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 PyPy2 (7.3.0) (judge verdict: Time Limit Exceeded)

import collections
n = raw_input()
ais = collections.Counter(map(int, raw_input().split()))
def f(a,b):
	
	seen = set([])
	k = 0
	temp = 0
	a1mb = (a - 1) % b
	r = -float('inf')
	while(((k*a) + a-1) % b not in seen):
		seen.add((k*a + a-1) % b)
		r = max(r, (k*a + a-1) % b)
		k +=1
	return r
	return max(list(seen))

r = 0

for i,ai in enumerate(ais):
	current = ais[ai] * (ai - 1)
	for j, aj in enumerate(ais):
		if not(i == j or ai == aj):
			current += ais[aj] * f(ai,aj)
	r = max(current, r)
print r