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;
const int maxn = 1e5+10;
int main()
{
  char s[maxn];
  cin>>s+1;
  int len = strlen(s+1);
  if(s[len] == '1' || s[1] == '0')
  {
    puts("-1");
    return 0;
  }
  for(int i = 1 ; i < len ; i++)
  {
    if(s[i] != s[len - i])
    {
      puts("-1");
      return 0;
    }
  }
  int root = 1;
  for(int i = 2 ; i <= len ; i++)
  {
    cout<<root<<" "<<i<<endl;
    if(s[i-1] == '1') root = i;
  }
}