Problem:
Score : 100 points

Problem Statement

You are given a string of length N. Calculate the number of distinct substrings of S.

Constraints

1 \leq N \leq 500,000

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer.

Sample Input 1

abcbcba

Sample Output 1

21

Sample Input 2

mississippi

Sample Output 2

53

Sample Input 3

ababacaca

Sample Output 3

33

Sample Input 4

aaaaa

Sample Output 4

5

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

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.Reflection.Metadata;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics.X86;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;

namespace AtCoder
{
	public class Program
	{
		static void Main()
		{
			using var cin = new Scanner();
			string s = cin.Next();
			long n = s.Length;

			long ans = n * (n + 1) / 2;
			var sa = StringEx.SuffixArray(s);
			var la = StringEx.LCPArray(s, sa);
			foreach (var lcp in la) {
				ans -= lcp;
			}

			Console.WriteLine(ans);
		}
	}

	public static class StringEx
	{
		/// <summary>
		/// 数列 <paramref name="sm"/> の Suffix Array をナイーブな文字列比較により求め、長さ |<paramref name="sm"/>| の配列として返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="sm"/>|&lt;10^8</para>
		/// <para>計算量: 時間O(|<paramref name="sm"/>|^2 log|<paramref name="sm"/>|), 空間O(|<paramref name="sm"/>|)</para>
		/// </remarks>
		private static int[] SANaive(ReadOnlyMemory<int> sm)
		{
			var n = sm.Length;
			var sa = Enumerable.Range(0, n).ToArray();
			Array.Sort(sa, Compare);
			return sa;

			int Compare(int l, int r)
			{
				// l == r にはなり得ない
				var s = sm.Span;
				while (l < s.Length && r < s.Length) {
					if (s[l] != s[r]) {
						return s[l] - s[r];
					}
					l++;
					r++;
				}

				return r - l;
			}
		}

		/// <summary>
		/// 数列 <paramref name="sm"/> の Suffix Array をダブリングにより求め、長さ |<paramref name="sm"/>| の配列として返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="sm"/>|&lt;10^8</para>
		/// <para>計算量: 時間O(|<paramref name="sm"/>|(log|<paramref name="sm"/>|)^2), 空間O(|<paramref name="sm"/>|)</para>
		/// </remarks>
		private static int[] SADoubling(ReadOnlyMemory<int> sm)
		{
			var s = sm.Span;
			var n = s.Length;
			var sa = Enumerable.Range(0, n).ToArray();
			var rnk = new int[n];
			var tmp = new int[n];
			s.CopyTo(rnk);

			for (int k = 1; k < n; k <<= 1) {
				Array.Sort(sa, Compare);
				tmp[sa[0]] = 0;
				for (int i = 1; i < sa.Length; i++) {
					tmp[sa[i]] = tmp[sa[i - 1]] + (Compare(sa[i - 1], sa[i]) < 0 ? 1 : 0);
				}
				(tmp, rnk) = (rnk, tmp);

				int Compare(int x, int y)
				{
					if (rnk[x] != rnk[y]) {
						return rnk[x] - rnk[y];
					}

					int rx = x + k < n ? rnk[x + k] : -1;
					int ry = y + k < n ? rnk[y + k] : -1;

					return rx - ry;
				}
			}

			return sa;
		}

		/// <summary>
		/// 数列 <paramref name="sm"/> の Suffix Array を SA-IS 等により求め、長さ |<paramref name="sm"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="sm"/>|&lt;10^8</para>
		/// <para>計算量: O(|<paramref name="sm"/>|)</para>
		/// </remarks>
		public static int[] SAIS(ReadOnlyMemory<int> sm, int upper) => SAIS(sm, upper, 10, 40);

		/// <summary>
		/// 数列 <paramref name="sm"/> の Suffix Array を SA-IS 等により求め、長さ |<paramref name="sm"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="sm"/>|&lt;10^8</para>
		/// <para>計算量: O(|<paramref name="sm"/>|)</para>
		/// </remarks>
		public static int[] SAIS(ReadOnlyMemory<int> sm, int upper, int thresholdNaive, int thresholdDouling)
		{
			var s = sm.Span;
			var n = s.Length;

			if (n == 0) {
				return Array.Empty<int>();
			} else if (n == 1) {
				return new int[] { 0 };
			} else if (n == 2) {
				if (s[0] < s[1]) {
					return new int[] { 0, 1 };
				} else {
					return new int[] { 1, 0 };
				}
			} else if (n < thresholdNaive) {
				return SANaive(sm);
			} else if (n < thresholdDouling) {
				return SADoubling(sm);
			}

			var sa = new int[n];
			var ls = new bool[n];

			for (int i = sa.Length - 2; i >= 0; i--) {
				// S-typeならtrue、L-typeならfalse
				ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
			}

			// バケットサイズの累積和（＝開始インデックス）
			var sumL = new int[upper + 1];
			var sumS = new int[upper + 1];

			for (int i = 0; i < s.Length; i++) {
				if (!ls[i]) {
					sumS[s[i]]++;
				} else {
					sumL[s[i] + 1]++;
				}
			}

			for (int i = 0; i < sumL.Length; i++) {
				sumS[i] += sumL[i];
				if (i < upper) {
					sumL[i + 1] += sumS[i];
				}
			}

			var lmsMap = GetFilledArray(-1, n + 1);
			int m = 0;
			for (int i = 1; i < ls.Length; i++) {
				if (!ls[i - 1] && ls[i]) {
					lmsMap[i] = m++;
				}
			}

			var lms = new List<int>(m);
			for (int i = 1; i < ls.Length; i++) {
				if (!ls[i - 1] && ls[i]) {
					lms.Add(i);
				}
			}

			Induce(lms);

			// LMSを再帰的にソート
			if (m > 0) {
				var sortedLms = new List<int>(m);
				foreach (var v in sa) {
					if (lmsMap[v] != -1) {
						sortedLms.Add(v);
					}
				}

				var recS = new int[m];
				var recUpper = 0;
				recS[lmsMap[sortedLms[0]]] = 0;

				// 同じLMS同士をまとめていく
				for (int i = 1; i < sortedLms.Count; i++) {
					var l = sortedLms[i - 1];
					var r = sortedLms[i];
					var endL = (lmsMap[l] + 1 < m) ? lms[lmsMap[l] + 1] : n;
					var endR = (lmsMap[r] + 1 < m) ? lms[lmsMap[r] + 1] : n;
					var same = true;

					if (endL - l != endR - r) {
						same = false;
					} else {
						while (l < endL) {
							if (s[l] != s[r]) {
								break;
							}
							l++;
							r++;
						}

						if (l == n || s[l] != s[r]) {
							same = false;
						}
					}

					if (!same) {
						recUpper++;
					}

					recS[lmsMap[sortedLms[i]]] = recUpper;
				}

				var recSA = SAIS(recS, recUpper, thresholdNaive, thresholdDouling);

				for (int i = 0; i < sortedLms.Count; i++) {
					sortedLms[i] = lms[recSA[i]];
				}

				Induce(sortedLms);
			}

			return sa;

			void Induce(List<int> lms)
			{
				var s = sm.Span;
				sa.AsSpan().Fill(-1);
				var buf = new int[sumS.Length];

				// LMS
				sumS.AsSpan().CopyTo(buf);
				foreach (var d in lms) {
					if (d == n) {
						continue;
					}
					sa[buf[s[d]]++] = d;
				}

				// L-type
				sumL.AsSpan().CopyTo(buf);
				sa[buf[s[n - 1]]++] = n - 1;
				for (int i = 0; i < sa.Length; i++) {
					int v = sa[i];
					if (v >= 1 && !ls[v - 1]) {
						sa[buf[s[v - 1]]++] = v - 1;
					}
				}

				// S-type
				sumL.AsSpan().CopyTo(buf);
				for (int i = sa.Length - 1; i >= 0; i--) {
					int v = sa[i];
					if (v >= 1 && ls[v - 1]) {
						sa[--buf[s[v - 1] + 1]] = v - 1;
					}
				}
			}
		}

		/// <summary>
		/// 各要素が <paramref name="value"/> で初期化された長さ <paramref name="length"/> の配列を取得する。
		/// </summary>
		private static T[] GetFilledArray<T>(T value, int length)
		{
			// Enumerable.Repeatより1-2割ほど高速（64bit環境、intの場合）
			// |           Method |     Mean |   Error |  StdDev |
			// |----------------- |---------:|--------:|--------:|
			// | EnumerableRepeat | 212.7 ms | 2.99 ms | 2.80 ms |
			// |         SpanFill | 178.7 ms | 1.29 ms | 1.14 ms |

			// ちなみにEnumerable.Rangeとnew[] + for文とでは有意差は見られない
			// |          Method |     Mean |   Error |  StdDev |
			// |---------------- |---------:|--------:|--------:|
			// | EnumerableRange | 225.6 ms | 4.35 ms | 3.85 ms |
			// |         SpanFor | 223.0 ms | 2.88 ms | 2.69 ms |

			var result = new T[length];
			result.AsSpan().Fill(value);
			return result;
		}

		/// <summary>
		/// 列 <paramref name="m"/> の Suffix Array として、長さ |<paramref name="m"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="m"/>|&lt;10^8</para>
		/// <para>計算量: 時間O(|<paramref name="m"/>|log|<paramref name="m"/>|), 空間O(|<paramref name="m"/>|)</para>
		/// </remarks>
		private static int[] SuffixArray<T>(ReadOnlyMemory<T> m)
		{
			var s = m.Span;
			var n = m.Length;
			var idx = Enumerable.Range(0, n).ToArray();
			Array.Sort(idx, Compare);
			var s2 = new int[n];
			var now = 0;

			// 座標圧縮
			for (int i = 0; i < idx.Length; i++) {
				if (i > 0 && !EqualityComparer<T>.Default.Equals(s[idx[i - 1]], s[idx[i]])) {
					now++;
				}
				s2[idx[i]] = now;
			}

			return SAIS(s2, now);

			int Compare(int l, int r)
			{
				var s = m.Span;
				return Comparer<T>.Default.Compare(s[l], s[r]);
			}
		}

		/// <summary>
		/// 文字列 <paramref name="s"/> の Suffix Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|&lt;10^8</para>
		/// <para>計算量: O(|<paramref name="s"/>|)</para>
		/// </remarks>
		public static int[] SuffixArray(string s)
		{
			var n = s.Length;
			int[] s2 = s.Select(c => (int)c).ToArray();
			return SAIS(s2, char.MaxValue);
		}


		/// <summary>
		/// 数列 <paramref name="s"/> の Suffix Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|&lt;10^8</para>
		/// <para>計算量: 時間O(|<paramref name="s"/>|log|<paramref name="s"/>|), 空間O(|<paramref name="s"/>|)</para>
		/// </remarks>
		public static int[] SuffixArray<T>(T[] s) => SuffixArray<T>(s.AsMemory());

		/// <summary>
		/// 数列 <paramref name="s"/> の Suffix Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>Suffix Array sa は (0,1,…,n−1) の順列であって、i=0,1,⋯,n−2 について s[sa[i]..n)&lt;s[sa[i+1]..n) を満たすもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|&lt;10^8, <paramref name="s"/> のすべての要素 x について 0≤x≤<paramref name="upper"/></para>
		/// <para>計算量: O(|<paramref name="s"/>|+<paramref name="upper"/>)</para>
		/// </remarks>
		public static int[] SuffixArray(int[] s, int upper)
		{
			Debug.Assert(0 <= upper);
			foreach (var si in s) {
				Debug.Assert(unchecked((uint)si) <= upper);
			}
			return SAIS(s, upper);
		}

		/// <summary>
		/// 列 <paramref name="s"/> の LCP Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>LCP Array とは、i 番目の要素が s[sa[i]..|<paramref name="s"/>|), s[sa[i+1]..|<paramref name="s"/>|) の LCP(Longest Common Prefix) の長さのもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|≤10^8, <paramref name="sa"/> は <paramref name="s"/> の Suffix Array</para>
		/// <para>計算量: O(|<paramref name="s"/>|)</para>
		/// </remarks>
		public static int[] LCPArray<T>(ReadOnlySpan<T> s, int[] sa)
		{
			Debug.Assert(1 <= s.Length);
			int[] rnk = new int[s.Length];
			for (int i = 0; i < s.Length; i++) {
				rnk[sa[i]] = i;
			}
			int[] lcp = new int[s.Length - 1];
			int h = 0;
			for (int i = 0; i < s.Length; i++) {
				if (h > 0) h--;
				if (rnk[i] == 0) continue;
				int j = sa[rnk[i] - 1];
				for (; j + h < s.Length && i + h < s.Length; h++) {
					if (!EqualityComparer<T>.Default.Equals(s[j + h], s[i + h])) break;
				}
				lcp[rnk[i] - 1] = h;
			}
			return lcp;
		}

		/// <summary>
		/// 文字列 <paramref name="s"/> の LCP Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>LCP Array とは、i 番目の要素が s[sa[i]..|<paramref name="s"/>|), s[sa[i+1]..|<paramref name="s"/>|) の LCP(Longest Common Prefix) の長さのもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|≤10^8, <paramref name="sa"/> は <paramref name="s"/> の Suffix Array</para>
		/// <para>計算量: O(|<paramref name="s"/>|)</para>
		/// </remarks>
		public static int[] LCPArray(string s, int[] sa) => LCPArray(s.AsSpan(), sa);

		/// <summary>
		/// 数列 <paramref name="s"/> の LCP Array として、長さ |<paramref name="s"/>| の配列を返す。
		/// </summary>
		/// <remarks>
		/// <para>LCP Array とは、i 番目の要素が s[sa[i]..|<paramref name="s"/>|), s[sa[i+1]..|<paramref name="s"/>|) の LCP(Longest Common Prefix) の長さのもの。</para>
		/// <para>制約: 0≤|<paramref name="s"/>|≤10^8, <paramref name="sa"/> は <paramref name="s"/> の Suffix Array</para>
		/// <para>計算量: O(|<paramref name="s"/>|)</para>
		/// </remarks>
		public static int[] LCPArray<T>(T[] s, int[] sa) => LCPArray((ReadOnlySpan<T>)s, sa);
	}

	public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>
	{
		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 (ContainsKey(key) == false) {
					base[key] = initialzier_(key);
				}

				return base[key];
			}

			set { base[key] = value; }
		}
	}

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

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

		public static ModInt Inverse(ModInt value) => Pow(value, P - 2);
		public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);
		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			for (k %= P - 1; k > 0; k >>= 1, value = value * value % P) {
				if ((k & 1) == 1) {
					ret = ret * value % P;
				}
			}
			return new ModInt(ret);
		}

		private long value_;

		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)
		{
			long exp = P - 2;
			while (exp > 0) {
				if (exp % 2 > 0) {
					lhs *= rhs;
				}

				rhs *= rhs;
				exp /= 2;
			}

			return lhs;
		}

		public static implicit operator ModInt(long n) => new ModInt(n, true);
		public long ToLong() => value_;
		public override string ToString() => value_.ToString();
	}

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

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

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToArray();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static List<T> List<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToList();

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

			return array;
		}
		[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[,,] Array3<T>(int n1, int n2, int n3, T init)
			where T : struct
		{
			var array = new T[n1, n2, n3];
			for (int i1 = 0; i1 < n1; i1++) {
				for (int i2 = 0; i2 < n2; i2++) {
					for (int i3 = 0; i3 < n3; i3++) {
						array[i1, i2, i3] = init;
					}
				}
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Array4<T>(int n1, int n2, int n3, int n4, T init)
			where T : struct
		{
			var array = new T[n1, n2, n3, n4];
			for (int i1 = 0; i1 < n1; i1++) {
				for (int i2 = 0; i2 < n2; i2++) {
					for (int i3 = 0; i3 < n3; i3++) {
						for (int i4 = 0; i4 < n4; i4++) {
							array[i1, i2, i3, i4] = init;
						}
					}
				}
			}

			return array;
		}

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoAt4(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			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) {
					action(d4i, d4j);
				}
			}
		}

		private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoAt8(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			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) {
					action(d8i, d8j);
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void ForEachSubBit(int bit, Action<int> action)
		{
			for (int sub = bit; sub >= 0; sub--) {
				sub &= bit;
				action(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 Join<T>(this IEnumerable<T> values, string separator = "")
			=> string.Join(separator, values);
	}

	public class Scanner : IDisposable
	{
		private const int BUFFER_SIZE = 1024;
		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 char Char()
		{
			byte b;
			do {
				b = Read();
			} while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b);

			return (char)b;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string Next()
		{
			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 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[] ArrayInt(int length, int offset = 0)
		{
			int[] 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[] ArrayLong(int length, long offset = 0)
		{
			long[] Array = new long[length];
			for (int i = 0; i < length; i++) {
				Array[i] = Long(offset);
			}
			return Array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double() => double.Parse(Next(), 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[] ArrayDouble(int length, double offset = 0)
		{
			double[] Array = new double[length];
			for (int i = 0; i < length; i++) {
				Array[i] = Double(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);
		}
	}
}