
        for (int i = 2; i < MAX; i++)
            fact[i] = (int) ((long) i * fact[i - 1] % MODULO);
    }

    public static long powMod(long a, long n) {
    	long res = 1;
    	long t = a;
    	for(int i = 0;i < 63; ++i) {
    		if((n & (1L << i)) != 0)
    			res = (res + t) % MODULO;
    		t = t * t % MODULO;
    	}
        return res;
    }
	public class DJSet {
	    public int[] upper;
	    public int[] pointsNum;
	    public int count;
	    public DJSet(int n) {
	        upper = new int[n];
	        count = n;
	        pointsNum = new int[n];
	        Arrays.fill(upper, -1);
	    }

	    public int root(int x) {
	        return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
	    }

	    public boolean equiv(int x, int y) {
	        return root(x) == root(y);
	    }

	    public boolean union(int x, int y) {
	        x = root(x);
	        y = root(y);
	        if (x != y) {
	            if (upper[y] < upper[x]) {
	                int d = x;
	                x = y;
	                y = d;
	            }
	            upper[x] += upper[y];
	            upper[y] = x;
	            pointsNum[x] += 1 + pointsNum[y];
	            --count;
	            return true;
	        } else {
	        	++pointsNum[x];
	        }
	        return false;
	    }

	    public int getCount() {
	        return count;
	    }

	    public long size(int u) {
	        return -upper[root(u)];
	    }

	    public void clear() {
	        Arrays.fill(upper, -1);
	    }
	}
	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	public void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in),32768);
			st = null;
			out = new PrintWriter(System.out);
			if(TC == 1) {
				for(int T = ni();T > 0; --T) {
					solve();
				}
			} else {
				solve();
			}
			br.close();
			out.close();
		} catch(IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	public char[] nsc( ) throws IOException {
		return ns().toCharArray();
	}
	public char[][] nm(int n, int m) throws IOException {
		char[][] map = new char[n][];
		for(int i = 0;i < n; ++i) {
			map[i] = nsc();
		}
		return map;
	}
	public String ns() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}
	public String nextLine() throws IOException {
		return br.readLine();
	}
	public int ni() throws IOException {
		return Integer.parseInt(ns());
	}

	public int[] na(int n) throws IOException {
		int[] a = new int[n];
		for(int i = 0;i < n; ++i) a[i] = ni();
		return a;
	}

	public long nl() throws IOException {
		return Long.parseLong(ns());
	}

	public long[] nal(int n) throws IOException {
		long[] a = new long[n];
		for(int i = 0;i < n; ++i) a[i] = nl();
		return a;
	}

	public double nd() throws IOException {
		return Double.parseDouble(ns());
	}
	private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private static void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}


import java.util.*;
import java.io.*;
import java.math.*;
import java.lang.*;
import java.awt.*;
import java.awt.geom.*;
import java.util.stream.*;

/**
 * @author Pradyumn
 */

public class Main implements Runnable{
	public int TC = 0;
	public static void main(String[] args) {
		new Thread(null, new Main(), ":)", 1L << 26).start();
	}

	static final int MODULO = (int)(1e9 + 7);

	@SuppressWarnings("Unchecked")
	public void solve() throws IOException {
	    int n = ni();
	    HashSet<Integer> x = new HashSet<>();
	    HashSet<Integer> y = new HashSet<>();
	    HashMap<Integer, Integer> mapX = new HashMap<>();
	    HashMap<Integer, Integer> mapY = new HashMap<>();
	    int[][] pp = new int[2][n];

	    for (int i = 0; i < n;  ++i) {
	    	for(int j = 0;j < 2; ++j) {
	    		pp[j][i] = ni();
	    		if(j == 0) x.add(pp[j][i]);
	    		else y.add(pp[j][i]);
	    	}
	    }

	    int mapIdx = 0;
	    for(int xx : x)
	    	if(!mapX.containsKey(xx))
	    		mapX.put(xx, mapIdx++);

	    for(int yy : y)
	    	if(!mapY.containsKey(yy))
	    		mapY.put(yy, mapIdx++);

	    DJSet ds = new DJSet(mapIdx);
	    for(int i = 0;i < n; ++i) {
	    	ds.union(mapX.get(pp[0][i]), mapY.get(pp[1][i]));
	    }

	    long res = 1;
	    factorial();
	    for (int i = 0; i < mapIdx; i++)
            if (ds.upper[i] < 0) {
                int numPoints = ds.pointsNum[i], lines = -ds.upper[i];
                long ways = 0;
                for (int j = 0; j <= Math.min(numPoints, lines); j++) {
                    ways += ncr(lines, j);
                    if (ways >= MODULO) ways %= MODULO;
                }
                res *= ways;
                res %= MODULO;
            }
	    out.println(res);
	}

	// O(1) nCr
    static int MAX = 5 * 100000 + 1;
    static int fact[] = new int[MAX];

    static int ncr(int n, int r) {
        return (int) ((long) fact[n] * ((inv(fact[r], MODULO) * inv(fact[n - r], MODULO)) % MODULO) % MODULO) % MODULO;
    }

    static long inv(long x, long mod) {
        long r, y;
        for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
            if ((y & 1) == 1)
                r = r * x % mod;
        return r;
    }

    static void factorial() {
        fact[0] = fact[1] = 1;
        for (int i = 2; i < MAX; i++)
            fact[i] = (int) ((long) i * fact[i - 1] % MODULO);
    }

    public static long powMod(long a, long n) {
    	long res = 1;
    	long t = a;
    	for(int i = 0;i < 33; ++i) {
    		if((n & (1L << i)) != 0)
    			res = (res + t) % MODULO;
    		t = t * t % MODULO;
    	}
        return res;
    }

	public class DJSet {
	    public int[] upper;
	    public int[] pointsNum;
	    public int count;
	    public DJSet(int n) {
	        upper = new int[n];
	        count = n;
	        pointsNum = new int[n];
	        Arrays.fill(upper, -1);
	    }

	    public int root(int x) {
	        return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
	    }

	    public boolean equiv(int x, int y) {
	        return root(x) == root(y);
	    }

	    public boolean union(int x, int y) {
	        x = root(x);
	        y = root(y);
	        if (x != y) {
	            if (upper[y] < upper[x]) {
	                int d = x;
	                x = y;
	                y = d;
	            }
	            upper[x] += upper[y];
	            upper[y] = x;
	            pointsNum[x] += 1 + pointsNum[y];
	            --count;
	            return true;
	        } else {
	        	++pointsNum[x];
	        }
	        return false;
	    }

	    public int getCount() {
	        return count;
	    }

	    public long size(int u) {
	        return -upper[root(u)];
	    }

	    public void clear() {
	        Arrays.fill(upper, -1);
	    }
	}

	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	public void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in),32768);
			st = null;
			out = new PrintWriter(System.out);
			if(TC == 1) {
				for(int T = ni();T > 0; --T) {
					solve();
				}
			} else {
				solve();
			}
			br.close();
			out.close();
		} catch(IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	public char[] nsc( ) throws IOException {
		return ns().toCharArray();
	}
	public char[][] nm(int n, int m) throws IOException {
		char[][] map = new char[n][];
		for(int i = 0;i < n; ++i) {
			map[i] = nsc();
		}
		return map;
	}
	public String ns() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}
	public String nextLine() throws IOException {
		return br.readLine();
	}
	public int ni() throws IOException {
		return Integer.parseInt(ns());
	}

	public int[] na(int n) throws IOException {
		int[] a = new int[n];
		for(int i = 0;i < n; ++i) a[i] = ni();
		return a;
	}

	public long nl() throws IOException {
		return Long.parseLong(ns());
	}

	public long[] nal(int n) throws IOException {
		long[] a = new long[n];
		for(int i = 0;i < n; ++i) a[i] = nl();
		return a;
	}

	public double nd() throws IOException {
		return Double.parseDouble(ns());
	}
	private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private static void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}


import java.util.*;
import java.io.*;
import java.math.*;
import java.lang.*;
import java.awt.*;
import java.awt.geom.*;
import java.util.stream.*;

/**
 * @author Pradyumn
 */

public class Main implements Runnable{
	public int TC = 0;
	public static void main(String[] args) {
		new Thread(null, new Main(), ":)", 1L << 26).start();
	}

	static final int MODULO = (int)(1e9 + 7);

	@SuppressWarnings("Unchecked")
	public void solve() throws IOException {
	    int n = ni();
	    HashSet<Integer> x = new HashSet<>();
	    HashSet<Integer> y = new HashSet<>();
	    HashMap<Integer, Integer> mapX = new HashMap<>();
	    HashMap<Integer, Integer> mapY = new HashMap<>();
	    int[][] pp = new int[2][n];

	    for (int i = 0; i < n;  ++i) {
	    	for(int j = 0;j < 2; ++j) {
	    		pp[j][i] = ni();
	    		if(j == 0) x.add(pp[j][i]);
	    		else y.add(pp[j][i]);
	    	}
	    }

	    int mapIdx = 0;
	    for(int xx : x)
	    	if(!mapX.containsKey(xx))
	    		mapX.put(xx, mapIdx++);

	    for(int yy : y)
	    	if(!mapY.containsKey(yy))
	    		mapY.put(yy, mapIdx++);

	    DJSet ds = new DJSet(mapIdx);
	    for(int i = 0;i < n; ++i) {
	    	ds.union(mapX.get(pp[0][i]), mapY.get(pp[1][i]));
	    }

	    long res = 1;
	    factorial();
	    for (int i = 0; i < mapIdx; i++)
            if (ds.upper[i] < 0) {
                int numPoints = ds.pointsNum[i], lines = -ds.upper[i];
                long ways = 0;
                for (int j = 0; j <= Math.min(numPoints, lines); j++) {
                    ways += ncr(lines, j);
                    if (ways >= MODULO) ways %= MODULO;
                }
                res *= ways;
                res %= MODULO;
            }
	    out.println(res);
	}

	// O(1) nCr
    static int MAX = 5 * 100000 + 1;
    static int fact[] = new int[MAX];

    static int ncr(int n, int r) {
        return (int) ((long) fact[n] * ((inv(fact[r], MODULO) * inv(fact[n - r], MODULO)) % MODULO) % MODULO) % MODULO;
    }

    static long inv(long x, long mod) {
        long r, y;
        for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
            if ((y & 1) == 1)
                r = r * x % mod;
        return r;
    }

    static void factorial() {
        fact[0] = fact[1] = 1;
        for (int i = 2; i < MAX; i++)
            fact[i] = (int) ((long) i * fact[i - 1] % MODULO);
    }

    public static long powMod(long a, long n) {
    	long res = 1;
    	long t = a;
    	for(int i = 0;i < 63; ++i) {
    		if((n & (1L << i)) != 0)
    			res = (res + t) % MODULO;
    		t = t * t % MODULO;
    	}
        return res;
    }

	public class DJSet {
	    public int[] upper;
	    public int[] pointsNum;
	    public int count;
	    public DJSet(int n) {
	        upper = new int[n];
	        count = n;
	        pointsNum = new int[n];
	        Arrays.fill(upper, -1);
	    }

	    public int root(int x) {
	        return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
	    }

	    public boolean equiv(int x, int y) {
	        return root(x) == root(y);
	    }

	    public boolean union(int x, int y) {
	        x = root(x);
	        y = root(y);
	        if (x != y) {
	            if (upper[y] < upper[x]) {
	                int d = x;
	                x = y;
	                y = d;
	            }
	            upper[x] += upper[y];
	            upper[y] = x;
	            pointsNum[x] += 1 + pointsNum[y];
	            --count;
	            return true;
	        } else {
	        	++pointsNum[x];
	        }
	        return false;
	    }

	    public int getCount() {
	        return count;
	    }

	    public long size(int u) {
	        return -upper[root(u)];
	    }

	    public void clear() {
	        Arrays.fill(upper, -1);
	    }
	}

	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	public void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in),32768);
			st = null;
			out = new PrintWriter(System.out);
			if(TC == 1) {
				for(int T = ni();T > 0; --T) {
					solve();
				}
			} else {
				solve();
			}
			br.close();
			out.close();
		} catch(IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	public char[] nsc( ) throws IOException {
		return ns().toCharArray();
	}
	public char[][] nm(int n, int m) throws IOException {
		char[][] map = new char[n][];
		for(int i = 0;i < n; ++i) {
			map[i] = nsc();
		}
		return map;
	}
	public String ns() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}
	public String nextLine() throws IOException {
		return br.readLine();
	}
	public int ni() throws IOException {
		return Integer.parseInt(ns());
	}

	public int[] na(int n) throws IOException {
		int[] a = new int[n];
		for(int i = 0;i < n; ++i) a[i] = ni();
		return a;
	}

	public long nl() throws IOException {
		return Long.parseLong(ns());
	}

	public long[] nal(int n) throws IOException {
		long[] a = new long[n];
		for(int i = 0;i < n; ++i) a[i] = nl();
		return a;
	}

	public double nd() throws IOException {
		return Double.parseDouble(ns());
	}
	private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private static void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}


import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.ByteArrayOutputStream;
import java.util.HashMap;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.io.File;
import java.util.List;
import java.util.TreeMap;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    E solver = new E();
    solver.solve(1, in, out);
    out.close();
  }

  static class E extends SimpleSavingChelperSolution {
    private int[] x;
    private int[] y;
    private int n;
    private Map<Integer, Integer> xMap;
    private Map<Integer, Integer> yMap;
    private List<Set<Integer>> edges;
    private boolean[] visited;
    private long MOD;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      wrapSolve(testNumber, in, out);
    }

    public void solve(int testNumber) {
      n = in.nextInt();

      x = new int[n];
      y = new int[n];

      xMap = new TreeMap<>();
      yMap = new TreeMap<>();

      edges = new ArrayList<>();

      for (int i = 0; i < n; i++) {
        edges.add(new HashSet<>());
      }

      Map<Integer, Integer> prevX = new HashMap<>();
      Map<Integer, Integer> prevY = new HashMap<>();

      for (int i = 0; i < n; i++) {
        x[i] = in.nextInt();
        y[i] = in.nextInt();

        xMap.put(x[i], xMap.getOrDefault(x[i], 0) + 1);
        yMap.put(y[i], yMap.getOrDefault(y[i], 0) + 1);

        Integer pX = prevX.get(x[i]);
        Integer pY = prevY.get(y[i]);

        if (pX != null) {
          edges.get(pX).add(i);
          edges.get(i).add(pX);
        }
        if (pY != null) {
          edges.get(pY).add(i);
          edges.get(i).add(pY);
        }

        prevX.put(x[i], i);
        prevY.put(y[i], i);
      }

      visited = new boolean[n];

      long ans = 1;

      MOD = 1000000007;

      for (int i = 0; i < n; i++) {
        if (visited[i]) {
          continue;
        }

        List<Integer> res = new ArrayList<>();
        dfs(i, res);

        Set<Integer> usedX = new HashSet<>();
        Set<Integer> usedY = new HashSet<>();

        for (Integer j : res) {
          usedX.add(x[j]);
          usedY.add(y[j]);
        }

        int K = usedX.size() + usedY.size();
        if (res.size() >= K) {
          ans = ans * twopow(K) % MOD;
        } else {
          ans = ans * ((twopow(K) - 1 + MOD) % MOD) % MOD;
        }
      }

      out.println(ans);
    }

    long twopow(int n) {
      if (n == 0) {
        return 1;
      }
      if (n % 2 == 0) {
        long t = twopow(n / 2);
        return t * t % MOD;
      }
      return twopow(n - 1) * 2 % MOD;
    }

    void dfs(int v, List<Integer> res) {
      if (visited[v]) {
        return;
      }
      visited[v] = true;
      res.add(v);

      for (int j : edges.get(v)) {
        dfs(j, res);
      }
    }

  }

  static class InputReader {
    private BufferedReader br;
    private StringTokenizer in;

    public InputReader(String fileName) {
      try {
        br = new BufferedReader(new FileReader(fileName));
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
    }

    public InputReader(InputStream inputStream) {
      br = new BufferedReader(new InputStreamReader(inputStream));
    }

    private boolean hasMoreTokens() {
      while (in == null || !in.hasMoreTokens()) {
        String s = nextLine();
        if (s == null) {
          return false;
        }
        in = new StringTokenizer(s);
      }
      return true;
    }

    public String nextString() {
      return hasMoreTokens() ? in.nextToken() : null;
    }

    public String nextLine() {
      try {
        in = null;
        return br.readLine();
      } catch (Exception e) {
        e.printStackTrace();
        return null;
      }
    }

    public int nextInt() {
      return Integer.parseInt(nextString());
    }

  }

  static class OutputWriter extends PrintWriter {

    public void close() {
      super.close();
    }

    public OutputWriter(String fileName) throws FileNotFoundException {
      super(fileName);
    }

    public OutputWriter(OutputStream outputStream) {
      super(outputStream);
    }

    public OutputWriter(Writer writer) {
      super(writer);
    }

  }

  static abstract class SimpleSavingChelperSolution extends SavingChelperSolution {

    public String processOutputPreCheck(int testNumber, String output) {
      return output;
    }

    public String processOutputPostCheck(int testNumber, String output) {
      return output;
    }

  }

  static abstract class SavingChelperSolution {
    protected int testNumber;
    public InputReader in;
    public OutputWriter out;
    private OutputWriter toFile;
    private boolean local = new File("chelper.properties").exists();
    public OutputWriter debug;

    {
      if (local) {
        debug = new OutputWriter(System.out);
      } else {
        debug = new OutputWriter(new OutputStream() {

          public void write(int b) {
          }
        });
      }
    }

    public SavingChelperSolution() {
      try {
        toFile = new OutputWriter("last_test_output.txt");
      } catch (FileNotFoundException e) {
        throw new RuntimeException(e);
      }
    }

    public abstract void solve(int testNumber);

    public abstract String processOutputPreCheck(int testNumber, String output);

    public abstract String processOutputPostCheck(int testNumber, String output);

    public void wrapSolve(int testNumber, InputReader in, OutputWriter out) {
      this.testNumber = testNumber;

      ByteArrayOutputStream substituteOutContents = new ByteArrayOutputStream();
      OutputWriter substituteOut = new OutputWriter(substituteOutContents);

      this.in = in;
      this.out = substituteOut;

      solve(testNumber);
      substituteOut.flush();

      String result = substituteOutContents.toString();

      result = processOutputPreCheck(testNumber, result);
      out.print(result);
      out.flush();

      if (local) {
        debug.flush();

        result = processOutputPostCheck(testNumber, result);
        toFile.print(result);
        toFile.flush();
      }
    }

  }
}


import java.io.*;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws IOException {

        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        HashSet<Integer> x = new HashSet<>(), y = new HashSet<>();
        HashMap<Integer, Integer> mapX = new HashMap<>(), mapY = new HashMap<>();
        int[][] arr = new int[2][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 2; j++) {
                arr[j][i] = sc.nextInt();
                if (j == 0) x.add(arr[j][i]);
                else y.add(arr[j][i]);
            }
        }

        int mapIdxX = 0;
        for (int xx : x) if (!mapX.containsKey(xx)) mapX.put(xx, mapIdxX++);
        for (int yy : y) if (!mapY.containsKey(yy)) mapY.put(yy, mapIdxX++);

        UnionFind uf = new UnionFind(mapIdxX);
        for (int i = 0; i < n; i++)
            uf.unionSet(mapX.get(arr[0][i]), mapY.get(arr[1][i]));

        uf.close();
        long res = 1;
        int mod = (int) 1e9 + 7;
        factorial();
        for (int i = 0; i < mapIdxX; i++)
            if (uf.p[i] == i) {
                int numPoints = uf.numPoints[i], lines = uf.sizeOfSet(i);
                long ways = 0;
                for (int j = 0; j <= Math.min(numPoints, lines); j++) {
                    ways += ncr(lines, j);
                    if (ways >= mod) ways -= mod;
                }
                res *= ways;
                res %= mod;

            }

        out.println(res);
        out.close();
    }

    // O(1) nCr
    static int MAX = 5 * 100000 + 1;
    static int fact[] = new int[MAX];
    static int MOD = (int) 1e9 + 7;

    static int ncr(int n, int r) {
        return (int) ((long) fact[n] * ((inv(fact[r], MOD) * inv(fact[n - r], MOD)) % MOD) % MOD) % MOD;
    }

    static long inv(long x, long mod) {
        long r, y;
        for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
            if ((y & 1) == 1)
                r = r * x % mod;
        return r;
    }

    static void factorial() {
        fact[0] = fact[1] = 1;
        for (int i = 2; i < MAX; i++)
            fact[i] = (int) ((long) i * fact[i - 1] % MOD);
    }

    public static long modular_exponentiation(long a, long b, long c) // returns ( a ^ b ) % c
    {
        long ans = 1L;
        while (b != 0) {
            if ((b & (1)) == 1)
                ans = (ans * a) % c;

            a = (a * a) % c;
            b >>= 1L;
        }

        return ans;
    }

    static class UnionFind {
        private int[] p, rank, setSize, numPoints;
        private int numSets;

        public UnionFind(int size) {
            p = new int[size];
            rank = new int[size];
            setSize = new int[size];
            numPoints = new int[size];
            numSets = size;
            for (int i = 0; i < size; ++i) {
                p[i] = i;
                numPoints[i] = 0;
                setSize[i] = 1;
            }
        }

        int findSet(int i) {
            return (p[i] == i) ? i : (p[i] = findSet(p[i]));
        }

        boolean isSameSet(int i, int j) {
            return findSet(i) == findSet(j);
        }

        void unionSet(int i, int j) {
            if (!isSameSet(i, j)) {
                --numSets;
                int x = findSet(i), y = findSet(j);
                if (rank[x] > rank[y]) {
                    p[y] = x;
                    setSize[x] = setSize[x] + setSize[y];
                    numPoints[x] = 1 + numPoints[x] + numPoints[y];
                } else {
                    p[x] = y;
                    setSize[y] = setSize[y] + setSize[x];
                    numPoints[y] = numPoints[y] + numPoints[x] + 1;
                    if (rank[x] == rank[y]) ++rank[y];
                }
            } else {
                numPoints[findSet(i)]++;
            }
        }

        int numDisjointSets() {
            return numSets;
        }

        void close() {
            for (int i = 0; i < p.length; i++)
                findSet(i);
        }

        int sizeOfSet(int i) {
            return setSize[findSet(i)];
        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}


import java.io.* ;
import java.util.* ;
import java.util.stream.* ;
import java.text.* ;
import java.math.* ;
public class Codeshefcode{
	public static void main(String[] args) throws IOException{
		Solver Machine = new Solver() ;
		Machine.Solve() ;
		Machine.Finish();
	}
}
class Mod{
	static long mod=1000000007 ;
	static long d(long a,long b){ return (a*MI(b))%mod ; }
	static long m(long a , long b){ return (a*b)%mod ; }
	static private long MI(long a ){ return pow(a,mod-2) ; }
	static long pow(long a,long b){
		if(b<0) return pow(MI(a),-b) ;
		long val=a ; long ans=1 ;
		while(b!=0){
			if((b&1)==1) ans = (ans*val)%mod ;
			val = (val*val)%mod ;
			b>>=1 ;
		}
		return ans ;
	}
}
class pair implements Comparable<pair>{
	long x ; int y ;
	pair(long x,int y){ this.x=x ; this.y=y ;}
	public int compareTo(pair p){
		return (this.x<p.x ? -1 : (this.x>p.x ? 1 : (this.y<p.y ? -1 : (this.y>p.y ? 1 : 0)))) ;
	}
}
class Solver{
	FasterScanner ip = new FasterScanner(System.in) ;
	PrintWriter op = new PrintWriter(System.out) ;
	long offset = 2000000001l ;
	void Solve() throws IOException{
		int m = ip.i() ;
		long edges[][] = new long[m][] ;
		for(int i=0 ; i<m ; i++){
			long tmp[] = {ip.l(),ip.l()+offset} ;
			edges[i] = tmp ;
		}
		myset set = new myset() ;
		for(int i=0 ; i<m ; i++){
			set.add(edges[i][0]) ;
			set.add(edges[i][1]) ;
		}
		mymap map = new mymap() ;
		int n=0 ;
		for(long elem : set) map.put(elem,n++) ;
		for(int i=0 ; i<m ; i++){
			long tmp[] = {map.get(edges[i][0]),map.get(edges[i][1])} ;
			edges[i] = tmp ;
		}
		mylist adj[] = new mylist[n] ;
		for(int i=0 ; i<n ; i++) adj[i] = new mylist() ;
		for(int i=0 ; i<m ; i++){
			int x = (int) edges[i][0] ;
			int y = (int) edges[i][1] ;
			adj[x].add(y) ; adj[y].add(x) ;
		}
		int comp[] = new int[n] ;
		Arrays.fill(comp,-1) ;
		int clr=0 ;
		for(int i=0 ; i<n ; i++){
			if(comp[i]==-1){
				mystack S = new mystack() ;
				S.add(i) ;
				comp[i]=clr ;
				while(!S.isEmpty()){
					int nd = S.pop() ;
					for(int nnd : adj[nd])
						if(comp[nnd]==-1){
							S.push(nnd) ;
							comp[nnd]=clr ;
						}
				}
				clr++ ;
			}
		}
		int cntn[] = new int[clr] ;
		int cntm[] = new int[clr] ;
		for(int i=0 ; i<n ; i++) cntn[comp[i]]++ ;
		for(int i=0 ; i<m ; i++) cntm[comp[(int) edges[i][0]]]++ ;
		long res=1 ;
		for(int i=0 ; i<clr ; i++){
			if(cntm[i]>=cntn[i])
				res = Mod.m(res,Mod.pow(2,cntn[i])) ;
			else
				res = Mod.m(res,Mod.pow(2,cntn[i])+(Mod.mod-1)) ;
		}
		pln(res) ;
	}
	void p(Object o){
		op.print(o) ;
	}
	void pln(Object o){
		op.println(o) ;
	}
	void pArr(String name,Object arr,char type){
		p(name+": [") ;
		if(type=='i'){
			int arr1[] = (int[]) arr ;
			for(int i=0 ; i<arr1.length ; i++) p(arr1[i]+(i+1==arr1.length ? "" : ",")) ;
		}else if(type=='l'){
			long arr1[] = (long[]) arr ;
			for(int i=0 ; i<arr1.length ; i++) p(arr1[i]+(i+1==arr1.length ? "" : ",")) ;
		}else if(type=='b'){
			boolean arr1[] = (boolean[]) arr ;
			for(int i=0 ; i<arr1.length ; i++) p((arr1[i] ? 1 : 0)+(i+1==arr1.length ? "" : ",")) ;
		}
		pln("]") ;
	}
	void Finish(){
		op.flush();
		op.close();
	}
}
@SuppressWarnings("serial")
class mylist extends ArrayList<Integer>{
}
@SuppressWarnings("serial")
class myset extends TreeSet<Long>{

}
@SuppressWarnings("serial")
class mystack extends Stack<Integer>{
}
@SuppressWarnings("serial")
class mymap extends TreeMap<Long,Integer>{
}
class FasterScanner {
	private InputStream mIs;
	private byte[] buf = new byte[1024];
	private int curChar,numChars;
	public FasterScanner() { this(System.in); }
	public FasterScanner(InputStream is) { mIs = is;}
	public int read() {
		if (numChars == -1) throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}
			if (numChars <= 0) return -1;
		}
		return buf[curChar++];
	}
	public String nextLine(){
		int c = read();
		while (isSpaceChar(c)) c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
	public String S(){
		int c = read();
		while (isSpaceChar(c)) c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		}while (!isSpaceChar(c));
		return res.toString();
	}
	public long l(){
		int c = read();
		while (isSpaceChar(c)) c = read();
		int sgn = 1;
		if (c == '-') { sgn = -1 ; c = read() ; }
		long res = 0;
		do{
			if (c < '0' || c > '9') throw new InputMismatchException();
			res *= 10 ; res += c - '0' ; c = read();
		}while(!isSpaceChar(c));
		return res * sgn;
	}
	public int i(){
		int c = read() ;
		while (isSpaceChar(c)) c = read();
		int sgn = 1;
		if (c == '-') { sgn = -1 ; c = read() ; }
		int res = 0;
		do{
			if (c < '0' || c > '9') throw new InputMismatchException();
		res *= 10 ; res += c - '0' ; c = read() ;
		}while(!isSpaceChar(c));
		return res * sgn;
	}
	public int[] ia(int n){
		int a[] = new int[n] ;
		for(int i=0 ; i<n ; i++) a[i] = i() ;
		return a ;
	}
	public long[] la(int n){
		long a[] = new long[n] ;
		for(int i=0 ; i<n ; i++) a[i] = l() ;
		return a ;
	}
	public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
	public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
}