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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let rec gcd n m =
  if m = 0 then n
  else gcd m (n mod m)

let lcm n m = n / gcd n m * m

let () = Scanf.scanf "%d\n" @@ fun n ->
  let as_ = Array.init n @@ fun _ ->
    Scanf.scanf "%d " @@ fun a -> a in
  let lcm = Array.fold_left lcm 1 as_ in
  Printf.printf "%d\n" @@ Array.fold_left ( + ) 0 @@ Array.map (fun a -> (lcm - 1) mod a) as_