Connectivity

AtCoder

IDarc065_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ cities. There are also $K$ roads and $L$ railways, extending between the cities. The $i$\-th road bidirectionally connects the $p_i$\-th and $q_i$\-th cities, and the $i$\-th railway bidirectionally connects the $r_i$\-th and $s_i$\-th cities. No two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities. We will say city $A$ and $B$ are _connected by roads_ if city $B$ is reachable from city $A$ by traversing some number of roads. Here, any city is considered to be connected to itself by roads. We will also define _connectivity by railways_ similarly. For each city, find the number of the cities connected to that city by both roads and railways. ## Constraints * $2 ≦ N ≦ 2*10^5$ * $1 ≦ K, L≦ 10^5$ * $1 ≦ p_i, q_i, r_i, s_i ≦ N$ * $p_i < q_i$ * $r_i < s_i$ * When $i ≠ j$, $(p_i, q_i) ≠ (p_j, q_j)$ * When $i ≠ j$, $(r_i, s_i) ≠ (r_j, s_j)$ ## Input The input is given from Standard Input in the following format: $N$ $K$ $L$ $p_1$ $q_1$ : $p_K$ $q_K$ $r_1$ $s_1$ : $r_L$ $s_L$ [samples]

Samples

Input #1

Output #1

1 2 2 1

All the four cities are connected to each other by roads.
By railways, only the second and third cities are connected. Thus, the answers for the cities are $1, 2, 2$ and $1$, respectively.

Input #2

Output #2

1 2 2 1

Input #3

Output #3

1 1 2 1 2 2 2

API Response (JSON)

{
  "problem": {
    "name": "Connectivity",
    "description": {
      "content": "There are $N$ cities. There are also $K$ roads and $L$ railways, extending between the cities. The $i$\\-th road bidirectionally connects the $p_i$\\-th and $q_i$\\-th cities, and the $i$\\-th railway bid",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc065_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities. There are also $K$ roads and $L$ railways, extending between the cities. The $i$\\-th road bidirectionally connects the $p_i$\\-th and $q_i$\\-th cities, and the $i$\\-th railway bid...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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