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
from collections import defaultdict
MOD=10**9+7
def swaps(s):
    for i in xrange(1, len(s)):
        yield s[:i-1]+s[i]+s[i-1]+s[i+1:]

n=int(raw_input())
cur={'':1}
for i in xrange(1, n+1):
    new = defaultdict(int)
    for k, v in cur.iteritems():
        for c in 'ACGT':
            k_ = (k+c)[-5:]
            if 'AGC' in k_ or any('AGC' in s for s in swaps(k_)): continue
            new[k_] = (new[k_]+v)%MOD
    #print(new)
    cur = new

total=0
for v in cur.itervalues():
    total = (total+v)%MOD
print(total)
