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;
template <class T>
bool umin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool umax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
string to_string(bool b) { return b ? "true" : "false"; }
string to_string(char c) { return string(1, c); }
string to_string(const char* second) { return string(second); }
string to_string(string second) { return second; }
template <class T>
string to_string(T v) {
  bool first = 1;
  string res;
  for (auto& x : v) {
    if (!first) res += ' ';
    first = 0;
    res += to_string(x);
  }
  return res;
}
template <class A>
void write(A x) {
  cout << to_string(x);
}
void print() { write("\n"); }
template <class H, class... T>
void print(const H& h, const T&... t) {
  write(h);
  if (sizeof...(t)) write(' ');
  print(t...);
}
const long long mod = 1e9 + 7;
const long long maxsize = 2e5 + 10;
const long long inf = 0x3f3f3f3f3f3f3f3f;
bool vis[maxsize];
long long n, m, nc;
long long a[maxsize], b[maxsize];
void solve() {
  cin >> n;
  long long fac = 1;
  long long pote = 1;
  for (long long i = 2; i <= n; i++) {
    fac *= i;
    pote *= 2ll;
    fac %= mod;
    pote %= mod;
  }
  cout << ((fac - pote) % mod + mod) % mod << "\n";
}
int main() {
  { ios_base::sync_with_stdio(false); }
  {
    cin.tie(NULL);
    cout.tie(NULL);
  }
  int t = 1;
  while (t--) solve();
  return 0;
}
