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 <bits/stdc++.h>

using namespace std ;

const int MAX = 1e5 + 10 ;

int arr[MAX] ;
int n ;
string s ;

int main()
{
	ios_base::sync_with_stdio(0) ;
	cin.tie(0) ;
	cin>>s ;
	n = s.size() ;
	if(s[0] == '0' || s[n-1] == '1')
		return cout<<"-1\n" , 0 ;
	for(int i = 0 ; i < n-1 ; ++i)
	{
		if(s[i] != s[n-2-i])
			return cout<<"-1\n" , 0 ;
	}
	int now = 1 , cur = 1 ;
	for(int i = n-2 ; i >= 0 ; --i)
	{
		cur++ ;
		cout<<now<<" "<<cur<<"\n" ;
		if(s[i] == '1')
			now = cur ;
	}
	return 0 ;
}