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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::prelude::*;

fn input<T: std::str::FromStr>() -> T {
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn with_stdout_lock<F: FnOnce(std::io::BufWriter<std::io::StdoutLock>)>(f: F) {
    let out = std::io::stdout();
    let w = std::io::BufWriter::new(out.lock());
    f(w);
}

fn main() {
    let s: Vec<char> = input::<String>().chars().collect();
    let n = s.len();

    let mut ok = s[0] == '1' && s[n - 1] == '0';
    for i in 0..n {
        let j = n - 2 - i;
        if i > j {
            break;
        }
        if s[i] != s[j] {
            ok = false;
            break;
        }
    }
    if !ok {
        println!("-1");
        return;
    }

    let mut ans = vec![];
    let mut zeros = vec![];
    let mut prev = n + 1;
    for i in 0..n {
        if i == n - 1 || s[i] == '1' {
            if prev <= n {
                ans.push((prev, i + 1));
                for &z in &zeros {
                    ans.push((i + 1, z));
                }
            }
            zeros.clear();
            prev = i + 1;
        } else {
            zeros.push(i + 1);
        }
    }

    with_stdout_lock(|mut w| {
        for (u, v) in ans {
            writeln!(w, "{} {}", u, v).unwrap();
        }
    });
}