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 (1.42.0) (judge verdict: Wrong Answer)

use std::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let s: Vec<char> = itr.next().unwrap().chars().collect();
    let n = s.len();

    //
    if s[0] == '0' || s[n - 1] == '1' {
        println!("-1");
        return;
    }

    let mut line = 0;
    let mut ok = true;
    for i in 0..=n / 2 {
        if s[i] == '1' && s[n - i - 2] == '0' {
            ok = false;
        }
        if s[i] == '1' && s[i + 1] == '0' {
            line = i;
            break;
        }
    }

    if ok {
        //
        let mut out = Vec::new();
        for i in 0..=line {
            writeln!(out, "{} {}", i + 1, i + 2).ok();
        }
        // line+1から他
        for i in line + 2..n {
            writeln!(out, "{} {}", line + 2, i + 1).ok();
        }
        stdout().write_all(&out).unwrap();
    } else {
        println!("-1");
    }
}