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: Wrong Answer)

fn input_one<T: std::str::FromStr> () -> Result<T, T::Err> {
    let mut n = String::new();
    std::io::stdin().read_line(&mut n).unwrap();
    n.trim().parse()
}

fn pf(n: usize) -> Vec<usize> {
    let mut d = vec![1];
    let mut n = n;
    for i in 2.. {
        if n == 1 || i * i > n {
            break
        }
        while n % i == 0 {
            n /= i;
            d.push(i);
        }
    }
    if n > 1 {
        d.push(n);
    }
    return d;
}

fn sum(arr: &Vec<usize>, mask: usize) -> usize {
    let mut r = 1;
    let mut l = 1;
    for i in 0..arr.len() {
        if mask & i > 0 {
            r *= arr[i];
        } else {
            l *= arr[i];
        }
    }
    return r + l - 2;
}

fn main() {
    let n: usize = input_one().unwrap();
    let d = pf(n);
    let mut r = 1000000000000;
    for mask in 1..(1 << d.len()) {
        let a = sum(&d, mask);
        if r > a {
            r = a;
        }
    }
    println!("{}", r);
}