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.*;
import java.io.*;

import static java.lang.System.in;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        String s = sc.next();
        s = "*"+s;
        char[] a = s.toCharArray();
        if(inValid(a)){
            System.out.println(-1);
            System.exit(0);
        }
        int n = a.length-1;
        ArrayList<Integer>[] map = new ArrayList[n+1];
        for(int i=0;i<=n;i++) map[i] = new ArrayList<>();
        int root = n-1;
        map[n-1].add(n);
        //int cnt = 2;
        for(int cnt=2;cnt<n;cnt++){
            if(a[cnt]=='0') map[root].add(n-cnt);
            else{
                map[n-cnt].add(root);
                root = n-cnt;
            }
        }
        PrintWriter out = new PrintWriter(System.out);
        for(int i=1;i<=n;i++){
            for(int w:map[i]){
                out.println(Integer.toString(i)+" "+Integer.toString(w));
            }
        }
        out.flush();
    }
    static boolean inValid(char[] a){
        int n = a.length-1;
        if(a[1]=='0'||a[n]=='1') return true;
        for(int i=1;i<=n/2;i++){
            if(a[i]!=a[n-i]) return true;
        }
        return false;
    }
}