You have a string s = s ₁ s ₂...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 _i s _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.

输入描述:

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

输出描述:

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 lici. Numbers lici 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 liciin the order of increasingli.

ABACABA
AAA

3
1 4
3 2
7 1
3
1 3
2 2
3 1