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: Accepted)

import java.util.*;
import java.math.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.next());
    ArrayList<BigInteger> list = new ArrayList<BigInteger>();
    BigInteger base = BigInteger.ONE;
    for(int i=0;i<N;i++){
      BigInteger bi = new BigInteger(sc.next());
      base = lcm(base, bi);
      list.add(bi);
    }
    base = base.subtract(BigInteger.ONE);
    BigInteger ans = BigInteger.ZERO;
    for(BigInteger bi:list){
      ans = ans.add(base.remainder(bi));
    }
    System.out.println(ans);
  }
  static BigInteger lcm (BigInteger a, BigInteger b) {
  	return a.multiply(b).divide(a.gcd(b));
  }
}