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.util.Scanner;

public class Main {
    public static void main(final String [] args) {
        final Scanner scanner = new Scanner(System.in);
        final String input = scanner.next();
        if (input.charAt(0) != '1' || input.charAt(input.length() - 1) != '0') {
            System.out.println(-1);
            return;
        }
        for (int i = 0, j = input.length() - 2; i < j; ++i, --j) {
            if (input.charAt(i) != input.charAt(j)) {
                System.out.println(-1);
                return;
            }
        }
        int currentEnd = 1;
        for (int i = 1; i < input.length(); ++i) {
            if (input.charAt(i - 1) == '1') {
                System.out.println(currentEnd + " " + (i + 1));
                currentEnd = (i + 1);
            } else {
                System.out.println(currentEnd + " " + (i + 1));
            }
        }
    }
}