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 <vector>
using namespace std;

int main(void){
	string s; cin >> s; bool ok = true; int n = s.size();
	if (s[0]=='0' || s[n-2]=='0' || s[n-1]=='1') ok = false;
	for(int i=2; i <= n-i; i++){
		if (s[i-1] != s[n-i-1]) ok = false;
		//cout << i << " " << n-i << endl;
	}
	if (!ok) {cout << -1 << endl; return 0;}
	s[n-1]='1';
	int w[n];
	for(int i=n-1; i>=0; i--) {
		if (s[i] == '1') w[i] = i+1;
		else w[i] = w[i+1];
	}
	for(int i=0; i<n-1; i++) {
		cout << i+1 << " " << w[i+1] << endl;
	}
}