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;
int main()
{
	string s;
	cin>>s;
	bool ok=1;
	int n=s.length();
	ok&=s[n-1]!='1';
	ok&=s[0]=='1';

	for(int i=1;i<n-1;i++)
		ok&=(s[i]==s[n-i-2]);
	if(!ok){puts("-1");return 0;}


	vector<int> pos;
	for(int i=0;i<n;i++)if(s[i]=='1')pos.push_back(i+1);

	int k=pos.size();
	
	//body
	for(int i=1;i<=k;i++)cout<<i<<" "<<i+1<<"\n";


	int cur=k+2;
	for(int i=2;i<=k;i++)
	{
		int prn=pos[i-1]-pos[i-2]-1;

		for(int j=0;j<prn;j++)
		cout<<i<<" "<<(cur++)<<"\n";
	}
}