Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstring>
#include <vector>
using namespace std;
typedef pair<int,int> P;
vector<P> ans;

int main() {
  string s;
  cin >> s;
  if(s[0] == '0' || s[s.length() - 1] == '1') {
    cout << -1 << endl;
    return 0;
  }

  int l = 0, r = s.length() - 2;
  while(l <= r) {
    if(s[l] == s[r]) {
      l++,r--;
    }
    else {
      cout << -1 << endl;
      return 0;
    }
  }

  int ances = s.length();
  for(int i = s.length() - 2; i >= 0; i--) {
    if(s[i] == '1') {
      ans.push_back(P(ances,i+1));
      ances = i+1;
    }
    else ans.push_back(P(ances,i+1));
  }

  for(int i = 0; i < ans.size(); i++) {
    cout << ans[i].first<<" "<<ans[i].second << endl;
  }
}