Problem3030--Prefixes and Suffixes

3030: Prefixes and Suffixes

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

Let's introduce several definitions:

  • A substring s[i..j] (1≤i≤j≤|s|) of string s is string sisi+1...sj.
  • 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 li ci. Numbers li ci mean that the prefix of the length li matches the suffix of length li and occurs in string s as a substring ci times. Print pairs li ci in the order of increasing li.

Examples
Input
ABACABA
Output
3
1 4
3 2
7 1
Input
AAA
Output
3
1 3
2 2
3 1

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