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"bits/stdc++.h"
using namespace std;
using ll = int64_t;

int main() {
    string s;
    cin >> s;

    const ll N = s.size();
    if (s.back() == '1') {
        cout << -1 << endl;
        return 0;
    }


    ll max_value = 0;
    for (ll i = 0; i < N / 2 - 1; i++) {
        if (s[i] != s[N - 2 - i]) {
            cout << -1 << endl;
            return 0;
        }

        if (i > 0 && s[i] == '1' && s[i - 1] == '0') {
            cout << -1 << endl;
        }

        if (s[i] == '1') {
            max_value = i;
        }
    }

    for (ll i = 2; i <= N; i++) {
        if (i <= N - max_value) {
            cout << 1 << " " << i << endl;
        } else {
            cout << i - 1 << " " << i << endl;
        }
    }
}