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 <vector>
#include <string>

using namespace std;
using ll = long long;

int main() {
  string s;
  cin >> s;
  s = '0' + s;
  string t(s);
  reverse(t.begin(), t.end());
  if (s != t || s[1] == '0') {
    cout << -1 << endl;
    return 0;
  }
  int k = 2;
  cout << "1 2" << '\n';
  for (int i = 2; i < s.size() - 1; i++) {
    cout << k << ' ' << i + 1 << '\n';
    if (s[i] == '1') {
      k = i + 1;
    }
  }
}