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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

long gcm(long long a, long long b) {
  long long result = a;
  long long k = 0;
  long long n = b;
  do {
    k = result % n;
    result = n;
    n = k;
  } while(k != 0);
  return result;
}

long lcm(long long a, long long b) {
	long long g;
	g = gcm(a, b);
	return a*b/g;
}

int main() {
  int N;
  cin >> N;

  long long A[N];
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }

  long long tmp = 0, ans = 0;

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

  for (int i = 0; i < N; i++) {
    ans += tmp % A[i];
  }

  cout << ans << endl;
}