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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.PrintWriter;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		char[] s = sc.next().toCharArray();
		int N = s.length;
		
		int[] parent = makeTree(s, N);
		if(parent==null) {
			pw.println(-1);
		} else {
			for(int i=0; i<N; i++) {
				if(parent[i]<0)
					continue;
				pw.println((i+1) + " " + (parent[i]+1));
			}
		}
		sc.close();
		pw.close();
	}
	
	static int[] makeTree(char[] s, int N) {
		if(s[N-1]=='1' || s[0]=='0' || s[N-2]=='0')
			return null;
		for(int i=1; i<N/2; i++)
			if(s[i]!=s[N-i-2])
				return null;
		
		int[] ans = new int[N];
		int p = 0;
		ans[1] = 0;
		for(int i=2; i<N/2+1; i++) {
			if(s[i-1]=='1') {
				ans[p] = i;
				p = i;
			} else {
				ans[i] = p;
			}
		}
		for(int i=N/2; i<N; i++)
			ans[i] = p;
		ans[p] = -1;
		return ans;
	}
}