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(dead_code)]
fn main() {
    let stdin = stdin();
    let mut reader = StdinReader::new(stdin.lock());
    let n = reader.u();
    let mut d = Vec::new();
    let mut l = 1;
    while l * l <= n {
        if n % l == 0 {
            d.push(l);
        }
        l += 1;
    }
    let mut ans = n;
    for d_i in d {
        ans = min(ans, d_i + n / d_i - 2);
    }
    println!("{}", ans);
}

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use std::{cmp::*, collections::*, io::*, num::*, str::*};
#[allow(unused_imports)]
use stdin_reader::StdinReader;

#[allow(dead_code)]
mod stdin_reader {
    use std::fmt::Debug;
    use std::io::*;
    use std::str::*;

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
        // Should never be empty
        pos: usize, // Should never be out of bounds as long as the input ends with '\n'
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(r: R) -> StdinReader<R> {
            StdinReader {
                reader: r,
                buf: Vec::new(),
                pos: 0,
            }
        }
        pub fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: Debug,
        {
            if self.buf.is_empty() {
                self._read_next_line();
            }
            let mut start = None;
            loop {
                if self.pos == self.buf.len() {
                    break;
                }
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) => self.pos += 1,
                    (b'\n', false) => self._read_next_line(),
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            from_utf8(target).unwrap().parse().unwrap()
        }

        fn _read_next_line(&mut self) {
            self.pos = 0;
            self.buf.clear();
            if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
                panic!("Reached EOF");
            }
        }

        pub fn str(&mut self) -> String {
            self.next()
        }
        pub fn s(&mut self) -> Vec<char> {
            self.next::<String>().chars().collect()
        }
        pub fn i(&mut self) -> i64 {
            self.next()
        }
        pub fn i2(&mut self) -> (i64, i64) {
            (self.next(), self.next())
        }
        pub fn i3(&mut self) -> (i64, i64, i64) {
            (self.next(), self.next(), self.next())
        }
        pub fn u(&mut self) -> usize {
            self.next()
        }
        pub fn u2(&mut self) -> (usize, usize) {
            (self.next(), self.next())
        }
        pub fn u3(&mut self) -> (usize, usize, usize) {
            (self.next(), self.next(), self.next())
        }
        pub fn u4(&mut self) -> (usize, usize, usize, usize) {
            (self.next(), self.next(), self.next(), self.next())
        }
        pub fn u5(&mut self) -> (usize, usize, usize, usize, usize) {
            (
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
            )
        }
        pub fn u6(&mut self) -> (usize, usize, usize, usize, usize, usize) {
            (
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
            )
        }
        pub fn f(&mut self) -> f64 {
            self.next()
        }
        pub fn f2(&mut self) -> (f64, f64) {
            (self.next(), self.next())
        }
        pub fn c(&mut self) -> char {
            self.next::<String>().pop().unwrap()
        }
        pub fn iv(&mut self, n: usize) -> Vec<i64> {
            (0..n).map(|_| self.i()).collect()
        }
        pub fn iv2(&mut self, n: usize) -> Vec<(i64, i64)> {
            (0..n).map(|_| self.i2()).collect()
        }
        pub fn iv3(&mut self, n: usize) -> Vec<(i64, i64, i64)> {
            (0..n).map(|_| self.i3()).collect()
        }
        pub fn uv(&mut self, n: usize) -> Vec<usize> {
            (0..n).map(|_| self.u()).collect()
        }
        pub fn uv2(&mut self, n: usize) -> Vec<(usize, usize)> {
            (0..n).map(|_| self.u2()).collect()
        }
        pub fn uv3(&mut self, n: usize) -> Vec<(usize, usize, usize)> {
            (0..n).map(|_| self.u3()).collect()
        }
        pub fn uv4(&mut self, n: usize) -> Vec<(usize, usize, usize, usize)> {
            (0..n).map(|_| self.u4()).collect()
        }
        pub fn fv(&mut self, n: usize) -> Vec<f64> {
            (0..n).map(|_| self.f()).collect()
        }
        pub fn cmap(&mut self, h: usize) -> Vec<Vec<char>> {
            (0..h).map(|_| self.s()).collect()
        }
    }
}