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. 
#include <bits/stdc++.h>
using namespace std;
void ingraph(vector<long long> graph[], long long m) {
  long long x, y;
  for (long long i = 0; i < m; i++) {
    cin >> x >> y;
    x--, y--;
    graph[x].push_back(y);
    graph[y].push_back(x);
  }
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
long long modmulti(long long a, long long b) {
  return ((a % 1000000007) * 1ll * (b % 1000000007)) % 1000000007;
}
long long modadd(long long a, long long b) {
  long long asdfgh =
      ((a % 1000000007) + (b % 1000000007) + 1000000007 + 1000000007) %
      1000000007;
  asdfgh = (asdfgh + 1000000007) % 1000000007;
  return asdfgh;
}
long long modpower(long long a, long long n) {
  if (n == 0) return 1;
  if (n == 1) return a % 1000000007;
  long long b = modpower(a, n / 2);
  b = modmulti(b, b);
  if (n % 2 == 0) return b;
  return modmulti(a, b);
}
long long modinv(long long a) { return modpower(a, 1000000007 - 2); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  long long n;
  cin >> n;
  long long fact[n + 5];
  fact[0] = 1;
  fact[1] = 1;
  for (int i = 2; i <= n; i++) {
    fact[i] = modmulti(fact[i - 1], i);
  }
  long long ans = modpower(2, n - 1);
  ans *= (-1);
  ans = modadd(fact[n], ans);
  cout << ans << '\n';
  return 0;
}
