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.io.PrintStream;
import java.util.Scanner;

public class Main {
    private static final PrintStream so = System.out;
    private static final Scanner     sc = new Scanner(System.in);

    public static void main(String[] args) {
        int n = sc.nextInt();
        long[] a = new long[n];
        
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextLong();
        }
        long lcm = 1;
        for (int i = 0; i < n; i++) {
            lcm = lcm(lcm, a[i]);
        }
        
        so.println(f(a, lcm-1));
    }
    
    public static long f(long[] a, long d) {
        long sum = 0;
        for (long i: a) {
            sum += d % i;
        }
        return sum;
    }
    
    private static long gcd(long a, long b) {
      long candidate = a;
      while (b % a != 0) {
        candidate = b % a;
        b = a;
        a = candidate;
      }
      return candidate;
    }

    private static long lcm(long a, long b) {
      return (a * b) / gcd(a, b);
    }
}