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: Time Limit Exceeded)

loop do
class Integer
  def divide2
    ar = []
    1.upto(self ** 0.5) do |i|
      ar.push([i, self / i]) if (self % i).zero?
    end
    ar
  end
end
loc = Struct.new(:x,:y) do
  def dist(s,t)
    (s-x)+(t-y)
  end
end

n=gets.to_i
now=loc.new(1,1)
puts n.divide2.map{|loc| now.dist(loc[0],loc[1])}.min

end