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)

#![allow(unused_imports)]
#![allow(dead_code)]
use std::cmp::{max, min, Ordering};
use std::collections;
use std::io::{stdin, BufRead};

macro_rules! get {
  ($rd:ident; V; $t:ty) => {
    scanl($rd, b'\n')
      .split_whitespace()
      .map(|w| get_inner!{w; $t})
      .collect::<Vec<_>>()
  };
  ($rd:ident; T; $($t:ty),+) => {
    {
      let s = scanl($rd, b'\n');
      let mut i = s.split_whitespace();
      ( $( get_inner!{i.next().unwrap(); $t}),+ )
    }
  };
  ($rd:ident; $t:ty) => (get_inner!{scanl($rd, b'\n'); $t});
}

macro_rules! get_inner {
  ($src:expr; $t:ty) => {
    $src.parse::<$t>().expect("Parse Error")
  };
}

macro_rules! gets {
  ($rd:ident; $n:expr; $($tok:tt)*) => {
    (0..)
      .take($n)
      .map(|_| get!{$rd; $($tok)*})
      .collect::<Vec<_>>()
  };
}

fn solve(rd: &mut BufRead) {
  let n = get!(rd; u64);
  let mut x = (n as f64).sqrt() as u64;

  loop {
    if n % x == 0 {
      break;
    }
    
    x -= 1;
  }
  
  println!("{}", n / x + x - 2);
}

fn scanl(rd: &mut BufRead, delim: u8) -> String {
  let mut buf = Vec::new();
  let _ = rd.read_until(delim, &mut buf).expect("Read Failed");
  String::from_utf8(buf)
    .expect("Invalid UTF-8 String")
    .trim_right()
    .to_string()
}

fn main() {
  let rd = stdin();
  let mut rd = rd.lock(); // std::io::StdinLock
  solve(&mut rd);
}