Tr/ee

AtCoder

IDarc103_c

Time2000ms

Memory256MB

Difficulty—

You are given a string $s$ of length $n$. 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 $v_i$. * If the $i$\-th character in $s$ is `1`, we can have a connected component of size $i$ by removing one edge from the tree. * If the $i$\-th character in $s$ is `0`, we cannot have a connected component of size $i$ by removing any one edge from the tree. If such a tree exists, construct one such tree. ## Constraints * $2 \leq n \leq 10^5$ * $s$ is a string of length $n$ consisting of `0` and `1`. ## Input Input is given from Standard Input in the following format: $s$ [samples]

Samples

Input #1

Output #1

\-1

It is impossible to have a connected component of size $n$ after removing one edge from a tree with $n$ vertices.

Input #2

Output #2

1 2
2 3
3 4

If Edge $1$ or Edge $3$ is removed, we will have a connected component of size $1$ and another of size $3$. If Edge $2$ is removed, we will have two connected components, each of size $2$.

Input #3

Output #3

1 2
1 3
1 4

Removing any edge will result in a connected component of size $1$ and another of size $3$.

API Response (JSON)

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    "name": "Tr/ee",
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      "content": "You are given a string $s$ of length $n$. 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,...,",
      "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_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $s$ of length $n$. Does a tree with $n$ vertices that satisfies the following conditions exist?\n\n*   The vertices are numbered $1,2,..., n$.\n*   The edges are numbered $1,2,...,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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