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'
# N = gets.to_i
# pd = N.prime_division
# ns = [1] + pd.flat_map { |n, e| [n] * e }.sort
# while ns.size > 2
#   a = ns.shift
#   b = ns.shift
#   c = a * b
#   ns = (ns + [c]).sort
# end

# x, y = ns
# ans = (x - 1) + (y - 1)
# puts ans

N = gets.to_i
ans = 1 << 60
(1..(Math.sqrt(N))).each do |n|
  if N % n == 0
    m = N / n
    step = (n - 1) + (m - 1)
    ans = step if step < ans
  end
end
puts ans