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 (2.7.1) (judge verdict: Time Limit Exceeded)

require "prime"
n = gets.chomp.to_i
pri = Prime.prime_division(n)
arr = []
pri.each do |pr|
	arr << Array.new(pr[1], pr[0])
end
arr.flatten!

min = n + 5
[false, true].repeated_permutation(arr.length) do |bits|
	a = 1 
	b = 1 
	bits.each_with_index do |bit, i|
		if bit 
			a *= arr[i]
		else
			b *= arr[i]
		end
	end
	#puts "a:#{a} b:#{b}"
	min = a + b - 2 if min > a + b - 2 
end
puts min