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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String s = sc.next();
        int N = s.length();
        char[] c = s.toCharArray();
        if (c[0]=='0' || c[N-2]=='0' || c[N-1]=='1') {
            System.out.println(-1);
            return;
        }
        int NN = N-1;
        for (int i=0;i<NN/2;i++) {
            if (c[i]!=c[NN-1-i]) {
                System.out.println(-1);
                return;
            }
        }

        int parent = 0;
        for (int i=0;i<N-1;i++) {
            System.out.println((parent+1)+" "+(i+2));
            if (c[i]=='1') {
                parent=i+1;
            }
        }
    }
}