Problem: Omkar and Akmar are playing a game on a circular board with n (2 ≤ n ≤ 10^6) cells. The cells are numbered from 1 to n so that for each i (1 ≤ i ≤ n-1) cell i is adjacent to cell i+1 and cell 1 is adjacent to cell n. Initially, each cell is empty.

Omkar and Akmar take turns placing either an A or a B on the board, with Akmar going first. The letter must be placed on an empty cell. In addition, the letter cannot be placed adjacent to a cell containing the same letter. 

A player loses when it is their turn and there are no more valid moves.

Output the number of possible distinct games where both players play optimally modulo 10^9+7. Note that we only consider games where some player has lost and there are no more valid moves.

Two games are considered distinct if the number of turns is different or for some turn, the letter or cell number that the letter is placed on were different.

A move is considered optimal if the move maximizes the player's chance of winning, assuming the other player plays optimally as well. More formally, if the player who has to move has a winning strategy, they have to make a move after which they will still have a winning strategy. If they do not, they can make any move.

Input

The only line will contain an integer n (2 ≤ n ≤ 10^6) — the number of cells on the board.

Output

Output a single integer — the number of possible distinct games where both players play optimally modulo 10^9+7.

Examples

Input


2


Output


4


Input


69420


Output


629909355


Input


42069


Output


675837193

Note

For the first sample case, the first player has 4 possible moves. No matter what the first player plays, the second player only has 1 possible move, so there are 4 possible games.

Solution (in CPP):

Solution:
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <vector>
#include <string>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <utility>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
using namespace std;

#ifdef DBG
  #define dbg 1
  #define dpf(...) fprintf(stderr, __VA_ARGS__);fflush(stderr);
#else
  #define dbg 0
  #define dpf(...) 42
#endif
 
#define SIZE(c) int((c).size())
#define REP(i,c) for(auto &i : (c))
#define ALL(c) (c).begin(),(c).end()
#define pb push_back
#define eb emplace_back
typedef long long i64;
typedef unsigned long long u64;
const double EPS = 1e-12;
const int INF = 1e9 + 10;
typedef vector<int> VI;
typedef vector<string> VS;
typedef pair<int, int> PI;

template <typename T>
using MinPQ = priority_queue<T, vector<T>, greater<T>>;

// Input: a, b. Sets x, y: ax+by=GCD(a,b).
// Returns: GCD(a,b), may be negative.
// Tested:
//   https://codeforces.com/contest/1500/submission/109926787
i64 GcdExt(i64 a,i64 b,i64 &x,i64 &y) {
    if(b==0) {
        x=1;y=0;
        return a;
    }
    i64 d=GcdExt(b,a%b,x,y);
    i64 tmp=y;
    y=x-y*(a/b);
    x=tmp;
    return d;
}

// Tested:
//   https://codeforces.com/contest/1525/submission/116969426
struct ModInt {
  static constexpr int MOD= 1e9+7 ;

  int v=0;

  ModInt() {}
  ModInt(i64 x) {
    v = x % MOD;
    if (v < 0) v += MOD;
  }

  ModInt& operator+=(const ModInt& r) { v+=r.v; if(v>=MOD) v-=MOD; return *this; }
  ModInt& operator-=(const ModInt& r) { v-=r.v; if(v<0) v+=MOD; return *this; }
  ModInt& operator*=(const ModInt& r) { v=((i64)v*r.v)%MOD; return *this; }
  ModInt& operator/=(const ModInt& r) { *this*=r.Inv(); return *this; }

  friend ModInt operator+(ModInt l, const ModInt& r) { l+=r; return l; } 
  friend ModInt operator-(ModInt l, const ModInt& r) { l-=r; return l; } 
  friend ModInt operator*(ModInt l, const ModInt& r) { l*=r; return l; }
  friend ModInt operator/(ModInt l, const ModInt& r) { l/=r; return l; }

  ModInt Inv() const {
    i64 x, y;
    assert(GcdExt(v, MOD, x, y) == 1);
    return x;
  }

  ModInt Pow(int n) {
    if (!n) return 1;
    ModInt r = Pow(n >> 1);
    r *= r;
    if (n & 1) r *= v;
    return r;
  }
};

const int MAXN=1e6+5;

int n;

void Init() {
  int n;
  int sg[MAXN][2];
  n=20;
  sg[0][0]=0;sg[0][1]=0;
  sg[1][0]=1;sg[1][1]=0;
  VI nxt;
  for(int i=2;i<=n;++i) {
    for(int j=0;j<=1;++j) {
      nxt.clear();
      for(int i2=0;i2<i;++i2) {
        for(int j2=0;j2<=1;++j2) {
          if(i2==0 && j2==0) continue;
          if(i2==i-1 && j2==j) continue;
          int sg0=sg[i2][j2],sg1=sg[i-1-i2][j^j2];
          nxt.pb(sg0^sg1);
        }
      }
      sort(ALL(nxt));
      nxt.resize(unique(ALL(nxt))-nxt.begin());

      int w=0;
      REP(x, nxt) {
        if(w!=x) break;
        ++w;
      }
      sg[i][j]=w;
    }
    dpf("%d: %d %d\n",i,sg[i][0],sg[i][1]);
  }
}

void Solve() {
  scanf("%d",&n);
  ModInt ans;
  --n;
  int i0 = 1 - n % 2;

  ModInt u;  // C(n-i+1, i)
  if(i0==0) u=1; else u=n;
  ModInt v=1;  // (n-i)!
  for(int i=n-i0;i>=1;--i) v*=i;
  for(int i=i0;;i++) {
    int x=n-i+1;
    if(x<i) break;
    if (i > i0) {
      u/=n-i+2;
      u/=i;
      u*=n-i*2+3;
      u*=n-i*2+2;

      v/=n-i+1;
    }
    if((i-i0)%2==0) {
      ans+=u*v;
      // dpf("%d %d : %d %d : %d\n", n,i,u.v,v.v, ans.v);
    }
  } 

  // dpf("%d\n",ans.v);
  ans*=(n+1)*2;
  printf("%d\n",ans.v);
}

int main() {
  int t=1;
  for (int i = 1; i <= t; ++i) {
    Solve();
  }

  return 0;
}