Problem:
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.

Sample Input 1

1111

Sample Output 1

-1

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

Sample Input 2

1110

Sample 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.

Sample Input 3

1010

Sample 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.

Solution in JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

(function(input) {
  'use strict';
  const lines = input.split("\n")
  lines.forEach(line => {
    if(!line) return
    const S = line.split('')
    const length = S.length
    if (S[length-1] != '0' || S[0] != '1') {
      console.log('-1')
      return
    }
    let i = 1
    while(true) {
      if (i == length-2) break
      if (S[i] != S[length-i-2]) {
        console.log('-1')
        return
      }
      i++
    }

    console.log('1 2')
    let j = 2
    let curVertice = 3
    while(true) {
      if (j >= length) break
      let next = j - 2
      while(true) {
        if ( S[next] == '1') break
        next-- 
      }
      const addCount = j - next - 1
      for(let k=0; k<addCount; k++)
      {
        console.log(`${j} ${curVertice}`)
        curVertice++
      }
      console.log(`${j} ${curVertice}`)
      j=curVertice
    }
    
  });
  
})(require('fs').readFileSync('/dev/stdin', 'utf8'))