using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;

namespace YukiCoder
{
	class Program
	{
		[MethodImpl(MethodImplOptions.AggressiveOptimization)]
		static void Main()
		{
			using var cin = new Scanner();
			int n = cin.Int();
			var xy = new (long x, long y)[n];
			for (int i = 0; i < n; i++) {
				xy[i] = cin.Long2();
			}

			long Area(long x1, long y1, long x2, long y2)
			{
				return Math.Abs(x1 * y2 - x2 * y1);
			}

			if (n == 2) {
				long tans = Area(xy[0].x, xy[0].y, xy[1].x, xy[1].y);
				Console.WriteLine(tans);
				return;
			}

			var ch = new ConvexHull();
			for (int i = 0; i < n; i++) {
				ch.Add(new Ipt(xy[i].x, xy[i].y));
			}

			var points = ch.Build();
			int m = points.Length;
			var slopes = new (Rational s, int i)[m];
			for (int i = 0; i < m; i++) {
				var p1 = points[i];
				var p2 = points[(i + 1) % m];
				if (p1.X - p2.X == 0) {
					var ss = new Rational(1000000000, 1);
					slopes[i] = (ss, i);
				} else {
					var ss = new Rational(p1.Y - p2.Y, p1.X - p2.X);
					slopes[i] = (ss, i);
				}
			}

			Array.Sort(slopes);

			var xy2 = xy.ToArray();
			Array.Sort(xy2, (x, y) => x.x.CompareTo(y.x));

			long ans = 0;
			for (int i = 0; i < n; i++) {
				var (x, y) = xy[i];
				if (x == 0) {
					var p1 = xy2[0];
					var p2 = xy2[n - 1];
					ans.UpdateMax(Area(p1.x, p1.y, x, y));
					ans.UpdateMax(Area(p2.x, p2.y, x, y));
				} else {
					var ss = new Rational(y, x);
					int ng = 0;
					int ok = m;
					while (ok - ng > 1) {
						int mid = (ok + ng) / 2;
						if (slopes[mid].s > ss) {
							ok = mid;
						} else {
							ng = mid;
						}
					}

					if (ok == m) {
						ok = 0;
					}

					var p1 = points[slopes[ok].i];
					ans.UpdateMax(Area(p1.X, p1.Y, x, y));
					var p2 = points[(slopes[ok].i - 1 + m) % m];
					ans.UpdateMax(Area(p2.X, p2.Y, x, y));
					var p3 = points[(slopes[ok].i + 1) % m];
					ans.UpdateMax(Area(p3.X, p3.Y, x, y));
				}
			}

			Console.WriteLine(ans);
		}
	}

	public struct Rational : IEquatable<Rational>, IComparable<Rational>
	{
		private readonly int sign_;
		private long n_;
		private long d_;

		public long Numerator => n_;
		public long Denominator => d_;
		public double ToDouble() => Sign * (double)n_ / d_;
		public bool IsZero => n_ == 0;

		public int Sign => sign_;

		public Rational(long numerator, long denominator = 1)
		{
			System.Diagnostics.Debug.Assert(denominator != 0);
			if (numerator == 0) {
				sign_ = 1;
				n_ = 0;
				d_ = 1;
			} else {
				sign_ = (numerator ^ denominator) >= 0 ? 1 : -1;
				n_ = Math.Abs(numerator);
				d_ = Math.Abs(denominator);
				Reduce();
			}
		}

		public static Rational operator -(Rational x) => new Rational(-x.n_, x.d_);
		public static Rational operator +(Rational lhs, Rational rhs)
		{
			var lcm = Lcm(lhs.d_, rhs.d_);
			var l = lhs.n_ * (lcm / lhs.d_) * lhs.sign_;
			var r = rhs.n_ * (lcm / rhs.d_) * rhs.sign_;
			return new Rational(l + r, lcm);
		}
		public static Rational operator -(Rational lhs, Rational rhs)
		{
			var c = Lcm(lhs.d_, rhs.d_);
			var x1a = lhs.n_ * (c / lhs.d_) * lhs.sign_;
			var x2a = rhs.n_ * (c / rhs.d_) * rhs.sign_;
			return new Rational(x1a - x2a, c);
		}
		public static Rational operator *(Rational lhs, Rational rhs)
			=> new Rational(lhs.n_ * lhs.sign_ * rhs.n_ * rhs.sign_, lhs.d_ * rhs.d_);
		public static Rational operator /(Rational x1, Rational x2)
			=> new Rational(x1.n_ * x1.sign_ * x2.d_, x2.n_ * x2.sign_ * x1.d_);
		public static bool operator ==(Rational x1, Rational x2) => x1.Equals(x2);
		public static bool operator !=(Rational x1, Rational x2) => !x1.Equals(x2);
		public static bool operator >(Rational x1, Rational x2) => x1.CompareTo(x2) > 0;
		public static bool operator <(Rational x1, Rational x2) => x1.CompareTo(x2) < 0;
		public static bool operator >=(Rational x1, Rational x2) => x1.CompareTo(x2) >= 0;
		public static bool operator <=(Rational x1, Rational x2) => x1.CompareTo(x2) <= 0;

		public static implicit operator Rational(long n) => new Rational(n, 1);

		public Rational Inverse() => new Rational(d_ * sign_, n_);

		public bool Equals(Rational other)
			=> sign_ == other.sign_ && n_ == other.n_ && d_ == other.d_;
		public override bool Equals(object obj) => obj is Rational x && Equals(x);
		public int CompareTo(Rational other)
			=> (sign_ * n_ * other.d_).CompareTo(other.sign_ * other.n_ * d_);

		public override int GetHashCode() => HashCode.Combine(sign_, n_, d_);
		public override string ToString() => n_ == 0
			? "0"
			: $"{(sign_ >= 0 ? "" : "-")}{n_}/{d_}";

		private void Reduce()
		{
			var c = Gcd(n_, d_);
			n_ /= c;
			d_ /= c;
		}

		private static long Gcd(long m, long n)
		{
			var x1 = Math.Max(m, n);
			var x2 = Math.Min(m, n);
			while (true) {
				var mod = x1 % x2;
				if (mod == 0) {
					return x2;
				}

				x1 = x2;
				x2 = mod;
			}
		}

		private static long Lcm(long m, long n)
		{
			var gcd = Gcd(m, n);
			return m / gcd * n;
		}
	}

	public class ConvexHull
	{
		private List<Ipt> _tempPoints = new List<Ipt>();
		private Ipt[] _points;

		public void Add(Ipt point)
		{
			_tempPoints.Add(point);
		}

		public ReadOnlySpan<Ipt> Build()
		{
			var points = _tempPoints.ToArray();
			Array.Sort(points, (x, y) => {
				if (x.X == y.X) {
					return x.Y.CompareTo(y.Y);
				} else {
					return x.X.CompareTo(y.X);
				}
			});

			int n = points.Length;
			int k = 0;
			var ret = new Ipt[n * 2];
			for (int i = 0; i < n; ++i) {
				while (k > 1 && (ret[k - 1] - ret[k - 2]).Det(points[i] - ret[k - 1]) <= 0) {
					--k;
				}

				ret[k] = points[i];
				++k;
			}

			for (int i = n - 2, t = k; i >= 0; --i) {
				while (k > t && (ret[k - 1] - ret[k - 2]).Det(points[i] - ret[k - 1]) <= 0) {
					--k;
				}

				ret[k] = points[i];
				++k;
			}

			_points = ret.AsSpan().Slice(0, k - 1).ToArray();
			return _points;
		}

		public long AreaX2()
		{
			int n = _points.Length;
			long area = 0;
			for (int i = 0; i < n - 1; i++) {
				area += (_points[i].X - _points[i + 1].X) * (_points[i].Y + _points[i + 1].Y);
			}

			area += (_points[n - 1].X - _points[0].X) * (_points[n - 1].Y + _points[0].Y);
			area = Math.Abs(area);
			return area;
		}

		public long GridPointCount()
		{
			long on = GridPointCountOnEdge();
			long within = AreaX2() - GridPointCountOnEdge() + 2;
			within >>= 1;
			return on + within;
		}

		public long GridPointCountOnEdge()
		{
			static long Gcd(long a, long b)
			{
				if (b == 0) {
					return a;
				}

				return Gcd(b, a % b);
			}

			int n = _points.Length;
			long count = 0;
			for (int i = 0; i < n - 1; i++) {
				count += Gcd(
					Math.Abs(_points[i].X - _points[i + 1].X),
					Math.Abs(_points[i].Y - _points[i + 1].Y));
			}

			count += Gcd(
					Math.Abs(_points[n - 1].X - _points[0].X),
					Math.Abs(_points[n - 1].Y - _points[0].Y));

			return count;
		}

		public long GridPointCountWithinEdges()
		{
			long count = AreaX2() - GridPointCountOnEdge() + 2;
			count >>= 1;
			return count;
		}
	}

	public struct Ipt
	{
		public long X { get; set; }
		public long Y { get; set; }

		public Ipt(long x, long y)
		{
			X = x;
			Y = y;
		}

		public static long Length2(Ipt p, Ipt q)
		{
			long x = p.X - q.X;
			long y = p.Y - q.Y;
			return x * x + y * y;
		}

		public static (long numerator, long denominator, bool squared)
			DistanceOfPointAndLine(Ipt p1, Ipt p2, Ipt q)
		{
			if ((p2 - p1).Dot(q - p1) < 0
				|| (p1 - p2).Dot(q - p2) < 0) {
				long distance2 = Math.Min(
					Ipt.Length2(p1, q),
					Ipt.Length2(p2, q));
				return (distance2, 1, true);
			} else {
				long numerator = (q - p1).Det(p2 - p1);
				long denominator2 = Ipt.Length2(p1, p2);
				return (numerator, denominator2, false);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static bool IsOnSegment(Ipt p1, Ipt p2, Ipt q)
			=> (p1 - q).Det(p2 - q) == 0 && (p1 - q).Dot(p2 - q) <= 0;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static bool IsOnLine(Ipt a, Ipt b, Ipt c)
			=> a.Y * (b.X - c.X) + b.Y * (c.X - a.X) + c.Y * (a.X - b.X) == 0;

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static bool IsCross(Ipt p1, Ipt p2, Ipt q1, Ipt q2)
		{
			var pp = p2 - p1;
			if (pp.Det(q1 - p1) * pp.Det(q2 - p1) > 0) {
				return false;
			}

			var qq = q2 - q1;
			if (qq.Det(p1 - q1) * qq.Det(p2 - q1) > 0) {
				return false;
			}

			return true;
		}

		public static Ipt operator +(Ipt lhs, Ipt rhs)
			=> new Ipt(lhs.X + rhs.X, lhs.Y + rhs.Y);
		public static Ipt operator -(Ipt lhs, Ipt rhs)
			=> new Ipt(lhs.X - rhs.X, lhs.Y - rhs.Y);
		public static Ipt operator *(Ipt src, long value)
			=> new Ipt(src.X * value, src.Y * value);
		public static Ipt operator *(long value, Ipt src)
			=> new Ipt(src.X * value, src.Y * value);

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Dot(Ipt target) => X * target.X + Y * target.Y;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Det(Ipt target) => X * target.Y - Y * target.X;

		public override int GetHashCode() => HashCode.Combine(X, Y);
	}

	public struct BitFlag
	{
		public static BitFlag Begin() => 0;
		public static BitFlag End(int bitCount) => 1 << bitCount;
		public static BitFlag FromBit(int bitNumber) => 1 << bitNumber;
		public static BitFlag Fill(int count) => (1 << count) - 1;

		public static IEnumerable<BitFlag> All(int n)
		{
			for (var f = Begin(); f < End(n); ++f) {
				yield return f;
			}
		}

		private readonly int flags_;
		public int Flag => flags_;
		public bool this[int bitNumber] => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag(int flags) { flags_ = flags; }

		public bool Has(BitFlag target) => (flags_ & target.flags_) == target.flags_;
		public bool Has(int target) => (flags_ & target) == target;
		public bool HasBit(int bitNumber) => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag OrBit(int bitNumber) => flags_ | (1 << bitNumber);
		public BitFlag AndBit(int bitNumber) => flags_ & (1 << bitNumber);
		public BitFlag XorBit(int bitNumber) => flags_ ^ (1 << bitNumber);
		public BitFlag ComplementOf(BitFlag sub) => flags_ ^ sub.flags_;
		public int PopCount() => BitOperations.PopCount((uint)flags_);

		public static BitFlag operator ++(BitFlag src) => new BitFlag(src.flags_ + 1);
		public static BitFlag operator --(BitFlag src) => new BitFlag(src.flags_ - 1);
		public static BitFlag operator |(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ | rhs.flags_);
		public static BitFlag operator |(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ | rhs);
		public static BitFlag operator |(int lhs, BitFlag rhs)
			=> new BitFlag(lhs | rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ & rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ & rhs);
		public static BitFlag operator &(int lhs, BitFlag rhs)
			=> new BitFlag(lhs & rhs.flags_);
		public static BitFlag operator ^(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ ^ rhs.flags_);
		public static BitFlag operator ^(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ ^ rhs);
		public static BitFlag operator ^(int lhs, BitFlag rhs)
			=> new BitFlag(lhs ^ rhs.flags_);
		public static BitFlag operator <<(BitFlag bit, int shift) => bit.flags_ << shift;
		public static BitFlag operator >>(BitFlag bit, int shift) => bit.flags_ >> shift;

		public static bool operator <(BitFlag lhs, BitFlag rhs) => lhs.flags_ < rhs.flags_;
		public static bool operator <(BitFlag lhs, int rhs) => lhs.flags_ < rhs;
		public static bool operator <(int lhs, BitFlag rhs) => lhs < rhs.flags_;
		public static bool operator >(BitFlag lhs, BitFlag rhs) => lhs.flags_ > rhs.flags_;
		public static bool operator >(BitFlag lhs, int rhs) => lhs.flags_ > rhs;
		public static bool operator >(int lhs, BitFlag rhs) => lhs > rhs.flags_;
		public static bool operator <=(BitFlag lhs, BitFlag rhs) => lhs.flags_ <= rhs.flags_;
		public static bool operator <=(BitFlag lhs, int rhs) => lhs.flags_ <= rhs;
		public static bool operator <=(int lhs, BitFlag rhs) => lhs <= rhs.flags_;
		public static bool operator >=(BitFlag lhs, BitFlag rhs) => lhs.flags_ >= rhs.flags_;
		public static bool operator >=(BitFlag lhs, int rhs) => lhs.flags_ >= rhs;
		public static bool operator >=(int lhs, BitFlag rhs) => lhs >= rhs.flags_;

		public static implicit operator BitFlag(int t) => new BitFlag(t);
		public static implicit operator int(BitFlag t) => t.flags_;

		public override string ToString() => $"{Convert.ToString(flags_, 2).PadLeft(32, '0')} ({flags_})";

		public SubBitsEnumerator SubBits => new SubBitsEnumerator(flags_);
		public struct SubBitsEnumerator : IEnumerable<BitFlag>
		{
			private readonly int flags_;
			public SubBitsEnumerator(int flags)
			{
				flags_ = flags;
			}

			IEnumerator<BitFlag> IEnumerable<BitFlag>.GetEnumerator() => new Enumerator(flags_);
			IEnumerator IEnumerable.GetEnumerator() => new Enumerator(flags_);
			public Enumerator GetEnumerator() => new Enumerator(flags_);
			public struct Enumerator : IEnumerator<BitFlag>
			{
				private readonly int src_;
				public BitFlag Current { get; private set; }
				object IEnumerator.Current => Current;

				public Enumerator(int flags)
				{
					src_ = flags;
					Current = flags + 1;
				}

				public void Dispose() { }
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public bool MoveNext() => (Current = --Current & src_) > 0;
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public void Reset() => Current = src_;
			}
		}
	}

	public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>
	{
		public static HashMap<TKey, TValue> Merge(
			HashMap<TKey, TValue> src1,
			HashMap<TKey, TValue> src2,
			Func<TValue, TValue, TValue> mergeValues)
		{
			if (src1.Count < src2.Count) {
				(src1, src2) = (src2, src1);
			}

			foreach (var key in src2.Keys) {
				src1[key] = mergeValues(src1[key], src2[key]);
			}

			return src1;
		}

		private readonly Func<TKey, TValue> initialzier_;
		public HashMap(Func<TKey, TValue> initialzier)
			: base()
		{
			initialzier_ = initialzier;
		}

		public HashMap(Func<TKey, TValue> initialzier, int capacity)
			: base(capacity)
		{
			initialzier_ = initialzier;
		}

		new public TValue this[TKey key]
		{
			get
			{
				if (TryGetValue(key, out TValue value)) {
					return value;
				} else {
					var init = initialzier_(key);
					base[key] = init;
					return init;
				}
			}

			set { base[key] = value; }
		}

		public HashMap<TKey, TValue> Merge(
			HashMap<TKey, TValue> src,
			Func<TValue, TValue, TValue> mergeValues)
		{
			foreach (var key in src.Keys) {
				this[key] = mergeValues(this[key], src[key]);
			}

			return this;
		}
	}

	public class JagList2<T> where T : struct
	{
		private readonly int n_;
		private readonly List<T>[] tempValues_;
		private T[][] values_;

		public int Count => n_;
		public List<T>[] Raw => tempValues_;
		public T[][] Values => values_;
		public T[] this[int index] => values_[index];

		public JagList2(int n)
		{
			n_ = n;
			tempValues_ = new List<T>[n];
			for (int i = 0; i < n; ++i) {
				tempValues_[i] = new List<T>();
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(int i, T value) => tempValues_[i].Add(value);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Build()
		{
			values_ = new T[n_][];
			for (int i = 0; i < values_.Length; ++i) {
				values_[i] = tempValues_[i].ToArray();
			}
		}
	}

	public class DijkstraQ
	{
		private int count_ = 0;
		private long[] distanceHeap_;
		private int[] vertexHeap_;

		public int Count => count_;
		public DijkstraQ()
		{
			distanceHeap_ = new long[8];
			vertexHeap_ = new int[8];
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Enqueue(long distance, int v)
		{
			if (distanceHeap_.Length == count_) {
				var newDistanceHeap = new long[distanceHeap_.Length << 1];
				var newVertexHeap = new int[vertexHeap_.Length << 1];
				Unsafe.CopyBlock(
					ref Unsafe.As<long, byte>(ref newDistanceHeap[0]),
					ref Unsafe.As<long, byte>(ref distanceHeap_[0]),
					(uint)(8 * count_));
				Unsafe.CopyBlock(
					ref Unsafe.As<int, byte>(ref newVertexHeap[0]),
					ref Unsafe.As<int, byte>(ref vertexHeap_[0]),
					(uint)(4 * count_));
				distanceHeap_ = newDistanceHeap;
				vertexHeap_ = newVertexHeap;
			}

			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			Unsafe.Add(ref dRef, count_) = distance;
			Unsafe.Add(ref vRef, count_) = v;
			++count_;

			int c = count_ - 1;
			while (c > 0) {
				int p = (c - 1) >> 1;
				var tempD = Unsafe.Add(ref dRef, p);
				if (tempD <= distance) {
					break;
				} else {
					Unsafe.Add(ref dRef, c) = tempD;
					Unsafe.Add(ref vRef, c) = Unsafe.Add(ref vRef, p);
					c = p;
				}
			}

			Unsafe.Add(ref dRef, c) = distance;
			Unsafe.Add(ref vRef, c) = v;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long distance, int v) Dequeue()
		{
			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			(long distance, int v) ret = (dRef, vRef);
			int n = count_ - 1;

			var distance = Unsafe.Add(ref dRef, n);
			var vertex = Unsafe.Add(ref vRef, n);
			int p = 0;
			int c = (p << 1) + 1;
			while (c < n) {
				if (c != n - 1 && Unsafe.Add(ref dRef, c + 1) < Unsafe.Add(ref dRef, c)) {
					++c;
				}

				var tempD = Unsafe.Add(ref dRef, c);
				if (distance > tempD) {
					Unsafe.Add(ref dRef, p) = tempD;
					Unsafe.Add(ref vRef, p) = Unsafe.Add(ref vRef, c);
					p = c;
					c = (p << 1) + 1;
				} else {
					break;
				}
			}

			Unsafe.Add(ref dRef, p) = distance;
			Unsafe.Add(ref vRef, p) = vertex;
			--count_;

			return ret;
		}
	}

	public struct ModInt
	{
		public const long P = 1000000007;
		//public const long P = 998244353;
		//public const long P = 2;
		public const long ROOT = 3;

		// (924844033, 5)
		// (998244353, 3)
		// (1012924417, 5)
		// (167772161, 3)
		// (469762049, 3)
		// (1224736769, 3)

		private long value_;

		public static ModInt New(long value, bool mods) => new ModInt(value, mods);
		public ModInt(long value) => value_ = value;
		public ModInt(long value, bool mods)
		{
			if (mods) {
				value %= P;
				if (value < 0) {
					value += P;
				}
			}

			value_ = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (lhs.value_ + rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator +(long lhs, ModInt rhs)
		{
			rhs.value_ = (lhs + rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator +(ModInt lhs, long rhs)
		{
			lhs.value_ = (lhs.value_ + rhs) % P;
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator -(long lhs, ModInt rhs)
		{
			rhs.value_ = (P + lhs - rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator -(ModInt lhs, long rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs) % P;
			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = lhs.value_ * rhs.value_ % P;
			return lhs;
		}
		public static ModInt operator *(long lhs, ModInt rhs)
		{
			rhs.value_ = lhs * rhs.value_ % P;
			return rhs;
		}
		public static ModInt operator *(ModInt lhs, long rhs)
		{
			lhs.value_ = lhs.value_ * rhs % P;
			return lhs;
		}

		public static ModInt operator /(ModInt lhs, ModInt rhs)
			=> lhs * Inverse(rhs);

		public static implicit operator ModInt(long n) => new ModInt(n, true);

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Inverse(ModInt value) => Pow(value, P - 2);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			while (k > 0) {
				if ((k & 1) != 0) {
					ret = ret * value % P;
				}

				value = value * value % P;
				k >>= 1;
			}

			return new ModInt(ret);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long ToLong() => value_;
		public override string ToString() => value_.ToString();
	}

	public static class Helper
	{
		public static long INF => 1L << 50;

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T Clamp<T>(this T value, T min, T max) where T : struct, IComparable<T>
		{
			if (value.CompareTo(min) <= 0) {
				return min;
			}

			if (value.CompareTo(max) >= 0) {
				return max;
			}

			return value;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) > 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) > 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) < 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) < 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static long BinarySearchOKNG(long ok, long ng, Func<long, bool> satisfies)
		{
			while (ng - ok > 1) {
				long mid = (ok + ng) / 2;
				if (satisfies(mid)) {
					ok = mid;
				} else {
					ng = mid;
				}
			}

			return ok;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static long BinarySearchNGOK(long ng, long ok, Func<long, bool> satisfies)
		{
			while (ok - ng > 1) {
				long mid = (ok + ng) / 2;
				if (satisfies(mid)) {
					ok = mid;
				} else {
					ng = mid;
				}
			}

			return ok;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, T initialValue) where T : struct
			=> new T[n].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, Func<int, T> initializer)
			=> Enumerable.Range(0, n).Select(x => initializer(x)).ToArray();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Fill<T>(this T[] array, T value)
			where T : struct
		{
			array.AsSpan().Fill(value);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, T initialValule) where T : struct
			=> new T[n, m].Fill(initialValule);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, Func<int, int, T> initializer)
		{
			var array = new T[n, m];
			for (int i = 0; i < n; ++i) {
				for (int j = 0; j < m; ++j) {
					array[i, j] = initializer(i, j);
				}
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Fill<T>(this T[,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,] array, int i)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, 0], array.GetLength(1));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Array3<T>(int n1, int n2, int n3, T initialValue)
			where T : struct
			=> new T[n1, n2, n3].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Fill<T>(this T[,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,] array, int i, int j)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, 0], array.GetLength(2));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Array4<T>(int n1, int n2, int n3, int n4, T initialValue)
			where T : struct
			=> new T[n1, n2, n3, n4].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Fill<T>(this T[,,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,,] array, int i, int j, int k)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, k, 0], array.GetLength(3));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Merge<T>(ReadOnlySpan<T> first, ReadOnlySpan<T> second) where T : IComparable<T>
		{
			var ret = new T[first.Length + second.Length];
			int p = 0;
			int q = 0;
			while (p < first.Length || q < second.Length) {
				if (p == first.Length) {
					ret[p + q] = second[q];
					q++;
					continue;
				}

				if (q == second.Length) {
					ret[p + q] = first[p];
					p++;
					continue;
				}

				if (first[p].CompareTo(second[q]) < 0) {
					ret[p + q] = first[p];
					p++;
				} else {
					ret[p + q] = second[q];
					q++;
				}
			}

			return ret;
		}

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<(int i, int j)> Adjacence4(int i, int j, int imax, int jmax)
		{
			for (int dn = 0; dn < 4; ++dn) {
				int d4i = i + delta4_[dn];
				int d4j = j + delta4_[dn + 1];
				if ((uint)d4i < (uint)imax && (uint)d4j < (uint)jmax) {
					yield return (d4i, d4j);
				}
			}
		}

		private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<(int i, int j)> Adjacence8(int i, int j, int imax, int jmax)
		{
			for (int dn = 0; dn < 8; ++dn) {
				int d8i = i + delta8_[dn];
				int d8j = j + delta8_[dn + 1];
				if ((uint)d8i < (uint)imax && (uint)d8j < (uint)jmax) {
					yield return (d8i, d8j);
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<int> SubBitsOf(int bit)
		{
			for (int sub = bit; sub > 0; sub = --sub & bit) {
				yield return sub;
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Reverse(string src)
		{
			var chars = src.ToCharArray();
			for (int i = 0, j = chars.Length - 1; i < j; ++i, --j) {
				var tmp = chars[i];
				chars[i] = chars[j];
				chars[j] = tmp;
			}

			return new string(chars);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Exchange(string src, char a, char b)
		{
			var chars = src.ToCharArray();
			for (int i = 0; i < chars.Length; i++) {
				if (chars[i] == a) {
					chars[i] = b;
				} else if (chars[i] == b) {
					chars[i] = a;
				}
			}

			return new string(chars);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void Swap(this string str, int i, int j)
		{
			var span = str.AsWriteableSpan();
			(span[i], span[j]) = (span[j], span[i]);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static char Replace(this string str, int index, char c)
		{
			var span = str.AsWriteableSpan();
			char old = span[index];
			span[index] = c;
			return old;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<char> AsWriteableSpan(this string str)
		{
			var span = str.AsSpan();
			return MemoryMarshal.CreateSpan(ref MemoryMarshal.GetReference(span), span.Length);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Join<T>(this IEnumerable<T> values, string separator = "")
			=> string.Join(separator, values);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string JoinNL<T>(this IEnumerable<T> values)
			=> string.Join(Environment.NewLine, values);
	}

	public static class Extensions
	{
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this List<T> list)
		{
			return Unsafe.As<FakeList<T>>(list).Array.AsSpan(0, list.Count);
		}

		private class FakeList<T>
		{
			public T[] Array = null;
		}
	}

	public class Scanner : IDisposable
	{
		private const int BUFFER_SIZE = 1024;
		private const int ASCII_SPACE = 32;
		private const int ASCII_CHAR_BEGIN = 33;
		private const int ASCII_CHAR_END = 126;
		private readonly string filePath_;
		private readonly Stream stream_;
		private readonly byte[] buf_ = new byte[BUFFER_SIZE];
		private int length_ = 0;
		private int index_ = 0;
		private bool isEof_ = false;

		public Scanner(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				stream_ = Console.OpenStandardInput();
			} else {
				filePath_ = file;
				stream_ = new FileStream(file, FileMode.Open);
			}

			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush = false
			});
		}

		public void Dispose()
		{
			Console.Out.Flush();
			stream_.Dispose();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string NextLine()
		{
			var sb = new StringBuilder();
			for (var b = Char(); b >= ASCII_SPACE && b <= ASCII_CHAR_END; b = (char)Read()) {
				sb.Append(b);
			}

			return sb.ToString();
		}


		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public char Char()
		{
			byte b;
			do {
				b = Read();
			} while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b);

			return (char)b;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string String()
		{
			var sb = new StringBuilder();
			for (var b = Char(); b >= ASCII_CHAR_BEGIN && b <= ASCII_CHAR_END; b = (char)Read()) {
				sb.Append(b);
			}

			return sb.ToString();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string[] ArrayString(int length)
		{
			var array = new string[length];
			for (int i = 0; i < length; ++i) {
				array[i] = String();
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int() => (int)Long();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int(int offset) => Int() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int) Int2(int offset = 0)
			=> (Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int) Int3(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int, int) Int4(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int, int, int) Int5(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int[] ArrayInt(int length, int offset = 0)
		{
			var array = new int[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Int(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Long()
		{
			long ret = 0;
			byte b;
			bool ng = false;
			do {
				b = Read();
			} while (b != '-' && (b < '0' || '9' < b));

			if (b == '-') {
				ng = true;
				b = Read();
			}

			for (; true; b = Read()) {
				if (b < '0' || '9' < b) {
					return ng ? -ret : ret;
				} else {
					ret = ret * 10 + b - '0';
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Long(long offset) => Long() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long) Long2(long offset = 0)
			=> (Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long) Long3(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long, long) Long4(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long, long, long) Long5(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long[] ArrayLong(int length, long offset = 0)
		{
			var array = new long[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Long(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big() => new BigInteger(Long());
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big(long offset) => Big() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger) Big2(long offset = 0)
			=> (Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger) Big3(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger, BigInteger) Big4(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger, BigInteger, BigInteger) Big5(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger[] ArrayBig(int length, long offset = 0)
		{
			var array = new BigInteger[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Big(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double() => double.Parse(String(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double(double offset) => Double() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double) Double2(double offset = 0)
			=> (Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double) Double3(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double, double) Double4(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double, double, double) Double5(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double[] ArrayDouble(int length, double offset = 0)
		{
			var array = new double[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Double(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal() => decimal.Parse(String(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal(decimal offset) => Decimal() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal) Decimal2(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal) Decimal3(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal, decimal) Decimal4(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal, decimal, decimal) Decimal5(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal[] ArrayDecimal(int length, decimal offset = 0)
		{
			var array = new decimal[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Decimal(offset);
			}

			return array;
		}

		private byte Read()
		{
			if (isEof_) {
				throw new EndOfStreamException();
			}

			if (index_ >= length_) {
				index_ = 0;
				if ((length_ = stream_.Read(buf_, 0, BUFFER_SIZE)) <= 0) {
					isEof_ = true;
					return 0;
				}
			}

			return buf_[index_++];
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}