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)

#[allow(unused_macros)]
macro_rules! input {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($( { splits.next().unwrap().parse::<$t>().unwrap() },)*)
    }}
}

#[allow(dead_code)]
fn factor2(n: u64) -> (u64, u64) {
    let max = (n as f64).sqrt().ceil() as u64;

    for i in (1..(max + 1)).rev() {
        if n % i == 0 {
            return (i, n / i);
        }
    }
    return (0, 0);
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (n, ) = input!(u64);

    let (a, b) = factor2(n);

    println!("{}", a + b - 2);
}

fn main() {
    solve();
}