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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	string s; cin>>s;
	int n=s.length();

	bool ok=true;
	if(s[0]=='0' || s[n-1]=='1') ok=false;
	rep(i,n/2) if(s[i]!=s[n-i-2]) ok=false;
	if(!ok){
		cout<<-1<<endl;
		return 0;
	}

	int u=1;
	rep(i,n-1){
		int v=i+2;
		cout<<u<<" "<<v<<endl;
		if(s[i]=='1') u=v;
	}

	return 0;
}