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();
        int a[] = new int[n];
        for(int i=0;i<n;i++)a[i] = c[i] - '0';
        sc.close();

        if(a[0]==0||a[n-1]==1){
            System.out.println(-1);
            return;
        }

        for(int i=1;i<n-1;i++){
            if(a[i]!=a[n-2-i]){
                System.out.println(-1);
                return;
            }
        }

        int ans[][] = new int[n-1][2];
        ans[0][0] = 0; ans[0][1] = 1;
        for(int i=1;i<n-1;i++){
            if(a[i-1] == 0){
                ans[i][0] = ans[i-1][0];
            }
            else{
                ans[i][0] = ans[i-1][1];
            }
            ans[i][1] = i+1; 
        }
        for(int i=0;i<n-1;i++){
            int from = ans[i][0] + 1, to = ans[i][1] + 1;
            System.out.println(from + " " + to);
        }
        System.out.println();
    }
}