Problem Statement

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.

Input

Input is given from Standard Input in the following format:
N M

Output

Print the number of permutations modulo M.

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.

Sample Input 1

1 998244353

Sample Output 1

6

All permutations of length 3 count.

Sample Input 2

2 998244353

Sample Output 2

261

Sample Input 3

314 1000000007

Sample Output 3

182908545

见题面 Input 部分

见题面 Output 部分