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 CPP):

Solution:
#include<iostream>
#include<cstdio>
using namespace std;
string s;
int cnt=1,root,lst;
int main(){
	cin>>s;
	if(s[0]=='0'||s[s.length()-1]=='1'){
		puts("-1");
		return 0;
	}
	for(register int i=0;i<(s.length()>>1);i++){
		if(s[i]!=s[s.length()-i-2]){
			puts("-1");
			return 0;
		}
	}
	for(register int i=0;i<s.length();i++){
		if(s[i]=='1'){
			root=cnt;
			printf("%d %d\n",root,++cnt);
			if(lst)for(register int j=1;j<i+1-lst;j++)printf("%d %d\n",root,++cnt);
			lst=i+1;
		}
	}
}