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 Python (3.4.3) (judge verdict: Wrong Answer)

import functools
n = int(input())
a_n = [int(x) for x in input().split()]


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    return a * b // gcd(a, b)


def f(m):
    return sum([m % a for a in a_n])


def check_f(a_n):
    a_n.sort(reverse=True)
    max_num = lcm(a_n[0], a_n[1])
    return max([f(x) for x in range(max_num+1)])


print(check_f(a_n))