Distance Sums

AtCoder

IDarc103_d

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $D_1, D_2, ..., D_N$ of length $N$. **The values of $D_i$ are all distinct.** Does a tree with $N$ vertices that satisfies the following conditions exist? * The vertices are numbered $1,2,..., N$. * The edges are numbered $1,2,..., N-1$, and Edge $i$ connects Vertex $u_i$ and $v_i$. * For each vertex $i$, the sum of the distances from $i$ to the other vertices is $D_i$, assuming that the length of each edge is $1$. If such a tree exists, construct one such tree. ## Constraints * $2 \leq N \leq 100000$ * $1 \leq D_i \leq 10^{12}$ * $D_i$ are all distinct. ## Input Input is given from Standard Input in the following format: $N$ $D_1$ $D_2$ $:$ $D_N$ [samples]

Samples

Input #1

Output #1

1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.
![image](https://img.atcoder.jp/arc103/92920696862ead4cacf3755c3c8135e0.png)

Input #2

2
1
2

Output #2

\-1

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Distance Sums",
    "description": {
      "content": "You are given a sequence $D_1, D_2, ..., D_N$ of length $N$. **The values of $D_i$ are all distinct.** Does a tree with $N$ vertices that satisfies the following conditions exist? *   The vertices ar",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc103_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $D_1, D_2, ..., D_N$ of length $N$. **The values of $D_i$ are all distinct.** Does a tree with $N$ vertices that satisfies the following conditions exist?\n\n*   The vertices ar...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments