Problem: 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.

Examples

Input

1111


Output

-1


Input

1110


Output

1 2
2 3
3 4


Input

1010


Output

1 2
1 3
1 4

Solution (in JAVA):

Solution:

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));
            }
        }
    }
}