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::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let s = read::<String>().chars().collect::<Vec<char>>();
    let n = s.len();
    if s[0] != '1' || s[n - 1] != '0' || s[n - 2] != '1' {
        println!("-1");
        return;
    }
    let mut cnts = vec![0; n];
    let mut parents = vec![0; n];
    let mut p = 0;
    for t in 1..n {
        parents[t] = p;
        cnts[p] += 1;
        if s[t - 1] == '1' {
            p = t;
        } else {
            //
        }
    }
    let mut visits = vec!['0'; n];
    let mut cnt = 0;
    let mut pos = n - 1;
    while pos != 0 {
        cnt += cnts[pos];
        visits[cnt] = '1';
        pos = parents[pos];
    }
    // println!("{:?}", parents);
    // println!("{:?}", visits);
    if s == visits {
        for i in 1..n {
            println!("{} {}", parents[i] + 1, i + 1);
        }
    } else {
        println!("-1");
    }
}