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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

class Program
{
    static void Main()
    {
        ulong n = ulong.Parse(Console.ReadLine());
        ulong[] a = Console.ReadLine().Split(' ').Select(ulong.Parse).ToArray();
        ulong ans = 0;
        ulong max = a[0];

        for (ulong i = 0; i < n; i++)
        {
            max = lcm(a[i], max);
        }
        ulong dist = sieve(max) - 1;
        ulong target = max - dist;
        for (ulong i = 0; i < n; i++)
        {
            ans += target % a[i];
        }
        Console.WriteLine(ans);
    }
    public static ulong gcd(ulong a, ulong b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    public static ulong lcm(ulong a, ulong b) => a / gcd(a, b) * b;
    public static ulong sieve(ulong n)
    {
        for (ulong i = 2; i <= n; i++)
        {
            if (n % i == 0)
            {
                return i;
            }
        }
        return n;
    }
}