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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string str = Console.ReadLine();
		long[]A = new long[str.Length];
		for(var i=0;i<str.Length;i++){
			A[i] = long.Parse(str.Substring(i,1));
		}
		long ans = 0;
		if(A[0] == 0){
			ans = -1;
		}
		if(A[str.Length-1] == 1){
			ans = -1;
		}
		if(str.Length % 2 == 0){
			for(var i=0;i<str.Length/2;i++){
				if(A[i] != A[str.Length-2-i]){
					ans = -1;
					break;
				}
			}
		} else {
			for(var i=0;i<(str.Length-1)/2;i++){
				if(A[i] != A[str.Length-2-i]){
					ans = -1;
					break;
				}
			}
		}
		if(ans == -1){
			Console.WriteLine(ans);
		} else {
			long act = 2;
			long[,] D = new long[str.Length-1,2];
			for(var i=0;i<str.Length-1;i++){
				D[i,0] = 1;
				D[i,1] = i+2;
			}
			for(var i=(str.Length-2)/2;i>0;i--){
				if(A[i] == 1){
					for(var j=(str.Length-2)/2;j>=(str.Length-2)/2-i+1;j--){
						D[j,0] = act;
					}
				}
				act += 1;
			}
			for(var i=0;i<str.Length-1;i++){
				Console.WriteLine(D[i,0]+" "+D[i,1]);
			}
		}
	}
}