Distance Pairs

AtCoder

IDcodefestival_2016_ex_a

Time2000ms

Memory256MB

Difficulty—

There is an undirected connected graph with $N$ vertices numbered $1$ through $N$. The lengths of all edges in this graph are $1$. It is known that for each $i (1≦i≦N)$, the distance between vertex $1$ and vertex $i$ is $A_i$, and the distance between vertex $2$ and vertex $i$ is $B_i$. Determine whether there exists such a graph. If it exists, find the minimum possible number of edges in it. ## Constraints * $2≦N≦10^5$ * $0≦A_i,B_i≦N-1$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ : $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

4

The figure below shows two possible graphs. The graph on the right has fewer edges.
![image](https://atcoder.jp/img/code-festival-2016-final/dd1e04d837fd7fc1be56b231cd8c2a17.png)

Input #2

Output #2

\-1

Such a graph does not exist.

API Response (JSON)

{
  "problem": {
    "name": "Distance Pairs",
    "description": {
      "content": "There is an undirected connected graph with $N$ vertices numbered $1$ through $N$. The lengths of all edges in this graph are $1$. It is known that for each $i (1≦i≦N)$, the distance between vertex $1",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "codefestival_2016_ex_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an undirected connected graph with $N$ vertices numbered $1$ through $N$. The lengths of all edges in this graph are $1$. It is known that for each $i (1≦i≦N)$, the distance between vertex $1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments