The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 175 (Div. 2) |
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Finished |

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bitmasks

combinatorics

dp

implementation

meet-in-the-middle

*1900

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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 2010-2024 Mike Mirzayanov

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