p03088 AtCoder Beginner Contest 122 - We Like AGC
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
```python
N = int(input())
memo = [{} for i in range(N + 1)]
MOD = 10 ** 9 + 7

def ok(last4):
    
    
    for i in range(4):
        t = list(last4)
        if i >= 1:
            t[i], t[i - 1] = t[i - 1], t[i]
        if "".join(t).count("AGC") >= 1:
            return False
        
    return True
        

def dfs(cur, last3):
    if last3 in memo[cur]:
        return memo[cur][last3]
    if cur == N:
        return 1
    ret = 0
    for c in "ACGT":
        if ok(last3 + c):
            ret = ret + dfs(cur + 1, last3[1:] + c)
    memo[cur][last3] = ret
    return ret

print(dfs(0, "TTT") % MOD)
```