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D. Permutation Sum

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPermutation *p* is an ordered set of integers *p*_{1}, *p*_{2}, ..., *p*_{n}, consisting of *n* distinct positive integers, each of them doesn't exceed *n*. We'll denote the *i*-th element of permutation *p* as *p*_{i}. We'll call number *n* the size or the length of permutation *p*_{1}, *p*_{2}, ..., *p*_{n}.

Petya decided to introduce the sum operation on the set of permutations of length *n*. Let's assume that we are given two permutations of length *n*: *a*_{1}, *a*_{2}, ..., *a*_{n} and *b*_{1}, *b*_{2}, ..., *b*_{n}. Petya calls the sum of permutations *a* and *b* such permutation *c* of length *n*, where *c*_{i} = ((*a*_{i} - 1 + *b*_{i} - 1) *mod* *n*) + 1 (1 ≤ *i* ≤ *n*).

Operation means taking the remainder after dividing number *x* by number *y*.

Obviously, not for all permutations *a* and *b* exists permutation *c* that is sum of *a* and *b*. That's why Petya got sad and asked you to do the following: given *n*, count the number of such pairs of permutations *a* and *b* of length *n*, that exists permutation *c* that is sum of *a* and *b*. The pair of permutations *x*, *y* (*x* ≠ *y*) and the pair of permutations *y*, *x* are considered distinct pairs.

As the answer can be rather large, print the remainder after dividing it by 1000000007 (10^{9} + 7).

Input

The single line contains integer *n* (1 ≤ *n* ≤ 16).

Output

In the single line print a single non-negative integer — the number of such pairs of permutations *a* and *b*, that exists permutation *c* that is sum of *a* and *b*, modulo 1000000007 (10^{9} + 7).

Examples

Input

3

Output

18

Input

5

Output

1800

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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