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 (1.42.0) (judge verdict: Accepted)

fn main(){
    let n: u64 = read();
    let ans: u64 = (1..).take_while(|i| i * i <= n)
        .filter(|i| n % i == 0).map(|i| i + n / i - 2).min().unwrap();
    
    println!("{}", ans);
}

#[allow(dead_code)]
fn read<T>() -> T
where T: std::str::FromStr,
      T::Err: std::fmt::Debug
{
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).expect("failed to read");
    buf.trim().parse().unwrap()
}