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: Wrong Answer)

#include <algorithm>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>
using namespace std;
using ll = long long;
#define fst first
#define snd second

/* clang-format off */
template <class T, size_t D> struct _vec { using type = vector<typename _vec<T, D - 1>::type>; };
template <class T> struct _vec<T, 0> { using type = T; };
template <class T, size_t D> using vec = typename _vec<T, D>::type;
template <class T> vector<T> make_v(size_t size, const T& init) { return vector<T>(size, init); }
template <class... Ts> auto make_v(size_t size, Ts... rest) { return vector<decltype(make_v(rest...))>(size, make_v(rest...)); }
/* clang-format on */

int main() {
  string S;
  while (cin >> S) {
    int N = S.size();
    bool ok = true;
    ok &= S[0] == '1';
    ok &= S[N - 1] == '0';
    for (int i = 0; i < N - 1; i++) {
      ok &= S[i] == S[N - 2 - i];
    }
    if (!ok) {
      cout << -1 << endl;
      continue;
    }
    vec<int, 2> G(N);
    int r = 0;
    int v = 1;
    int pre = 1;
    for (int i = 1; i < (N + 1) / 2; i++) {
      if (S[i] == '0') continue;
      G[v].push_back(r);
      r = v;
      ++v;
      int need = (i + 1) - 1 - pre;
      for (int j = 0; j < need; j++) {
        G[r].push_back(v);
        ++v;
      }
      pre = i + 1;
    }
    while (v < N) {
      G[r].push_back(v);
      ++v;
    }
    for (int i = 0; i < N; i++) {
      for (int j : G[i]) {
        cout << (i + 1) << " " << (j + 1) << endl;
      }
    }
  }
  return 0;
}