>=<

AtCoder

IDarc146_d

Time4000ms

Memory256MB

Difficulty—

A _fantastic IS_ is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition. * For every integer $i$ such that $1 \le i \le K$, one of the following holds. * $A_{P_i} < X_i$ and $A_{Q_i} < Y_i$; * $A_{P_i} = X_i$ and $A_{Q_i} = Y_i$; * $A_{P_i} > X_i$ and $A_{Q_i} > Y_i$. Determine whether a fantastic IS exists. If it does, find the minimum possible sum of the elements in a fantastic IS. ## Constraints * $1 \le N,M,K \le 2 \times 10^5$ * $1 \le P_i,Q_i \le N$ * $1 \le X_i,Y_i \le M$ * $P_i \neq Q_i$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ $P_1$ $X_1$ $Q_1$ $Y_1$ $P_2$ $X_2$ $Q_2$ $Y_2$ $\vdots$ $P_K$ $X_K$ $Q_K$ $Y_K$ [samples]

Samples

Input #1

Output #1

6

$A=(2,3,1)$ fully satisfies the condition and thus is a fantastic IS, whose sum of the elements is $6$.
There is no fantastic IS whose sum of the elements is less than $6$, so the answer is $6$.

Input #2

2 2 2
1 1 2 2
2 1 1 2

Output #2

\-1

There is no fantastic IS, so $-1$ should be printed.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": ">=<",
    "description": {
      "content": "A _fantastic IS_ is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition. *   For every integer $i$ such that $1 \\le i \\le K",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc146_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A _fantastic IS_ is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition.\n\n*   For every integer $i$ such that $1 \\le i \\le K...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments