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)

use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let mut ans = n - 1;
    for i in 2..(n as f64).sqrt() as usize + 1 {
        if n % i == 0 {
            let a = i;
            let b = n / i;
            ans = std::cmp::min(ans, (a - 1) + (b - 1))
        }
    }

    println!("{}", ans)
}

#[allow(dead_code)]
fn main_abc100_c() {
    let n = read::<usize>();
    let mut d = 0;
    for _ in 0..n {
        let mut a = read::<usize>();
        while a % 2 == 0 {
            a /= 2;
            d += 1
        }
    }
    println!("{}", d)
}