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: Wrong Answer)

require 'prime'

n = gets.chomp.to_i

factors = n.prime_division
if factors.size == 1
  puts n-1
  exit
end

x, y = 1, 1
dir = 1
while x * y < n
  if dir == 1
    x += 1
    if n % x == 0 
      dir *= -1
      break if x * y == n
    end
  else
    y += 1
    if n % y == 0 
      dir *= -1
      break if x * y == n
    end
  end
end

puts x + y - 2