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::*;
use std::str::FromStr;

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n: u64 = sc.next();
    let mut ans = std::u64::MAX;

    for a in 1.. {
        if a * a > n {
            break;
        }

        if n % a == 0 {
            let b = n / a;
            ans = std::cmp::min(ans, a + b - 2);
        }
    }
    println!("{}", ans);
}

/* ========== Scanner ========== */

struct Scanner<R: Read> {
    reader: R,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(reader: R) -> Scanner<R> {
        Scanner { reader: reader }
    }

    fn read<T: FromStr>(&mut self) -> Option<T> {
        let token = self
            .reader
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            token.parse::<T>().ok()
        }
    }

    fn next<T: FromStr>(&mut self) -> T {
        if let Some(s) = self.read() {
            s
        } else {
            writeln!(stderr(), "Terminated with EOF").unwrap();
            std::process::exit(0);
        }
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.next()).collect()
    }

    fn char(&mut self) -> char {
        self.next::<String>().chars().next().unwrap()
    }
}