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>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;

char str[100003]; int N;

int main(){
	scanf("%s" , str + 1); N = strlen(str + 1);
	if(str[1] == '0' || str[N] == '1'){puts("-1"); return 0;}
	for(int i = 1 ; i < N ; ++i) if(str[i] != str[N - i]){puts("-1"); return 0;}
	int pre = 1;
	for(int i = 2 ; 2 * i <= N ; ++i){
		if(str[i] == '1') while(pre < i) cout << pre++ << ' ' << i << endl;
	}
	while(pre < N) cout << pre++ << ' ' << N << endl;
    return 0;
}