A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

Consider a permutation p of length n, we build a graph of size n using it as follows: 

  * For every 1 ≤ i ≤ n, find the largest j such that 1 ≤ j < i and p_j > p_i, and add an undirected edge between node i and node j 
  * For every 1 ≤ i ≤ n, find the smallest j such that i < j ≤ n and p_j > p_i, and add an undirected edge between node i and node j 



In cases where no such j exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices.

For clarity, consider as an example n = 4, and p = [3,1,4,2]; here, the edges of the graph are (1,3),(2,1),(2,3),(4,3).

A permutation p is cyclic if the graph built using p has at least one simple cycle. 

Given n, find the number of cyclic permutations of length n. Since the number may be very large, output it modulo 10^9+7.

Please refer to the Notes section for the formal definition of a simple cycle

Input

The first and only line contains a single integer n (3 ≤ n ≤ 10^6).

Output

Output a single integer 0 ≤ x < 10^9+7, the number of cyclic permutations of length n modulo 10^9+7.

Examples

Input


4


Output


16

Input


583291


Output


135712853

Note

There are 16 cyclic permutations for n = 4. [4,2,1,3] is one such permutation, having a cycle of length four: 4 → 3 → 2 → 1 → 4.

Nodes v_1, v_2, …, v_k form a simple cycle if the following conditions hold: 

  * k ≥ 3. 
  * v_i ≠ v_j for any pair of indices i and j. (1 ≤ i < j ≤ k) 
  * v_i and v_{i+1} share an edge for all i (1 ≤ i < k), and v_1 and v_k share an edge. 
import sys
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s); sys.stdout.write('\n')
def wi(n): sys.stdout.write(str(n)); sys.stdout.write('\n')
def wia(a, sep=' '): sys.stdout.write(sep.join([str(x) for x in a])); sys.stdout.write('\n')


from itertools import permutations
from collections import deque


def has_cycle(n, g):
    for start in range(n):
        prev = [-1] * n
        t = [-1] * n

        q = deque()
        q.append(start)
        t[start] = 0

        while q:
            v = q.popleft()

            for w in g[v]:
                if t[w] != -1:
                    if t[w] >= t[v]:
                        return True
                else:
                    t[w] = t[v] + 1
                    prev[w] = v
                    q.append(w)
    return False


def test(n, a):
    g = [[] for _ in range(n)]
    for i in range(n):
        j = i - 1
        while j >= 0 and a[j] < a[i]:
            j -= 1
        if j >= 0:
            g[i].append(j)
            g[j].append(i)
        j = i + 1
        while j < n and a[j] < a[i]:
            j += 1
        if j < n:
            g[i].append(j)
            g[j].append(i)
    return has_cycle(n, g)


def main():
    m = 1000000007
    n = ri()

    ans = 1

    for i in range(1, n + 1):
        ans = (ans * i) % m

    p2 = 1
    for i in range(n-1):
        p2 = (p2 * 2) % m

    ans = (ans - p2) % m

    wi(ans)
    return


    # for n in range(3, 10):
    #     a = [i + 1 for i in range(n)]
    #
    #     cnt = 0
    #     for p in permutations(a):
    #         if test(n, p):
    #             cnt += 1
    #
    #     wia([n, cnt])


if __name__ == '__main__':
    main()
