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: Runtime Error)

import java.io.IOException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		try (Scanner sc = new Scanner(System.in);) {
			int a = Integer.parseInt(sc.next());
			List<Integer> list = new ArrayList<>();
			for (int i = 0; i < a; i++) {
				list.add(Integer.parseInt(sc.next()));
			}
			Collections.sort(list, Collections.reverseOrder());

			long lc = lcm(list.get(0), list.get(1));
			for (int i = 1; i < a - 1; i++) {
				lc = lcm(lc, list.get(i + 1));
			}

			lc -= 1;
			long all = 0;
			for (int i = 0; i < a; i++) {
				all += lc % list.get(i);
			}
			System.out.println(all);
		}

	}

	private static long gcd(long m, long n) {
		if (m < n)
			return gcd(n, m);
		if (n == 0)
			return m;
		return gcd(n, m % n);
	}

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

}