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;
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
double distance(int x1, int y1, int x2, int y2) {
  return sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2) * 1.0);
}
const int mod = 1e9 + 7;
int factorial(int n) {
  return (n == 1 || n == 0) ? 1 : (n + mod) % mod * factorial(n - 1);
}
bool comp(pair<int, double> a, pair<int, double> b) {
  if (a.second == b.second) return a.first < b.first;
  return a.second > b.second;
}
const int X[] = {1, 0, -1, 0, 1, 1, -1, -1};
const int Y[] = {0, 1, 0, -1, 1, -1, 1, -1};
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) {
    long long n;
    cin >> n;
    long long nas = 0;
    long long u = 1;
    for (long long i = 2; i <= n; i++) {
      u = ((u % mod) * (i % mod)) % mod;
      u %= mod;
    }
    long long h = 1;
    for (long long i = 1; i <= n - 1; i++) {
      h = ((h % mod) * (2)) % mod;
      h %= mod;
    }
    nas = u - h;
    nas = (nas + mod) % mod;
    cout << nas << '\n';
  }
  return 0;
}
