#include<iostream>
#include<vector>
using namespace std;
const long long INF = 1000000007ll;
int k[4];
void ku(int a) {
  for (int i = 3; i >= 0; i --) {
    k[i] = a % 4;
    a /= 4;
  }
}
bool ok(int a) {
  for (int i = 0; i < 4; i ++) {
    ku(a);
    if (i >= 1) swap(k[i - 1], k[i]);
    if (k[0] == 0 && k[1] == 1 && k[2] == 2) return false;
    if (k[1] == 0 && k[2] == 1 && k[3] == 2) return false;
  }
  return true;
}
int N;
vector<vector<long long>>memo(101, vector<long long>(64, -1));
long long dfs(int cur, int last3) {
  if (memo[cur][last3] != -1) return memo[cur][last3];
  if (cur == N) return 1;
  long long ret = 0;
  for (int i = 0; i < 4; i ++) {
    if (ok(last3 * 4 + i)) {
      int jun = last3 % 16;
      jun *= 4;
      jun += i;
      ret = (ret + dfs(cur + 1, jun)) % INF;
    }
  }
  memo[cur][last3] = ret;
  return ret;
}
int main () {
  cin >> N;
  cout << dfs(0, 63) << endl;
}
  

### Prompt

Please create a solution in cpp to the following problem:

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

### Response

```cpp
#include<iostream>
#include<vector>
using namespace std;
const long long INF = 1000000007ll;
int k[4];
void ku(int a) {
  for (int i = 3; i >= 0; i --) {
    k[i] = a % 4;
    a /= 4;
  }
}
bool ok(int a) {
  for (int i = 0; i < 4; i ++) {
    ku(a);
    if (i >= 1) swap(k[i - 1], k[i]);
    if (k[0] == 0 && k[1] == 1 && k[2] == 2) return false;
    if (k[1] == 0 && k[2] == 1 && k[3] == 2) return false;
  }
  return true;
}
int N;
vector<vector<long long>>memo(101, vector<long long>(64, -1));
long long dfs(int cur, int last3) {
  if (memo[cur][last3] != -1) return memo[cur][last3];
  if (cur == N) return 1;
  long long ret = 0;
  for (int i = 0; i < 4; i ++) {
    if (ok(last3 * 4 + i)) {
      int jun = last3 % 16;
      jun *= 4;
      jun += i;
      ret = (ret + dfs(cur + 1, jun)) % INF;
    }
  }
  memo[cur][last3] = ret;
  return ret;
}
int main () {
  cin >> N;
  cout << dfs(0, 63) << endl;
}
  

```