Problem:
Score : 300 points

Problem Statement

You are given N positive integers a_1, a_2, ..., a_N.

For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).

Here, X\ mod\ Y denotes the remainder of the division of X by Y.

Find the maximum value of f.

Constraints

All values in input are integers.

2 \leq N \leq 3000

2 \leq a_i \leq 10^5

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum value of f.

Sample Input 1

3
3 4 6

Sample Output 1

10

f(11) = (11\ mod\ 3) + (11\ mod\ 4) + (11\ mod\ 6) = 10 is the maximum value of f.

Sample Input 2

5
7 46 11 20 11

Sample Output 2

90

Sample Input 3

7
994 518 941 851 647 2 581

Sample Output 3

4527

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(let* ((n (read))
       (a (loop repeat n
                collect (read)))
       (lcma (lcm a))
       (gcda (gcd a)))
  (labels ((f (m)
             (apply #'+
                    (mapcar #'mod
                            (loop repeat n
                                  collect m)
                            a))))
    (princ
      (apply #'max (loop for m from 1 to lcma
                         when (not (zerop (mod m gcda)))
                         collect (f m))))))