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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string s = Console.ReadLine();
		int n = s.Length;
    bool answer = true;
    if(s[n-1] == '1') answer = false;
    if(s[0] == '0') answer = false;
    int[][] answers = new int[n-1][];

    for(int i = 0; i < n-1; i++)
    {
      if(s[i] != s[n-2-i]) answer = false;
      answers[i] = new int[2];
    }

    if(!answer) Console.WriteLine(-1);
    else
    {
      answers[0][0] = 1;
      answers[0][1] = 2;
      int nowVertex = 2;
      for(int i = 1; i < n-1; i++)
      {
        answers[i][0] = nowVertex;
        answers[i][1] = i+2;
        if(s[i] == '1')
        {
          nowVertex = i+2;
        }
      }

      var answerText = new StringBuilder();
      for(long i = 0; i < answers.Length; i++)
      {
        answerText.AppendLine(string.Join(" ", answers[i]));
      }
      Console.Write(answerText);
    }
	}
}