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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		char[] s = br.readLine().toCharArray();
		br.close();

		int n = s.length;
		if (s[0] == '0' || s[n - 2] == '0' || s[n - 1] == '1') {
			System.out.println(-1);
			return;
		}
		for (int i = 2; i <= n / 2; i++) {
			if (s[i - 1] != s[n - 1 - i]) {
				System.out.println(-1);
				return;
			}
		}

		PrintWriter pw = new PrintWriter(System.out);
		pw.println("1 " + n);
		int now = 1;
		for (int i = 2; i <= n / 2; i++) {
			pw.println(now + " " + i);
			if (s[i - 1] == '1') {
				now = i;
			}
		}
		for (int i = n / 2 + 1; i < n; i++) {
			pw.println(now + " " + i);
		}
		pw.flush();
	}
}