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 <bits/stdc++.h>
using namespace std;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... U> void assign(V<T>& v, int n, const U&... u) { v.resize(n); for (auto&& i : v) assign(i, u...); }

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  string s; cin >> s;
  int n = s.size();
  if (s[0] != '1' or s[n - 2] != '1' or s[n - 1] != '0') return cout << -1 << '\n', 0;
  for (int i = 1; i < n / 2; i++) if (s[i] != s[n - 2 - i]) return cout << -1 << '\n', 0;
  V< pair<int, int> > res;
  res.emplace_back(0, 1);
  int p = 1, t = 1;
  for (int i = 1; i < n / 2; i++) if (s[i] == '0') {
    res.emplace_back(p, ++t);
  } else {
    res.emplace_back(p, ++t);
    p = t;
  }
  while (res.size() < n - 1) res.emplace_back(p, ++t);
  for (int i = 0; i < n - 1; i++) cout << res[i].first + 1 << ' ' << res[i].second + 1 << '\n';
}