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)

require 'prime'

n = gets.chomp.to_i

def divisor_list(i)
  return [1] if i == 1
  i.prime_division.map do |e|
    Array.new(e[1]+1).map.with_index do |element, i|
      e[0]**i
    end
  end.inject{|p,q| p.product(q)}.map do |a|
    [a].flatten.inject(&:*)
  end.sort
end

min = Float::INFINITY
divisor_list(n).each do |d|
  a = n / d
  min = [min, a + d - 2].min
end

puts min