You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:

* The string does not contain characters other than `A`, `C`, `G` and `T`.
* The string does not contain `AGC` as a substring.
* The condition above cannot be violated by swapping two adjacent characters once.

Constraints

* 3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:


N


Output

Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.

Examples

Input

3


Output

61


Input

4


Output

230


Input

100


Output

388130742
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 1000000007
#define A 1
#define C 2
#define G 3
#define T 4
ll dp(int i,int a,int b,int c);
ll memo[109][5][5][5];
int n;

int main(){
  memset(memo,-1,sizeof(memo));
  cin>>n;
  cout<<dp(0,0,0,0)<<endl;
  return(0);
}

ll dp(int i,int a,int b,int c){
  ll rec=0;
  if(memo[i][a][b][c]!=-1)return memo[i][a][b][c];
  if(i==n)return 1;
  rec+=dp(i+1,b,c,A);
  if(!(b==A&&c==G)&&!(a==A&&b==G)&&!(a==A&&c==G)&&!(b==G&&c==A)){
    rec+=dp(i+1,b,c,C);
  }
  if(!(b==A&&c==C)){
    rec+=dp(i+1,b,c,G);
  }
  rec+=dp(i+1,b,c,T);
  return memo[i][a][b][c]=rec%mod;
}

// AGC
//AG C
//A GC
// GAC
// ACG
