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: Time Limit Exceeded)

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

class Main {

    // Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
    public static void main(String[] args) throws Exception {
        final Scanner sc = new Scanner(System.in);
        String s;
        s = sc.next();
        solve(s);
    }

    static void solve(String s){
        String[] str = s.split("");
        int n = str.length;
        int k[] = new int[(int)n+1];
        for(int i = 1 ; i <= n ; i++) k[i] = Integer.parseInt(str[i-1]);
        if( k[1] == 0 || k[n] == 1) exit();
        for(int i = 1 ; i < (n+1)/2 ; i++){
            if(k[i] != k[n-i]) exit();
        }
        int v[] = new int[(int)n];
        for(int i = 1 ; i < n ; i++){
            for(int j = i+1 ; j < n ; j++){
                if(k[j] == 1){
                    v[i] = j;
                    break;
                }
            }
            v[n-1] = n;
            System.out.println(i + " " + v[i]);
        }
    }

    static void exit(){
        System.out.println(-1);
        System.exit(0);
    }
}