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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
 
fn main() {
  input! {
    n: usize
  }
  
  let mut a = 1;
  let mut b = n;
  let mut min = usize::max_value();
  while a <= b {
    if n % a == 0 {
      min = std::cmp::min(min, (a - 1) + (n / a - 1));
    }
    a += 1;
    b = n / a;
  }
  
  println!("{}", min);
}