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<algorithm>
#include<iostream>

using namespace std;
int check_pal(string s){
	for(int i = 0; i < s.length()/2; i++){
		if(s[i] != s[s.length()-  i - 2])	
			return 1;
	}
	return 0;
}
int main(){
	string s;
	cin  >> s;
	int root = 1;
	if(s[s.length() - 1] == '1' || s[0] == '0' || check_pal(s))
		return cout << "-1",0;
	for(int i = 1; i < s.length(); i++){
		cout << root << " " << i+1 << "\n";
		if(i > 1 && s[i-1] == '1'){
			root = i+1;
		}
	}
}