{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $2 \\leq n \\leq 10^5$\n*   $s$ is a string of length $n$ consisting of `0` and `1`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$s$"},{"iden":"sample input 1","content":"1111"},{"iden":"sample output 1","content":"\\-1\n\nIt is impossible to have a connected component of size $n$ after removing one edge from a tree with $n$ vertices."},{"iden":"sample input 2","content":"1110"},{"iden":"sample output 2","content":"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 $2$."},{"iden":"sample input 3","content":"1010"},{"iden":"sample output 3","content":"1 2\n1 3\n1 4\n\nRemoving any edge will result in a connected component of size $1$ and another of size $3$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}