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 <iostream>
using namespace std;
int N,memo[101][4][4][4];
int mod=1000000007;
int check(int len,int a,int b,int c){
  if(len==N)return 1;
  if(memo[len][a][b][c]>0)return memo[len][a][b][c];
  int ret = 0;
  for(int d=0;d<4;d++){
    if(b==0&&c==1&&d==2)continue;
    if(b==1&&c==0&&d==2)continue;
    if(b==0&&c==2&&d==1)continue;
    if(a==0&&c==1&&d==2)continue;
    if(a==0&&b==1&&d==2)continue;
    ret += check(len+1,b,c,d);
    ret %= mod;
  }
  memo[len][a][b][c] = ret;
  return ret;
}
int main() {
  cin>>N;
  cout<<check(0,3,3,3);
  return 0;
}
