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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <string>
#include <algorithm>

using namespace std;

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

    int n = s.size();

    bool ok = (s[0] == '1' && s[n - 1] == '0');

    for (int i = 0; i < n - 1; i++) {
        if (s[i] != s[n - i - 2]) {
            ok = false;
            break;
        }
    }

    if (!ok) {
        cout << -1 << endl;
    } else {
        s[n - 1] = '1';

        for (int i = n - 2; i >= 0; i--) {
            for (int j = i + 1; j < n; j++) {
                if (s[j] == '1') {
                    cout << i + 1 << ' ' << j + 1 << endl;
                    break;
                }
            }
        }
    }
}