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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var array = Console.ReadLine().Split().Select(long.Parse).ToArray();

            Array.Sort(array);

            long max = 0;
            long min = int.MaxValue;
            
            for (var i = 1; i < N; i++)
            {
                min = Math.Min(Gcd(array[i], array[i - 1]), min);
            }

            var tmp = array[0];
            for (var i = 1; i < N; i++)
            {
                max = tmp * array[i] / min;
                tmp = max;
            }

            max--;
            var total = 0L;
            for (var i = 0; i < N; i++)
            {
                total += max % array[i];
            }

            Console.WriteLine(total);
        }

        static long Gcd(long a, long b)
        {
            if (a < b) Gcd(b, a);
            if (b == 0) return a;
            return Gcd(b, a % b);
        }
    }
}