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: Wrong Answer)

require 'prime'
n = gets.strip.to_i

ans = [1,1]
divs=Prime.prime_division(n)

if divs.length==1
  p n-1
  exit
end


divs = divs.map {|pr, cnt|
  if cnt>=2
    ans[0] *= (pr**(cnt/2))
    ans[1] *= (pr**(cnt/2))
    if cnt%2==0
      nil
    else
      [pr, 1]
    end
  else
    [pr, cnt]
  end
}.compact

if divs.length.zero?
  p ans.inject(:+)-2
  exit
end

nums = divs.map{|pr,c| [pr]*c } .flatten

#p nums

result = Float::INFINITY
(nums.length).times do|c|
  temp = ans.first*nums[0..c].inject(:*) + ans.last*nums[c+1..-1].inject(1,:*)-2
#p [c, temp, ans.first*nums[0..c].inject(:*), ans.last*nums[c+1..-1].inject(1,:*)]
  result = [temp, result].min
end

p result