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 <iostream>
using namespace std;

int euclid(int a, int b){ //ただし a > b
    while(1){
        if(a < b){
            int cache = a;
            a = b;
            b = cache;
        }
        if(a % b == 0){
            return b;
        }
        a = a % b;
    }
}

int main() {
    int N;
    int a[3000];
    cin >> N;
    for(int i = 0; i < N; i++){
        cin >> a[i];
    }
    int current_GCD = 0;
    long long current_LCM = 0;
    current_GCD = euclid(a[0], a[1]);
    current_LCM = (a[0] * a[1]) / current_GCD;
    for(int i = 2; i < N; i++){
        current_GCD = euclid(a[i], current_GCD);
        current_LCM = (current_LCM * a[i]) / current_GCD;
    }
    long long m = current_LCM - 1, sum = 0;
    for(int i = 0; i < N; i++){
        sum += m % a[i];
    }
    cout << sum << endl;
}