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)

def divisor(num)
    result = []
    i = 1
    while i <= num do
      remainder = num % i
      if remainder == 0
        result << i
      end 
      i += 1
    end
    return result
end

num = gets.to_i
divisions = divisor(num)

distance_lists = []

for d in divisions do
  width_count = (d - 1)
  vertical_count = (num / d - 1)
  distance_lists << width_count + vertical_count
end

ans = distance_lists.min 
puts(ans)