Wrong Algorithm

Lorenzo devised an innovative yet incorrect algorithm to count the number of inversions\footnote{An inversion for an array $A_0, \ldots, A_{N - 1}$ is a pair $(i, j)$ such that $0 \le i < j \le N - 1$ and $A_i > A_j$.} for any given permutation of $N$ elements.

Full of optimism, he computed this number for a permutation $P_0, \ldots, P_{N - 1}$ simply as the sum

Task

Unfortunately his formula has some flaws and the algorithm fails to consistently produce the correct output. Lorenzo is now wondering how often his algorithm yields the wrong answer: help him by counting the number of permutations for which his algorithm fails in computing the number of inversions!

Since the answer might be quite large, you are asked to print it modulo $10^9 + 7$.

Input data

The input file consists of a line containing integer $N$.

Output data

The output file must contain a single line consisting of integer $S$.

Constraints and clarifications

• $1 \leq N \leq 10^6$

Example 1

stdin

3

stdout

1

Explanation

In the first sample case, Lorenzo's algorithm computes an incorrect value only for the permutation $[2, 1, 0]$.

Example 2

stdin

4

stdout

10