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)

class Integer
  def divisor_list
    require 'prime'

    return [] if self <= 0
    return [1] if self == 1

    prime_division.map.with_index { |(base, k), i|
      s = i.zero? ? 0 : 1
      (s..k).map { |n| base ** n }
    }.inject { |res, e| res + res.flat_map { |t| e.map { |v| t * v } } }.sort
  end
end

N = gets.to_i

ans = Float::INFINITY

N.divisor_list.each do |n|
  m = N / n
  s = (m + n) - 2

  ans = s if s < ans
end

puts ans