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;
use std::cmp::min;

#[allow(unused_mut)]
fn main() {
    input! {
        n: usize
    }
    let sqrt_n = (n as f64).sqrt().ceil() as usize;
    let mut res = std::usize::MAX;
    for i in 1..sqrt_n + 1 {
        if n % i != 0 {
            continue;
        }
        res = min(res, i + n / i - 2);
    }
    println!("{}", res);
}