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 n;
string s;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>s;
    for (int i=1;i<s.length()-1;i++)
        if (s[0]=='0'|| s[s.length()-1]=='1' || s[i]!=s[s.length()-i-2]) {
            cout<<-1;
            return 0;
        }
    cout<<1<<" "<<2<<endl;
    int last = 1;
    for (int i=1;i<=s.length()-2;i++) {
        cout<<last<<" "<<i+2<<endl;
        if (s[i]=='1') last=i+2;
    }
}