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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
    {
    	static void Main(string[] args)
    	{
            string s = Console.ReadLine();
            
            int n = s.Length;

            if (s[n-1] == '1' || s[0] == '0' || s[n-2] == '0')
            {
                Console.WriteLine(-1);
                return;
            }

            for (int i=0; i<(n-1)/2; i++)
            {
                if (s[i] != s[n - 2 - i])
                {
                    Console.WriteLine(-1);
                    return;
                }
            }
            int count = 1;
            for (int i=0; i<n-1; i++)
            {
                int root = count;
                while (s[i] == '0')
                {
                    Console.WriteLine(root + " " + (count+1));
                    count++;
                    i++;
                }
                Console.WriteLine(root + " " + (count+1));
                count++;
            }
        }
    }