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 <algorithm>
#include <iostream>
#include <vector>

using namespace std;
using ll = long long int;

// to format a document: ctrl + K -> ctrl + D

ll gcd(ll a, ll b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b) {
    return a * b / gcd(a, b);
}

int main() {
    int N;
    cin >> N;
    vector<ll> a(N);
    for (auto& i : a) cin >> i;

    ll m = a[0];
    for (int i = 1; i < N; i++) {
        m = lcm(m, a[i]);
    }
    --m;
    ll ans = 0;
    for (int i = 0; i < N; i++) {
        ans += m % a[i];
    }

    cout << ans << endl;
    


    return 0;
}