Problem:
Score : 200 points

Problem Statement

You are going to take the entrance examination of Kyoto University tomorrow
and have decided to memorize a set of strings S that is expected to appear in the examination.
Since it is really tough to memorize S as it is,
you have decided to memorize a single string T that efficiently contains all the strings in S.

You have already confirmed the following conditions for S and T are satisfied.

Every string in S is a consecutive subsequence(1) in T .

For every pair of strings x, y (x \neq y) in S ,
x is not a subsequence(2) of y.

Note that (1) is ''consecutive subsequence'', while (2) is ''subsequence''.

The next day, you opened the problem booklet at the examination
and found that you can get a full score only if you remember S.
However, You have forgot how to reconstruct S from T .
Since all you remember is that T satisfies the above conditions,
first you have decided to find the maximum possible number of elements in S .

Constraints

1 \leq |T| \leq 10^5

T consists of only lowercase letters.

Partial points

30 points will be awarded for passing the test set satisfying the condition: 1 \leq |T| \leq 50 .

Another 30 points will be awarded for passing the test set satisfying the condition: 1 \leq |T| \leq 10^3.

Input

The input is given from Standard Input in the following format:

T

The input only consists of T on one line.

Output

Print the maximum number of elements inS .

Sample Input 1

abcabc

Sample Output 1

3

In this case, ab，ca and bc are an example of the optimum answers.

Sample Input 2

abracadabra

Sample Output 2

7

Sample Input 3

abcbabbcabbc

Sample Output 3

8

Sample Input 4

bbcacbcbcabbabacccbbcacbaaababbacabaaccbccabcaabba

Sample Output 4

44

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var t=sc.S;
		Console.WriteLine("{0}",t.Length-new Sa(t,'a','z',false,false).lcp.Max());
	}
}
public class Sa{
	private readonly int n,m,o;
	public readonly string s;
	public readonly int[] sa,lcp;
	public readonly Spt lcps,sas1,sas2;
	public Sa(string s,int a,int z,bool b1,bool b2){
		m=z-a+2;
		o=a-1;
		s+=(char)o;
		this.s=s;
		n=s.Length;
		int[] h=new int[n];
		var lms=new List<int>();
		int[] sub=new int[n];
		int[] hi=new int[m];
		int[] hc1=new int[m];
		int[] hc2=new int[m];
		int[] hc3=new int[m];
		hi[s[n-1]-o]=hc2[s[n-1]-o]=hc3[s[n-1]-o]=1;
		for(int i = n-2,k=n-1;i>=0;i--) {
			h[i]=s[i]!=s[i+1]?(s[i]>s[i+1]?1:0):h[i+1];
			hi[s[i]-o]++;
			if(h[i]==1&&h[i+1]==0){
				h[i+1]=2;
				lms.Add(i+1);
				sub[i+1]=k-i;
				k=i+1;
			}
		}
		for(int i = 1;i<m;i++) {
			hi[i]+=hi[i-1];
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		int c=lms.Count;
		sa=new int[n];
		for(int i = 0;i<c;i++) {
			hc2[s[lms[i]]-o]--;
			sa[hc2[s[lms[i]]-o]]=lms[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[hc1[s[sa[i]-1]-o]]=sa[i]-1;
				hc1[s[sa[i]-1]-o]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]-o]--;
				sa[hc3[s[sa[i]-1]-o]]=sa[i]-1;
			}
		}
		int[] lh=new int[c];
		for(int i = 0,j=c-1;i<n&&j>=0;i++) {
			if(h[sa[i]]==2){lh[j]=sa[i];j--;}
		}
		lcp=new int[n];
		int[] lmsc=new int[c];
		bool jf=false;
		int ki=0;
		for(int i = c-2;i>=0;i--) {
			if(sub[lh[i]]==sub[lh[i+1]]){
				bool bo=false;
				for(int j = 0;j<sub[lh[i]];j++) {if(s[lh[i]+j]!=s[lh[i+1]+j]){bo=true;break;}}
				if(bo){ki++;}
				else{jf=true;}
			}
			else{ki++;}
			lcp[lh[i]]=ki;
		}
		for(int i = c-1;i>=0;i--) {lmsc[c-i-1]=lcp[lms[i]];}
		hc2[0]=hc3[0]=hi[0];
		hc1[0]=0;
		for(int i = 1;i<m;i++) {
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		if(jf){
			lh=Fu2(lmsc,ki+1);
			for(int i = 0;i<c;i++) {lh[i]=lms[c-1-lh[i]];}
		}
		sa=new int[n];
		for(int i = 0;i<c;i++) {
			hc2[s[lh[i]]-o]--;
			sub[lh[i]]=hc2[s[lh[i]]-o];
			sa[hc2[s[lh[i]]-o]]=lh[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sub[sa[i]-1]=hc1[s[sa[i]-1]-o];
				sa[hc1[s[sa[i]-1]-o]]=sa[i]-1;
				hc1[s[sa[i]-1]-o]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]-o]--;
				sub[sa[i]-1]=hc3[s[sa[i]-1]-o];
				sa[hc3[s[sa[i]-1]-o]]=sa[i]-1;
			}
		}
		lcp=new int[n];
		for(int i = 0;i<n-1;i++) {
			if(sub[i]==n-1){continue;}
			int p=n-Max(i,sa[sub[i]+1]),q=0;
			if(i!=0&&lcp[sub[i-1]]>1){lcp[sub[i]]=q=lcp[sub[i-1]]-1;}
			for(;q<p;q++) {if(s[i+q]!=s[sa[sub[i]+1]+q]){break;}}
			lcp[sub[i]]=q;
		}
		lcps=new Spt(lcp,false);
		if(b1){sas1=new Spt(sa,false);}
		if(b2){sas2=new Spt(sa,true);}
	}
	public int Fb1(string t){return Bs1(t);}
	public int Fb2(string t){return Bsl1(t);}
	public Tuple<int,int> Ft1(string t){
		int p=Bs1(t);
		return p==-1?Tuple.Create(-1,-1):Tuple.Create(p,Bs2(t)-1);
	}
	public Tuple<int,int> Ft2(string t){
		int p=Bsl1(t);
		return p==-1?Tuple.Create(-1,-1):Tuple.Create(p,Bsl2(t)-1);
	}
	public int Lb(int a,int l){
		if(l==0||l>lcp[a]){return a;}
		int lb=a,mid=0,ub=n-1;
		while(ub-lb>1){
			mid=(ub+lb)>>1;
			if(lcps.Get(a,mid)<l){ub=mid;}
			else{lb=mid;}
		}
		return ub;
	}
	private int Bs1(string t){
		int l=t.Length-1;
		int lb=-1,mid=0,ub=n-1;
		while(ub-lb>1){
			mid=(ub+lb)>>1;
			int ti=0;
			while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
			if(s[sa[mid]+ti]>=t[ti]){ub=mid;}
			else{lb=mid;}
		}
		bool bo=true;
		for(int i = 0;i<=l;i++) {if(s[sa[ub]+i]!=t[i]){bo=false;break;}}
		return bo?ub:-1;
	}
	private int Bs2(string t){
		int l=t.Length;
		int lb=-1,mid=0,ub=n;
		while(ub-lb>1){
			mid=(ub+lb)>>1;
			int tm=Min(l,n-sa[mid])-1,ti=0;
			while(s[sa[mid]+ti]==t[ti]&&ti<tm){ti++;}
			if(s[sa[mid]+ti]>t[ti]){ub=mid;}
			else{lb=mid;}
		}
		return ub;
	}
	private int Bsl1(string t){
		int l=t.Length-1;
		int lb=-1,ub=n-1,mid=(ub+lb)>>1,pr=mid;
		int ti=0;
		while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
		if(s[sa[mid]+ti]>=t[ti]){ub=mid;}
		else{lb=mid;}
		while(ub-lb>1){
			mid=(ub+lb)>>1;
			int d=mid<pr?lcps.Get(mid,pr-1):lcps.Get(pr,mid-1);
			if(d==ti){
				while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
				pr=mid;
				if(s[sa[mid]+ti]>=t[ti]){ub=mid;}
				else{lb=mid;}
			}
			else if(d<ti){
				if(mid>pr){ub=mid;}
				else{lb=mid;}
			}
			else{
				if(mid>pr){lb=mid;}
				else{ub=mid;}
			}
		}
		if(sa[ub]+ti>=n){return -1;}
		ti=0;
		while(ti<=l&&s[sa[ub]+ti]==t[ti]){ti++;}
		return ti==l+1?ub:-1;
	}
	private int Bsl2(string t){
		int l=t.Length-1;
		int lb=-1,ub=n,mid=(ub+lb)>>1,pr=mid;
		int ti=0;
		while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
		if(s[sa[mid]+ti]>t[ti]){ub=mid;}
		else{lb=mid;}
		while(ub-lb>1){
			mid=(ub+lb)>>1;
			int d=mid<pr?lcps.Get(mid,pr-1):lcps.Get(pr,mid-1);
			if(d==ti){
				while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
				pr=mid;
				if(s[sa[mid]+ti]>t[ti]){ub=mid;}
				else{lb=mid;}
			}
			else if(d<ti){
				if(mid>pr){ub=mid;}
				else{lb=mid;}
			}
			else{
				if(mid>pr){lb=mid;}
				else{ub=mid;}
			}
		}
		return ub;
	}
	private int[] Fu2(int[] s,int m){
		int n=s.Length;
		var lms=new List<int>();
		int[] h=new int[n],sub=new int[n],sa=new int[n];
		int[] hi=new int[m],hc1=new int[m],hc2=new int[m],hc3=new int[m];
		hi[s[n-1]]=hc2[s[n-1]]=hc3[s[n-1]]=1;
		for(int i = n-2,k=n-1;i>=0;i--) {
			h[i]=s[i]!=s[i+1]?(s[i]>s[i+1]?1:0):h[i+1];
			hi[s[i]]++;
			if(h[i]==1&&h[i+1]==0){
				h[i+1]=2;
				lms.Add(i+1);
				sub[i+1]=k-i;
				k=i+1;
			}
		}
		int lm=lms.Count;
		for(int i = 1;i<m;i++) {
			hi[i]+=hi[i-1];
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		for(int i = 0;i<lm;i++) {
			hc2[s[lms[i]]]--;
			sa[hc2[s[lms[i]]]]=lms[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[hc1[s[sa[i]-1]]]=sa[i]-1;
				hc1[s[sa[i]-1]]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]]--;
				sa[hc3[s[sa[i]-1]]]=sa[i]-1;
			}
		}
		int[] sl=new int[lm];
		for(int i = 0,j=lm-1;i<n&&j>=0;i++) {
			if(h[sa[i]]==2){sl[j]=sa[i];j--;}
		}
		int[] lmsz=new int[n];
		bool jf=false;
		int ki=0;
		for(int i = lm-2;i>=0;i--) {
			if(sub[sl[i]]==sub[sl[i+1]]){
				bool bo=false;
				for(int j = 0;j<sub[sl[i]];j++) {if(s[sl[i]+j]!=s[sl[i+1]+j]){bo=true;break;}}
				if(bo){ki++;}
				else{jf=true;}
			}
			else{ki++;}
			lmsz[sl[i]]=ki;
		}
		int[] lmsc=new int[lm];
		for(int i = lm-1;i>=0;i--) {lmsc[lm-i-1]=lmsz[lms[i]];}
		hc2[0]=hc3[0]=hi[0];
		hc1[0]=0;
		for(int i = 1;i<m;i++) {
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		if(jf){
			sl=Fu2(lmsc,ki+1);
			for(int i = 0;i<lm;i++) {sl[i]=lms[lm-1-sl[i]];}
		}
		sa=new int[n];
		for(int i = 0;i<lm;i++) {
			hc2[s[sl[i]]]--;
			sa[n-1-hc2[s[sl[i]]]]=sl[i];
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[n-1-hc1[s[sa[i]-1]]]=sa[i]-1;
				hc1[s[sa[i]-1]]++;
			}
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]]--;
				sa[n-1-hc3[s[sa[i]-1]]]=sa[i]-1;
			}
		}
		return sa;
	}
}
public class Spt{
	private readonly int[][] d;
	private readonly int[] l;
	private Func<int,int,int> Fu;
	public Spt(int[] a,bool bo){
		int n=a.Length,m=(int)Log(n,2)+1;
		d=new int[m][];
		d[0]=new int[n];
		l=new int[n+1];
		if(bo){Fu=(y,x)=>Max(y,x);}
		else{Fu=(y,x)=>Min(y,x);}
		for(int i=0;i<n;i++){
			d[0][i]=a[i];
			l[i+1]=l[i>>1]+1;
		}
		for(int i=1,k=1;i<m;i++,k<<=1){
			int p=n+1-(k<<1);
			d[i]=new int[p];
			for(int j=0;j<p;j++){d[i][j]=Fu(d[i-1][j],d[i-1][j+k]);}
		}
	}
	public int Get(int a,int b){
		if(a>b){a^=b;b^=a;a^=b;}
		int p=l[b-a];
		return Fu(d[p][a],d[p][b+1-(1<<p)]);
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}