{"problem":{"name":"Tr/ee","description":{"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 $1,2,..., n-1$, and Edge $i$ connects Vertex $u_i$ and $v_i$.\n*   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.\n*   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.\n\nIf such a tree exists, construct one such tree.\n\n## Constraints\n\n*   $2 \\leq n \\leq 10^5$\n*   $s$ is a string of length $n$ consisting of `0` and `1`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$s$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc103_c","tags":[],"sample_group":[["1111","\\-1\n\nIt is impossible to have a connected component of size $n$ after removing one edge from a tree with $n$ vertices."],["1110","1 2\n2 3\n3 4\n\nIf 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 $2$."],["1010","1 2\n1 3\n1 4\n\nRemoving any edge will result in a connected component of size $1$ and another of size $3$."]],"created_at":"2026-03-03 11:01:14"}}