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, MOD = map(int, input().split())

n3 = n * 3
dp = [[0] * int(i * 1.5 + 5) for i in range(n3 + 1)]
dp[0][0] = dp[1][1] = dp[2][2] = dp[2][-1] = 1

for i in range(3, n3 + 1):
    i12 = (i - 1) * (i - 2)
    dpi3, dpi2, dpi1, dpi = dp[i - 3:i + 1]
    for j in range(-(i // 2), i + 1):
        tmp = dpi3[j] * i12
        tmp += dpi2[j + 1] * (i - 1)
        tmp += dpi1[j - 1]
        dpi[j] = tmp % MOD

print(sum(dp[-1][:n3 + 1]) % MOD)
