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 <algorithm>
#include <string>

using namespace std;

int main() {
    string s;
    cin >> s;
    int n = s.size();
    bool sym = true;
    for (int i=0; i<n/2; i++) 
        if (s[i] != s[n-2-i]) {
            sym = false;
            break;
        }
    if (s[0] == '0' || s[n-1] == '1' || !sym) {
        cout << -1 << '\n';
        return 0;
    }
    int now = 1;
    for (int i=2; i<=n; i++) {
        cout << now << ' ' << i << '\n';
        if (i - 2 < n / 2 && s[i-2] == '1') now = i;
    }
    return 0;
}