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();
    int[] a = new int[N];

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

    sc.close(); 

    int max = 0;

    long gcd = gcd(a[0],a[1]);
    long lcm = a[0] * a[1] / gcd;

    for (int i = 2; i < N; i++) {
      gcd = gcd(lcm, a[i]);
      lcm = lcm * a[i] / gcd;
    }

    long m = lcm - 1;

    for (int i = 0; i < N; i++){
      max += m % a[i]; 
    }

    System.out.println(max);

  }


  public static long gcd(long x, long y){

    if (x < y) {
      long t = x;
      x = y;
      y = t;
    }

    while (y > 0) {
      long r = x % y;
      x = y;
      y = r;
    }

    return x;
    
  }

}