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 <vector>
#include <iostream>
using namespace std;
int main(int argc, char const *argv[]) {
string s;cin>>s;
int n=s.length();
bool b=0;
if(s[n-1]=='1'||s[0]=='0')b=true;
for(int i=0;i<n-1;i++)if(s[i]!=s[n-2-i])b=true;
if(b)cout<<-1<<endl;
else{
int l = 1, i = 2;
for(;i<=n;++i){
cout << l << " " << i <<endl;
if(s[i-2]=='1')l = i;
}
}
return 0;
}