D. Prefixes and Suffixes
time limit per test
1 second
memory limit per test
256 megabytes
input
stdin
output
stdout

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