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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun search-value (target &optional (i 1) (result-list (list nil)))
  (if (> (* i i) target)
      (car (sort (cdr (reverse result-list)) #'<))
      (progn
        (when (= (mod target i) 0)
          (let ((j (/ target i)))
            (push (- (+ i j) 2) result-list)))
        (search-value target (1+ i) result-list))))

(princ (search-value (read)))