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)

class PrimeFactorization
    # 素因数分解
    def decomposit_prime(n)
      # 割る数の初期値
      num1 = 1
      num2 = 1
      tmp = 0
      a = 2
  
      # √n ≧ a ( n ≧ a * a ) の間ループ処理
      while n >= a * a
        
        if n % a == 0
          #print "#{a} * "
          if num1 > num2 then
                tmp = num1
                num1 = num2
                num2 = tmp
          end
            num1 = num1 * a
          n /= a
        else
          a += 1
        end
      end
      if num1 > num2 then
            tmp = num1
            num1 = num2
            num2 = tmp
      end
      if n > 0 then
        num1 = num1 * n
      end
      # 最後に残った n は素因数
      
          sum = num1 + num2 -2
      puts sum
    end
  end
  

  # 計算クラスインスタンス化
  obj = PrimeFactorization.new
    # データ入力
    print "自然数 ( 0 : 終了 )："
    int_num = gets.chomp.to_i
    # 素因数分解
    obj.decomposit_prime(int_num)