Beautiful Permutations

You are given a single integer n representing the number of elements from 1 to n. A permutation of these n integers is called beautiful if the sum of absolute differences between consecutive elements is even. In other words, if P = [p₁, p₂, ..., p_n] is a permutation, it is beautiful if

$$\sum_{i=1}^{n-1} |p_{i+1} - p_i| \equiv 0 \pmod{2}. $$

It can be proven that the number of beautiful permutations of n elements is given by:

• If n is odd, the answer is n!.
• If n is even, the answer is \(\frac{n!}{2}\).

Since the answer can be very large, output it modulo \(10^9+7\). Use modular arithmetic for computing factorials and for division (when n is even) compute the division using modular inverse.

inputFormat

The input is read from stdin and consists of a single integer n (1 ≤ n ≤ 10⁵).

outputFormat

Output the number of beautiful permutations modulo \(10^9+7\> to stdout.

## sample

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