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 <queue>
#include <vector>
#include <algorithm>
#include <set>
#include <math.h>
#include <tuple>
#include <map>
using namespace std;
typedef long long ll;

int main() {
    string s;
    cin >> s;
    int n = s.size();

    if (char(s[0]) != '1' || char(s[n - 1]) != '0') {
        cout << -1 << endl;
        return 0;
    }

    int a[100010], b[100010], bef = 0, idx = 0;
    if (1) {
        for (int i = 0; i < n - 1; i++) {
            if (i < n / 2 && char(s[i]) != char(s[n - 2 - i])) {
                cout << -1 << endl;
                return 0;
            }
            a[idx] = bef;
            b[idx] = i + 1;
            idx++;
            /*
            a[idx] = n - 1 - bef;
            b[idx] = n - 2 - i;
            idx++;
            */
            if (char(s[i]) == '1') bef = i + 1;
        }
        for (int i = 0; i < idx; i++) {
            cout << a[i] + 1 << " " << b[i] + 1 << endl;
        }
    }

}