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::stdin;

fn main() {
    let n = {
        let mut s = String::new();
        stdin().read_line(&mut s).unwrap();
        let n: f64 = s.trim_right().parse().unwrap();
        n
    };

    let m = n.sqrt().floor() as i64;

    let mut res = 0;
    for i in (1..(m+1)).rev() {
        if (n as i64) % i == 0 {
            let j = (n as i64) / i;
            res += (i - 1);
            res += (j - 1);
            break;
        }
    }
    println!("{}", res);
}