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.to_i
prime_div = n.prime_division
primes = []

prime_div.each do |i|
  i.last.times do
    primes << i.first
  end
end

while primes.size > 2
  m1 = primes.delete_at(primes.index(primes.min))
  m2 = primes.delete_at(primes.index(primes.min))
  primes.push m1*m2
end


p primes.size > 1 ? primes.first + primes.last - 2 : primes.first - 1