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 Ruby (2.3.3) (judge verdict: Accepted)

def gcd_of_two(a, b)
  small, large = [a, b].sort
  if small == 0
    return large
  else
    gcd_of_two(small, large % small)
  end
end

def gcd_of_many(array)
  current = array.shift
  until array.empty?
    following = array.shift
    current = gcd_of_two(current, following)
  end
  return current
end

def lcm_of_two(a, b)
  gcd = gcd_of_two(a, b)
  return a * b / gcd
end

def lcm_of_many(array)
  current = array.shift
  until array.empty?
    following = array.shift
    current = lcm_of_two(current, following)
  end
  return current
end

n = gets
as = gets.split.map(&:to_i)
lcm = lcm_of_many(as.dup)
puts as.map { |e| (lcm-1)%e }.inject(:+)