Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn walk_on_multiplication_table() -> Result<u64, &'static str> {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;
    let n = input.trim_right().parse::<f64>()
        .map_err(|_| "parse error")?;

    let m = n.sqrt().ceil() as u64;
    let n = n as u64;
    let mut sum = n;

    for a in 1..(m + 1) {
        let s = n / a;
        if s * a != n {
            continue;
        }
        if s + a - 2 < sum {
            sum = s + a - 2;
        }
    }
    Ok(sum)
}

fn main() {
    println!("{}", walk_on_multiplication_table().unwrap());
}