Max Permutation

AtCoder

IDarc176_c

Time2000ms

Memory256MB

Difficulty—

Print the number, modulo $998244353$, of permutations $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$ that satisfy all of the following conditions: * $\max(P_{A_i},P_{B_i}) = C_i\ (1 \le i \le M)$. ## Constraints * $2 \le N \le 2 \times 10^5$ * $1 \le M \le 2 \times 10^5$ * $1 \le A_i < B_i \le N$ * $1 \le C_i \le N$ * $(A_i,B_i) \neq (A_j,B_j)$ if $i \neq j$. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $C_1$ $A_2$ $B_2$ $C_2$ $\vdots$ $A_M$ $B_M$ $C_M$ [samples]

Samples

Input #1

4 2
1 2 4
2 3 2

Output #1

2

The two permutations $P$ that satisfy the conditions are $(4,1,2,3)$ and $(4,2,1,3)$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Max Permutation",
    "description": {
      "content": "Print the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ that satisfy all of the following conditions: *   $\\max(P_{A_i},P_{B_i}) = C_i\\ (1 \\le i \\le M)$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc176_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Print the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ that satisfy all of the following conditions:\n\n*   $\\max(P_{A_i},P_{B_i}) = C_i\\ (1 \\le i \\le M)$.\n\n## ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments