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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

class Main {
    public static void main(String[] args) {
        new Solver().run();
    }
}

class Solver {

    long gcd(long a, long b) {
        return b > 0 ? gcd(b, a % b) : a;
    }

    long lcm(long x, long y) {
        return x / gcd(x, y) * y;
    }

    public void run() {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];

        for (int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
        }

        long l = 1;
        for (int i = 0; i < N; i++) {
            l = lcm(Math.max(l, a[i]), Math.min(l, a[i]));
        }

        long ans = 0;
        for (int i = 0; i < N; i++) {
            ans += (l - 1) % a[i];
        }

        System.out.println(ans);
        return;
    }

}