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 <iomanip>
#include <string>
#include <vector>
#include <tuple>
#include <queue>
#include <bitset>
#include <unordered_map>
#include <tuple>
#include <utility>
#include <cmath>
#include <algorithm>
#include <numeric>
#include <sys/time.h>

using namespace std;

void solve(string s){
  long long n = s.size();
  if (s[n-1] == '1') {
    std::cout << -1 << std::endl;
    return;
  }
  if (s[0] == '0') {
    std::cout << -1 << std::endl;
    return;
  }
  for (int i = 0; i < n-1; i++) {
    if (s[i] != s[n-2-i]) {
      std::cout << -1 << std::endl;
      return;
    }
  }
  long long u = 1;
  long long v = 2;
  for (int i = 0; i < n-1; i++) {
    if (s[i] == '0') {
      std::cout << u << " " << v << std::endl;
      v++;
    } else {
      std::cout << u << " " << v << std::endl;
      u = v;
      v++;
    }
  }
}

int main(){
  string s;
  cin >> s;
  solve(s);
  return 0;
}