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>
using namespace std;

int main(){
  string s; cin >> s;
  int len=s.size();
  bool flag=(s.at(0)=='1' && s.at(len-1)=='0');
  for(int i=0;i<len-1;i++){
    if(s.at(i)!=s.at(len-2-i))flag=false;
  }
  if(!flag){
    cout << -1 << "\n";
    return 0;
  }
  flag=1;
  int temp=0;
  for(int i=1;i<len;i++){
    printf("%d %d\n",temp+1,i+1);
    if(flag)temp=i;
    if(s.at(i)=='1')flag=1;
    else flag=0;
  }
}