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.*;
class Main
{
    public static void main (String[] args)
    {
        Scanner sc = new Scanner(System.in);
        String s = sc.next();
        int l = s.length();
        boolean flag = true;
        if(s.charAt(l - 1) == '1' || s.charAt(0) == '0') flag = false;
        else{
            for(int i = 0; i < l / 2; i++){
                if(s.charAt(i) != s.charAt(l - i - 2)){
                    flag = false;
                    break;
                }
            }
        }
        if(flag){
            int[] from = new int[l-1];
            int[] to = new int[l-1];
            int[] t = new int[l];
            int tnum = -1;
            for(int i = 0; i < l; i++){
                if(s.charAt(i) == '1'){
                    t[++tnum] = i;
                }
            }
            for(int i = 0; i < l-1; i++){
                from[i] = i; 
            }
            int tind = 0;
            for(int i = 0; i < l-2; i++){
                if(s.charAt(i) == '1'){
                    to[i] = t[++tind];
                }
                else{
                    to[i] = t[tind];
                }
                System.out.println((from[i]+1) + " " + (to[i]+1));
            }
            System.out.println((l-1) + " " + l);
        }
        else{
            System.out.println(-1);
        }
    }
 }