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(a, b)
  if a > b
    return a if b == 0

    _gcd(b, a % b)
  else
    return b if a == 0

    _gcd(a, b % a)
  end
end

def gcd(numbers)
  ans = numbers.first

  numbers[1..-1].each do |n|
    ans = _gcd(ans, n)
  end

  return ans
end

def _lcm(a, b)
  return a * b / _gcd(a, b)
end

def lcm(numbers)
  ans = numbers.first

  numbers[1..-1].each do |n|
    ans = _lcm(ans, n)
  end

  return ans
end

n = gets.to_i
A = gets.split.map(&:to_i)
lcm = lcm(A)

ans = A.inject(0) do |sum, a|
  sum + (lcm - 1) % a
end

puts ans