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;
use std::f64;

mod utils {
    use std::io::BufRead;
    use std::str::{self, FromStr};

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(reader: R) -> StdinReader<R> {
            StdinReader {
                reader: reader,
                buf: Vec::new(),
            }
        }

        #[allow(unused)]
        #[inline]
        pub fn reads<T: FromStr>(&mut self) -> T {
            self.read_until(b' ')
        }

        #[allow(unused)]
        #[inline]
        pub fn readl<T: FromStr>(&mut self) -> T {
            self.read_until(b'\n')
        }

        #[allow(unused)]
        #[inline]
        pub fn read_vec<T: FromStr>(&mut self) -> Vec<T> {
            return self.read_until::<String>(b'\n').trim().split_whitespace().map(|c| c.parse().ok().unwrap()).collect();
        }

        #[inline]
        pub fn read_until<T: FromStr>(&mut self, delim: u8) -> T {
            loop {
                self.buf.clear();
                let len = self.reader
                    .read_until(delim, &mut self.buf)
                    .expect("failed reading bytes");
                match len {
                    0 => panic!("early eof"),
                    1 if self.buf[0] == delim => (),
                    _ => {
                        if self.buf[len - 1] == delim {
                            self.buf.truncate(len - 1);
                        }
                        break;
                    }
                }
            }

            let elem = unsafe { str::from_utf8_unchecked(&self.buf) };
            elem.parse().unwrap_or_else(|_| panic!(format!("failed parsing: {}", elem)))
         }
    }
}


fn main(){
    let stdin = stdin();
    let mut r = utils::StdinReader::new(stdin.lock());
    let n:usize = r.readl();

    let mut greatest_multiple = 1;
    let mut i = 1;

    for i in 1..((f64::sqrt(n as f64) + 1e-9) as usize + 1){
        if n % i == 0{
            greatest_multiple = i;
        }
    }

    println!("{}",greatest_multiple - 1 + (n / greatest_multiple) - 1);
}