1 or 2

AtCoder

IDabc126_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ cards placed face down in a row. On each card, an integer $1$ or $2$ is written. Let $A_i$ be the integer written on the $i$\-th card. Your objective is to guess $A_1, A_2, ..., A_N$ correctly. You know the following facts: * For each $i = 1, 2, ..., M$, the value $A_{X_i} + A_{Y_i} + Z_i$ is an even number. You are a magician and can use the following magic any number of times: **Magic**: Choose one card and know the integer $A_i$ written on it. The cost of using this magic is $1$. What is the minimum cost required to determine all of $A_1, A_2, ..., A_N$? It is guaranteed that there is no contradiction in given input. ## Constraints * All values in input are integers. * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq X_i < Y_i \leq N$ * $1 \leq Z_i \leq 100$ * The pairs $(X_i, Y_i)$ are distinct. * There is no contradiction in input. (That is, there exist integers $A_1, A_2, ..., A_N$ that satisfy the conditions.) ## Input Input is given from Standard Input in the following format: $N$ $M$ $X_1$ $Y_1$ $Z_1$ $X_2$ $Y_2$ $Z_2$ $\vdots$ $X_M$ $Y_M$ $Z_M$ [samples]

Samples

Input #1

3 1
1 2 1

Output #1

2

You can determine all of $A_1, A_2, A_3$ by using the magic for the first and third cards.

Input #2

Output #2

Input #3

100000 1
1 100000 100

Output #3

API Response (JSON)

{
  "problem": {
    "name": "1 or 2",
    "description": {
      "content": "There are $N$ cards placed face down in a row. On each card, an integer $1$ or $2$ is written. Let $A_i$ be the integer written on the $i$\\-th card. Your objective is to guess $A_1, A_2, ..., A_N$ cor",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc126_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cards placed face down in a row. On each card, an integer $1$ or $2$ is written.\nLet $A_i$ be the integer written on the $i$\\-th card.\nYour objective is to guess $A_1, A_2, ..., A_N$ cor...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments