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;

typedef long long ll;

string s;
int n;

bool is_valid() {
    if (s[n-1]=='1') {
        return false;
    }
    if (s[0]=='0')
        return false;
    for (int i=0; i<n/2; ++i) {
        if (s[i]!=s[n-2-i]) {
            return false;
        }
    }
    return true;
}

int main() {
    cin >> s;
    n=s.size();
    if (!is_valid()) {
        cout << -1;
        return 0;
    }
    int cur_root=1;
    int cur_size=n-1;
    int cur_v=2;
    for (int i=(n-1)/2; i>=0; --i) {
        if (s[i]=='1') {
            int sub_size=i+1;
            for (int k=0; k<cur_size-sub_size; ++k) {
                cout << cur_v << ' ' << cur_root << endl;
                ++cur_v;
            }
            cout << cur_v << ' ' << cur_root << endl;
            cur_size=i;
            cur_root=cur_v;
            ++cur_v;
        }
    }
    return 0;
}