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 'pp'
require 'prime'

def gets; ARGF.gets; end

class Solver

  def initialize
  end

  def main
    n = gets.chomp.to_i

    # 素因数分解
    primes = Prime.prime_division(n)  #=> [[5, 1], [197, 1], [461, 1]]
    # puts primes

    # 総当り
    min_step = 1000000000000
    primes.each do |(p, cnt)|
      cur = 1
      0.upto(cnt) do |i|
        d = n / cur

        step = (cur - 1) + (d - 1)
        if step < min_step
          min_step = step
        end

        cur *= p
      end
    end

    puts min_step
  end
end

if __FILE__ == $0
  Solver.new.main
end