CF285D Permutation Sum

Permutation $ 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

The single line contains integer $ n\ (1

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 $ ).