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 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")
}

//約数を返す
fn get_divs(n: i64) -> Vec<i64> {
  let mut i = 1;
  let mut ret : Vec<i64> = Vec::new();
  while i * i <= n {
    if n % i == 0 {
      ret.push(i);
      if i * i != n {
        ret.push(n / i);
      }
    }
    i+=1;
  }
  
  ret
}

fn main() {
  let n: i64 = read();
  
  let divs = get_divs(n);
  
  let mut mv = -1;
  let mut mvi = 1.0e+18;
  let sqrt_n = (n as f64).sqrt();
  
  for d in divs {
    if mvi > (sqrt_n - (d as f64)).abs() {
      mv = d;
      mvi = (sqrt_n - (d as f64)).abs();
    }
  }
  
  println!("{}", mv + n / mv - 2);
}