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 solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();

    let mut ans = n - 1;
    for i in 1..1_000_001 {
        if n % i == 0 {
            ans = std::cmp::min(ans, i + n / i - 2);
        }
    }

    format!("{}\n", ans)
}
#[test]
fn test_solve() {
   assert_eq!(solve("10\n"), "5\n");
   assert_eq!(solve("50\n"), "13\n");
   assert_eq!(solve("10000000019\n"), "10000000018\n");
}
fn main() {
    let mut buf = String::new();
    use std::io::Read;
    std::io::stdin().read_to_string(&mut buf).unwrap();
    use std::io::Write;
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<I> {
    src: I,
}
impl<'a> Scanner<std::str::SplitWhitespace<'a>> {
    fn from_str(src: &'a str) -> Self {
        Scanner {
            src: src.split_whitespace(),
        }
    }
}
#[allow(dead_code)]
impl<'a, I> Scanner<I>
where
    I: std::iter::Iterator<Item = &'a str>,
{
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.src.next().unwrap().parse().ok().expect("Parse error")
    }
    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    fn chars(&mut self) -> Vec<char> {
        self.src.next().unwrap().chars().collect()
    }
}