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)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use std::cmp::min;

#[fastout]
fn main() {
    input! {
    n: usize,
    }
    let mut ans = std::usize::MAX;
    let d = divisor(n);
    for i in 0..d.len() {
        let t = d[i] + n / d[i] - 2;
        ans = min(ans ,t);
    }
    println!("{}", ans);
}
fn divisor(m: usize) -> Vec<usize> {
    let mut l = Vec::new();
    for i in 1.. {
        if i * i > m {break}
        if m % i == 0 {
            l.push(i);
            l.push(m / i);
        }
    }
    l.sort();
    l.dedup();
    l
}