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)

require 'prime'

n = gets.chomp.to_i

def divisors(x)
  list = [1]
  primes = []

  Prime.prime_division(x).each do |prime|
    prime[1].times do
      primes << prime[0]
    end
  end

  1.upto(primes.size) do |i|
    primes.combination(i) do |prime|
      list << prime.inject(:*)
    end
  end

  list.uniq!
  list.sort!
  return list
end

result = 10**12 + 1
divisors = divisors(n)

# puts divisors

divisors.select { |i| i <= n / 2 }.each do |divisor|
  another_divisor = n / divisor
  i = divisor + another_divisor
  if result > i
    result = i
  end
end

puts result - 2