Score : $700$ points

Problem Statement

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:

$s$

Output

If a tree with $n$ vertices that satisfies the conditions does not exist, print -1.

If a tree with $n$ vertices that satisfies the conditions exist, print $n-1$ lines. The $i$-th line should contain $u_i$ and $v_i$ with a space in between. If there are multiple trees that satisfy the conditions, any such tree will be accepted.

1111

-1

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

1110

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 $2$.

1010

1 2
1 3
1 4

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