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.

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