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>
#define int long long
#define iris 998244353
using namespace std;

int arr[100010];

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