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 \le i \le j \le |s|) of string s is string sisi+1...sj. The prefix of string s of length l (1 \le l \le |s|) is string s[1..l]. The suffix of string s of length l (1 \le l \le |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.

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

In the first line, print integer k (0 \le k \le |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.