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.strip.to_i

ans = [1,1]
divs=Prime.prime_division(n)
nums = divs.map{|pr,c| [pr]*c } .flatten


if nums.length==1
  p n-1
  exit
end

dnums = nums.dup

until nums.length==2
  t = nums.shift*nums.shift
  nums.push(t)
  nums.sort!
end

until dnums.length==2
  t = dnums.shift*dnums.pop
  dnums.push(t)
  dnums.sort!
end



p [dnums.first+dnums.last-2, nums.first+nums.last-2].min