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)

// 標準入力から一行を読み取り、指定の型に変換する
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn main() {
    let number: u64 = read();
    // 初期の最小値として非常に大きな値を指定する
    let mut min_number_of_trials: u64 = 10u64.pow(12);

    // 探索範囲は対称性からsqrt(N)までで良い。
    for i in 1..(number as f64).sqrt() as u64 + 1
    {
        // 割り切れる値を発見したら、試行回数が最小値であるかどうか調べ、最小値であればアップデートする。
        if number % i == 0
        {
            let now_number_of_trials = (number / i) + i - 2;
            if now_number_of_trials < min_number_of_trials
            {
                min_number_of_trials = now_number_of_trials;
            }
        }
    }

    println!("{}", min_number_of_trials);
}