Given is a positive integer N. Find the number of permutations (P_1,P_2,\cdots,P_{3N}) of (1,2,\cdots,3N) that can be generated through the procedure below. This number can be enormous, so print it modulo a prime number M.

* Make N sequences A_1,A_2,\cdots,A_N of length 3 each, using each of the integers 1 through 3N exactly once.
* Let P be an empty sequence, and do the following operation 3N times.
* Among the elements that are at the beginning of one of the sequences A_i that is non-empty, let the smallest be x.
* Remove x from the sequence, and add x at the end of P.

Constraints

* 1 \leq N \leq 2000
* 10^8 \leq M \leq 10^9+7
* M is a prime number.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M


Output

Print the number of permutations modulo M.

Examples

Input

1 998244353


Output

6


Input

2 998244353


Output

261


Input

314 1000000007


Output

182908545
N,M=map(int,input().split())

dp=[[0 for i in range(2*N+1)] for j in range(3*N+1)]

for j in range(N+1):
    dp[0][j]=1

for i in range(1,3*N+1):
    for j in range(2*N+1):
        if 2*N-1>=j>=1:
            dp[i][j]=(dp[i-1][j-1]+dp[i-2][j+1]*(i-1)+dp[i-3][j]*(i-1)*(i-2))%M
        elif j==0:
            dp[i][j]=(dp[i-1][j]+dp[i-2][j+1]*(i-1)+dp[i-3][j]*(i-1)*(i-2))%M
        else:
            dp[i][j]=(dp[i-1][j-1]+dp[i-3][j]*(i-1)*(i-2))%M

print(dp[3*N][N]%M)
