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 LL long long
#define RG register
#define R RG int
using namespace std;
const int N=1e5+9;
char s[N];
int e[N];
int main(){
	R n,i,x=1;
	cin>>(s+1);n=strlen(s+1);
	if(s[n]&1||!(s[1]&1))return puts("-1"),0;
	for(i=1;i<n;++i)
		if(s[i]!=s[n-i])return puts("-1"),0;
	for(i=2;i<=n;++i){
		e[i]=x;if(s[i-1]&1)x=i;
	}
	for(i=2;i<=n;++i)cout<<e[i]<<' '<<i<<endl;
	return 0;
}