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 Scala (2.11.7) (judge verdict: Accepted)

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)

    val N = sc.nextInt()
    val A = Array.fill(N)(BigInt(sc.nextLong()))

    def gcd(a: BigInt, b: BigInt): BigInt =
      if (a % b == 0L) b
      else gcd(b, a % b)

    def lcm(a: BigInt, b: BigInt): BigInt =
      a * (b / gcd(a, b))

    val LCM = A.reduce((a, b) => lcm(a, b)) - 1
    val r = A.foldLeft(BigInt(0))((b, n) => b + LCM % n)
    println(r)
  }

}