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. 
66
 652615
 482331
 336161
 33
 1000000
 79531
 768208
 3
 885131

257415584
 960319213
 722928541
 234634596
 762187807
 23581336
 162141608
 635322133
 2
 329995454

#include <bits/stdc++.h>
using namespace std;
const long long int mod = 1e9 + 7;
long long int gcd(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long bin_to_integer(string s) {
  long long r = 1, sum = 0;
  for (long long i = s.length() - 1; i >= 0; i--) {
    if (s[i] == '1') {
      sum += r;
    }
    r *= 2;
  }
  return sum;
}
string to_binary(int n) {
  string s;
  while (n > 0) {
    if (n & 1) {
      s += '1';
    } else {
      s += '0';
    }
    n >>= 1;
  }
  reverse(s.begin(), s.end());
  return s;
}
int compare(const void* a, const void* b) {
  const long long* x = (long long*)a;
  const long long* y = (long long*)b;
  if (*x > *y)
    return 1;
  else if (*x < *y)
    return -1;
  return 0;
}
long long fact(long long int x) {
  if (x == 1)
    return 1;
  else
    return ((x * fact(x - 1)) % mod);
}
void solve() {
  long long n;
  cin >> n;
  long long factril = 1, n2 = n, twopow = 1;
  while (n2 > 0) {
    factril = (factril * n2) % mod;
    n2--;
  }
  n2 = n - 1;
  while (n2--) {
    twopow = twopow * 2 % mod;
  }
  long long ans = factril - twopow;
  if (ans % mod < 0) ans += mod;
  cout << ans % mod << endl;
  return;
}
int main() {
  int t = 1, z = 1;
  while (z <= t) {
    solve();
    z++;
  }
  return 0;
}
