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)

// Template from https://techracho.bpsinc.jp/jhonda/2019_08_05/78537

// input macro for competive-programming from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        input_inner!{$s, $($r)*}
    };
}

#[allow(unused_macros)]
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)*}
    };

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

#[allow(unused_macros)]
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>>()
    };

    ($iter:expr, bytes) => {
        read_value!($iter, String).into_bytes()
    };

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

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&s));
}

macro_rules! test {
    ($($exp_input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                let start = std::time::Instant::now();
                let input = solve($exp_input);
                let end = start.elapsed();
                assert_eq!(input, $output, "{}.{:03}", end.as_secs(), end.subsec_millis());
                assert!(end.as_secs() <= 2, "expected_sec: {}sec, actual_sec: {}sec", 2, end.as_secs());
                assert!(end.as_secs() <= 1, "expected_sec: {}sec, actual_sec: {}sec", 1, end.as_secs());
                assert!(end.subsec_millis() <= 10, "expected_ms: {}ms, actual_ms: {}ms", 10, end.subsec_millis());
                assert!(end.subsec_millis() <= 2, "expected_ms: {}ms, actual_ms: {}ms", 2, end.subsec_millis());
            )*
        }
    };
}

test! {
r#"10"# => r#"5"#,
r#"50"# => r#"13"#,
r#"10000000019"# => r#"10000000018"#,
r#"10000000020"# => r#"202826"#,
}

fn solve(src: &str) -> String {
    let mut src_iter = src.split_whitespace();
    input! {
        source = src_iter,
        n: u64,
    }
    let mut ans = 1_000_000_000_000;

    for i in 1..((n as f64).sqrt() as u64) + 1 {
        if i * i > n {
            break;
        }

        if n % i != 0 {
            continue;
        }

        let j = n / i;

        if j < i {
            break;
        }

        ans = std::cmp::min((i - 1) + (j - 1), ans);
    }

    ans.to_string()
}