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)

#set
n = gets.chomp.to_i
pair_arr = Array.new
arr_count = 0
min_sum = n + 1
temp_sum = 0
arr_address = 0
answer = 0

#main
1.upto(n / 2) do |i|
  if n % i == 0 then
    j = n / i
    pair_arr[arr_count] = [i,j]
    arr_count += 1
  end
end

0.upto(arr_count - 1) do |x|
  temp_sum = pair_arr[x][0] + pair_arr[x][1]
  if temp_sum <= min_sum then
    min_sum = temp_sum
  end
end
answer = min_sum - 2
print ("#{answer}\n")