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.Generic;
using System.Linq;
using System.Text;

//using System.Numerics;
using CS=System.Runtime.CompilerServices;
//using System.Diagnostics;
using static System.Math;
using ll=System.Int64;
using static Contest_I.Lib_IO;
using static Contest_I.Lib_Minifunc;


namespace Contest_I {

public static class Entry
{

	public static void Main() {
		checked{
			string s;
			Lib_IO.rm(out s);

			SuffixArray sais = new SuffixArray(s);
			sais.BuildLCP();
			long ans = 0;
			for (int i = 1; i <= sais[0]; i++)
			{
				ans += s.Length-sais[i+1]-sais.GetLCP(sais[i],sais[i+1]);
			}

			Lib_IO.wm(ans);
		}
	}

public class SuffixArray {
	int[] S;
	int N;
	int[] SA;
	int[] rank;
	sparseTableRMQ rmq;
	public SuffixArray(string str) {
		N = str.Length;
		S = new int[N + 1];
		for (int i = 0; i < N; i++)
			S[i] = str[i];
		SA = sais(S, S.Max());
		rank = new int[N + 1];
		for (int i = 0; i <= N; i++) rank[SA[i]] = i;
	}

	void createBeginBucket(int[] v, int[] b) {
		for (int i = 0; i < b.Length; i++) b[i] = 0;
		for (int i = 0; i < v.Length; i++) b[v[i]]++;
		int sum = 0;
		for (int i = 0; i < b.Length; i++) { b[i] += sum; var tmp = b[i]; b[i] = sum; sum = tmp; }
	}
	void createEndBucket(int[] v, int[] b) {
		for (int i = 0; i < b.Length; i++) b[i] = 0;
		for (int i = 0; i < v.Length; i++) b[v[i]]++;
		for (int i = 1; i < b.Length; i++) b[i] += b[i - 1];
	}
	void inducedSort(int[] v, int[] sa, int mv, int[] b, bool[] isl) {
		createBeginBucket(v, b);
		for (int i = 0; i < v.Length; i++) if (sa[i] > 0 && isl[sa[i] - 1]) sa[b[v[sa[i] - 1]]++] = sa[i] - 1;
	}
	void invertInducedSort(int[] v, int[] sa, int mv, int[] b, bool[] isl) {
		createEndBucket(v, b);
		for (int i = v.Length - 1; i >= 0; i--)
			if (sa[i] > 0 && !isl[sa[i] - 1]) sa[--b[v[sa[i] - 1]]] = sa[i] - 1;
	}
	int[] sais(int[] v, int mv) {
		if (v.Length == 1) return new int[] { 0 };
		var isl = new bool[v.Length];
		var b = new int[mv + 1];
		var sa = new int[v.Length];
		for (int i = 0; i < v.Length; i++)
			sa[i] = -1;
		for (int i = v.Length - 2; i >= 0; i--)
			isl[i] = v[i] > v[i + 1] || (v[i] == v[i + 1] && isl[i + 1]);
		createEndBucket(v, b);
		for (int i = 0; i < v.Length; i++) if (isLMS(i, isl)) sa[--b[v[i]]] = i;
		inducedSort(v, sa, mv, b, isl);
		invertInducedSort(v, sa, mv, b, isl);


		var cur = 0;
		var ord = new int[v.Length];
		for (int i = 0; i < v.Length; i++) if (isLMS(i, isl)) ord[i] = cur++;
		var next = new int[cur];
		cur = -1;
		int prev = -1;
		for (int i = 0; i < v.Length; i++)
		{
			if (!isLMS(sa[i], isl)) continue;
			var diff = false;
			for (int d = 0; d < v.Length; d++)
			{
				if (prev == -1 || v[sa[i] + d] != v[prev + d] || isl[sa[i] + d] != isl[prev + d])
				{
					diff = true; break;
				}
				else if (d > 0 && isLMS(sa[i] + d, isl)) break;
			}
			if (diff) { cur++; prev = sa[i]; }
			next[ord[sa[i]]] = cur;
		}
		var reord = new int[next.Length];
		for (int i = 0; i < v.Length; i++) if (isLMS(i, isl)) reord[ord[i]] = i;
		var nextsa = sais(next, cur);
		createEndBucket(v, b);
		for (int i = 0; i < sa.Length; i++) sa[i] = -1;
		for (int i = nextsa.Length - 1; i >= 0; i--) sa[--b[v[reord[nextsa[i]]]]] = reord[nextsa[i]];
		inducedSort(v, sa, mv, b, isl);
		invertInducedSort(v, sa, mv, b, isl);
		return sa;
	}
	bool isLMS(int x, bool[] isl) { return x > 0 && isl[x - 1] && !isl[x]; }

	public void BuildLCP() {
		var k = 0;
		var h = new int[N];
		for (int i = 0; i < N; i++)
		{
			var j = SA[rank[i] - 1];
			if (k > 0) k--;
			for (; j + k < N && i + k < N; k++) if (S[j + k] != S[i + k]) break;
			h[rank[i] - 1] = k;
		}
		rmq = new sparseTableRMQ(h);
	}
	/// <summary>
	/// s[<paramref name="i"/>:] と s[<paramref name="j"/>:] の最大共通接頭辞を O(loglogN) で計算します。
	/// </summary>
	/// <returns></returns>
	public int GetLCP(int i, int j) {
		i = rank[i]; j = rank[j];
		return rmq.Query(Math.Min(i, j), Math.Max(i, j));
	}
	/// <summary>
	/// rankがiのものを返す
	/// </summary>
	public int this[int index] {
		get { return index == 0 ? N : SA[index - 1]; }
	}
	/// <summary>
	/// s[i:]のランクを返す
	/// </summary>
	public int Rank(int index) {
		return rank[index];
	}

	public class sparseTableRMQ {
		int n;
		int[] A;
		public sparseTableRMQ(int[] a) {
			var k = 1;
			n = a.Length;
			for (int i = 1; i < n; i <<= 1) k++;

			A = new int[n * k];
			for (int i = 0; i < n; i++)
				A[i] = a[i];
			var d = 0;
			for (int i = 1; i < n; i <<= 1, d += n)
			{
				for (int j = 0; j < n; j++)
					A[d + n + j] = A[d + j];
				for (int j = 0; j < n - i; j++)
					A[d + n + j] = Math.Min(A[d + j], A[d + j + i]);
			}
		}
		/// <summary>
		/// value of [l,r)
		/// </summary>
		public int Query(int l, int r) {
			r--;
			int z = r - l, k = 0, e = 1, s;
			s = ((z & 0xffff0000) != 0 ? 1 : 0) << 4; z >>= s; e <<= s; k |= s;
			s = ((z & 0x0000ff00) != 0 ? 1 : 0) << 3; z >>= s; e <<= s; k |= s;
			s = ((z & 0x000000f0) != 0 ? 1 : 0) << 2; z >>= s; e <<= s; k |= s;
			s = ((z & 0x0000000c) != 0 ? 1 : 0) << 1; z >>= s; e <<= s; k |= s;
			s = ((z & 0x00000002) != 0 ? 1 : 0) << 0; z >>= s; e <<= s; k |= s;
			//var vl = A[l + n * k];
			//var vr = A[r - e + 1 + (n * k)];
			return Math.Min(A[l + (n * k)], A[r + (n * k) - e + 1]);
		}
	}
}













}



#region BaseModule


public static class Lib_Minifunc{
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
	[CS.MethodImpl(256)] public static void swap1<T>(ref T a,ref T b) { T t = a; a = b; b = t; }
	[CS.MethodImpl(256)] public static void swap2<T>(ref T a,ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換

	[CS.MethodImpl(256)] public static bool chmin<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)== 1)) a = b; return r; }  // b の方が小さければ a を更新
	[CS.MethodImpl(256)] public static bool chmax<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)==-1)) a = b; return r; }  // b の方が大きければ a を更新
	[CS.MethodImpl(256)] public static bool inside(long i,long n) => (0<=i&&i<n);
	[CS.MethodImpl(256)] public static bool inside(long x,long y,long w,long h) => (inside(x,w)&&inside(y,h));
	[CS.MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmin(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmax(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static long mod(long a,long m=MOD1) { var v = a%m; return (v<0?(m<0?v-m:v+m):v); }
	[CS.MethodImpl(256)] public static long ceil(long a,long b) => (a%b==0||(a<0&&0<b)||(0<a&&b<0)?a/b:a/b+1);	// 整数商の切り上げ
	[CS.MethodImpl(256)] public static long round(double a) => Convert.ToInt64(a);	// 四捨五入
	public static string YES(bool a) => a?"YES":"NO";
	public static string yes(bool a) => a?"Yes":"No";
	[CS.MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[CS.MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[CS.MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	public static T[] initc<T>(long l1) where T : new() { var m = new T[l1]; for (int i=0;i<m.Length;i++) m[i] = new T(); return m; }	// new制約は遅い
	public static int[] range(long s, long c) => Enumerable.Range((int)s,(int)c).ToArray();
	[CS.MethodImpl(256)] public static T[] inita<T>(long l1,T v=default(T)) => Enumerable.Repeat(v,(int)l1).ToArray();
	public static T[][] inita<T>(long l1,long l2,T v=default(T)) { var m = new T[l1][]; for (int i=0;i<m.Length;i++) m[i] = inita(l2,v); return m; }
	public static void shift(this IList<int> l,int o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	public static void shift(this IList<long> l,long o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	[CS.MethodImpl(256)] public static bool initd<T,U>(this IDictionary<T,U> d, T k, U v=default(U)) { if(d.ContainsKey(k)) { return false; } else { d[k] = v; return true; } }
	public static void sort<T>(this T[] a,int o=1, Comparison<T> f=null) where T : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.CompareTo(y));break;
			case -1: Array.Sort(a,(x,y)=>y.CompareTo(x));break;
			default: break;
		}
	}
	public static void sort<T,U>(this P<T,U>[] a,int o, Comparison<P<T,U>> f=null) where T : IComparable where U : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			default: break;
		}
	}
	public static void sort<T,U,V>(this P<T,U,V>[] a,int o, Comparison<P<T,U,V>> f=null) where T : IComparable where U : IComparable where V : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			default: break;
		}
	}
	public static void sort<T,U,V,W>(this P<T,U,V,W>[] a,int o, Comparison<P<T,U,V,W>> f=null) where T : IComparable where U : IComparable where V : IComparable where W : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			case  4: Array.Sort(a,(x,y)=>x.D.CompareTo(y.D));break;
			case -4: Array.Sort(a,(x,y)=>y.D.CompareTo(x.D));break;
			default: break;
		}
	}
}


public struct P<T,U>
{
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V>
{
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W>
{
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO
{
	class Prt : System.IO.StreamWriter
	{
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[CS.MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[CS.MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[CS.MethodImpl(256)] static T cv<T>(string s) =>
		eq<T,int>()	? ct<T,int>(int.Parse(s))
	  : eq<T,long>()   ? ct<T,long>(long.Parse(s))
	  : eq<T,double>() ? ct<T,double>(double.Parse(s,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = new T[z.Length];
		for(int i=0;i<a.Length;i++) a[i] = cv<T>(z[i]);
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[CS.MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length-1;i++) Console.Write(wfm(a[i].GetType())+" ",a[i]);
			Console.WriteLine(wfm(a[a.Length-1].GetType()),a[a.Length-1]);
		});
	}
	public static void wa<T>(IList<T> a) { wxa(new IList<T>[]{a}, " "); }
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			if(a.Count==0){
				Console.WriteLine();
			}else{
				foreach(T x in a) Console.WriteLine(f,x);
			}
		});
	}
	static void wxa<T>(IList<IList<T>> a, string s) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + s;
			foreach(var b in a) {
				if(b.Count==0){
					Console.WriteLine();
				}else{
					for(int i=0;i<b.Count-1;i++) Console.Write(g,b[i]);
					Console.WriteLine(f,b[b.Count-1]);
				}
			}
		});
	}
	public static void wx<T>(IList<IList<T>> a) { wxa(a, " "); }
	public static void wg<T>(IList<IList<T>> a) { wxa(a, ""); }
}

#endregion



}