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: Accepted)

require 'prime'

def divisors(num)
  num.prime_division.inject([1]) do |arr, (p, e)|
    (0..e).map { |e1| p**e1 }.product(arr).map { |a, b| a * b }
  end.sort
end

n = gets.to_i
d = divisors(n)
ans = (n - 1)
((d.length + 1) / 2).times do |i|
  xdiff = (d[i] - 1)
  ydiff = (d[-1 * (i + 1)] - 1)

  ans = xdiff + ydiff if xdiff + ydiff <= ans
end

puts ans