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)

// stdin
macro_rules! stdin {
    () => {{
        use std::io::Read;
        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }};
}

// input
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

// Test
macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input), $output);
            )*
        }
    };
}

#[allow(dead_code)]
fn gcd(x: i64, y: i64) -> i64 {
    if y == 0 {
        return x;
    }
    gcd(y, x % y)
}

#[test]
fn test_primes() {
    assert_eq!(primes(1), vec![1]);
    assert_eq!(primes(140), vec![1, 2, 2, 5, 7])
}

#[allow(dead_code)]
fn primes(num: i64) -> Vec<i64> {
    let mut ans = vec![1];
    let mut cur = num;
    for i in 2.. {
        if i * i > num { break; }
        if cur % i == 0 {
            while cur % i == 0 {
                ans.push(i);
                cur /= i;
            }
        }
    }
    if cur > 1 {
        ans.push(cur);
    }
    return ans;
}


test! {
r"10
" => r"5",

r"50
" => r"13",

r"10000000019
" => r"10000000018"
}

fn solve(src: &str) -> String {
    input! {
        source=src,
        n:i64,
//        a:[i32;n],
    }
    let n: i64 = n;
    let primes = primes(n);
    let (x, rest) = primes.split_last().unwrap();

    let mut y = 1;
    for &tmp in rest {
        y *= tmp;
    }

    let ans = (x - 1) + (y - 1);
    format!("{}", ans)
}


fn main() {
    println!("{}", solve(&stdin!()));
}