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: Wrong Answer)

#[allow(unused_imports)]
use proconio::{fastout, input};

#[fastout]
fn main() {
    input!(n: usize);

    let n_sqrt = (n as f64).sqrt() as usize;
    let mut vec = Vec::new();
    let mut buff = n;
    for i in 2..n_sqrt {
        while buff % i == 0 {
            buff = buff / i;
            vec.push(i);
        }
        if buff == 1 {
            break;
        }
    }

    vec.push(buff);
    let mut l_num = 1;
    let mut r_num = 1;

    for i in 0..vec.len() {
        if l_num < r_num {
            l_num *= vec[i];
        } else {
            r_num *= vec[i];
        }
    }

    println!("{}", l_num - 1 + r_num - 1);
}