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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        long[] a = new long[N];

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

        long lcm = a[0];
        for (int i = 1; i < N; i++) {
            lcm = lcm(lcm, a[i]);
        }
        lcm--;

        long ans = 0;
        for (int i = 0; i < N; i++) {
            ans += lcm % a[i];
        }
        System.out.println(ans);
    }

    static long lcm(long m, long n) {
        return m / gcd(m, n) * n;
    }

    static final long gcd(long a, long b) {
        if (a < b) {
            long tmp = a;
            a = b;
            b = tmp;
        }

        long r = -1;
        while (r != 0) {
            r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
}