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 Ruby (2.3.3) (judge verdict: Accepted)

# frozen_string_literal: true

require 'prime'
n = gets.to_i

class Integer
  def divisors
    return [1] if self == 1

    Prime.prime_division(self).map do |e|
      Array.new(e[1] + 1).map.with_index do |_e, i|
        e[0]**i
      end
    end.reduce { |p, q| p.product(q) }.map do |a|
      [a].flatten.inject(&:*)
    end.sort
  end
end

mid = Math.sqrt(n)
ds = n.divisors.sort_by { |e| (e - mid).abs }

puts ds[0..1].map { |e| n / e + e - 2 }.min