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;

pub fn main() {
    let stdin = io::stdin();
    let mut buf = String::new();
    stdin.read_line(&mut buf).ok();
    let line: Vec<i64> = buf.split_whitespace().into_iter().map(|s| s.parse().unwrap()).collect();
    let N = line[0];
    let mut x = 1;
    let mut y = N;
    let mut i = 1;
    loop {
        i += 1;
        if i * i > N {
            break
        }
        if N % i != 0 {
            continue
        }
        x = i;
        y = N / i;
    }
    println!("{}", x + y - 2)
}