CodeForces 432D Prefixes and Suffixes

Description

You have a string s = s₁s₂...s_|s|, where |s| is the length of string s, and s_i its i-th character.

Let's introduce several definitions:

• A substring s[i..j](1 ≤ i ≤ j ≤ |s|) of string s is string s_is_i + 1...s_j.
• The prefix of string s of length l(1 ≤ l ≤ |s|) is string s[1..l].
• The suffix of string s of length l(1 ≤ l ≤ |s|) is string s[|s| - l + 1..|s|].

Your task is, for any prefix of string s which matches a suffix of string s, print the number of times it occurs in string s as a substring.

Input

The single line contains a sequence of characters s₁s₂...s_|s|(1 ≤ |s| ≤ 10⁵) — string s. The string only consists of uppercase English letters.

Output

In the first line, print integer k(0 ≤ k ≤ |s|) — the number of prefixes that match a suffix of string s. Next print k lines, in each line print two integers l_ic_i. Numbers l_ic_i mean that the prefix of the length l_i matches the suffix of length l_i and occurs in string s as a substring c_itimes. Print pairs l_ic_iin the order of increasingl_i.

Sample Input

Input

ABACABA

Output

3
1 4
3 2
7 1

Input

AAA

Output

3
1 3
2 2
3 1

前缀和后缀，当然是kmp算法的应用，我竟然想了好久

#include<map>
#include<set>
#include<stack>
#include<queue>
#include<cmath>
#include<vector>
#include<cstdio>
#include<string>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define  inf 0x0f0f0f0f

using namespace std;

char p[100000+10];
int f[100000+10],a[100000+10],dp[100000+10];
void getf()
{
    int m=strlen(p);
    f[0]=f[1]=0;
    for (int i=1;i<m;i++)
    {
        int j=f[i];
        while(j && p[i]!=p[j]) j=f[j];
        f[i+1]=(p[i]==p[j]?j+1:0);
    }
}

int main()
{
    scanf("%s",p);
    getf();
    int L=strlen(p);
    int i=L,k=0;
    while(f[i]>0)
    {
        if (f[i])
        {
            a[k++]=f[i];
        }
        i=f[i];
    }
    printf("%d
",k+1);
    memset(dp,0,sizeof(dp));
    for (int i=L;i>=0;i--)
    {
        dp[i]++;
        dp[f[i]]+=dp[i];
    }
    for (int i=k-1;i>=0;i--)
    {
        printf("%d %d
",a[i],dp[a[i]]);
    }
    printf("%d 1",L);
    return 0;
}

作者 chensunrise