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: Runtime Error)

require "prime"
list = []
n = gets.to_i(10).prime_division
n.each do |factor|
    factor.last.times {list << factor.first}
end

while(list.length > 2) do
    max = list.max
    min = list.min
    list.append(max*min)
    list.delete_at(list.find_index(max))
    list.delete_at(list.find_index(min)) 
end

list.append(1) if list.length == 1
p (list.first + list.last - 2)