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