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)

use std::io;
use std::str::FromStr;

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn divisors(n: u64) -> Vec<u64> {
  let mut divs: Vec<u64> = Vec::new();
  for i in 1..(n as f64).sqrt() as u64 + 1 {
    if n % i == 0 {
      divs.push(i);
      if i != (n / i) {
        divs.push(n/i);
      }
    }
  }
  divs.sort();
  divs
}


fn main() {
    let n: u64 = input();
    let divs: Vec<u64> = divisors(n);
    if divs.len() % 2 == 0 {
        println!("{}", divs[divs.len() / 2 - 1] + divs[divs.len() / 2] - 2);
    } else {
        println!("{}", divs[divs.len() / 2] * 2 - 2);
    }

}