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 <string>

using namespace std;

int n;
string s;

int main(void)
{
	cin >> s;
	n = s.size();
	s = '#' + s;
	
	if(s[n] == '1' || s[1] == '0'){
		cout << -1 << endl;
		return 0;
	}
	for(int i = 1; i <= n-1; i++){
		if(s[i] != s[n-i]){
			cout << -1 << endl;
			return 0;
		}
	}
	
	int p = 1, id = 2;
	for(int i = 1; i <= n-1; i++){
		if(s[i] == '0'){
			cout << p << " " << id++ << endl;
		}else{
			cout << p << " " << id++<< endl;
			p = id-1;
		}
	}
	
	return 0;
}