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G. Palindrome Partition

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGiven a string *s*, find the number of ways to split *s* to substrings such that if there are *k* substrings (*p*_{1}, *p*_{2}, *p*_{3}, ..., *p*_{k}) in partition, then *p*_{i} = *p*_{k - i + 1} for all *i* (1 ≤ *i* ≤ *k*) and *k* is even.

Since the number of ways can be large, print it modulo 10^{9} + 7.

Input

The only line of input contains a string *s* (2 ≤ |*s*| ≤ 10^{6}) of even length consisting of lowercase Latin letters.

Output

Print one integer, the number of ways of partitioning the string modulo 10^{9} + 7.

Examples

Input

abcdcdab

Output

1

Input

abbababababbab

Output

3

Note

In the first case, the only way to partition the string is *ab*|*cd*|*cd*|*ab*.

In the second case, the string can be partitioned as *ab*|*b*|*ab*|*ab*|*ab*|*ab*|*b*|*ab* or *ab*|*b*|*abab*|*abab*|*b*|*ab* or *abbab*|*ab*|*ab*|*abbab*.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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