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)

n = gets.chomp.to_i
la = gets.split(" ").map(&:to_i)

def gcd(a, b)
  a, b = b, a if a < b
  return a if b == 0
  _mod = a.modulo(b)
  if _mod == 0
    b
  else
    gcd(b, _mod)
  end
end

def lcm(a, b)
  a * b / gcd(a, b)
end

ri = la.inject{|a,b| a.lcm(b)}-1

maxa = la.sort[-1]
m = maxa * 2 - 1

sum = 0
n.times do |i|
  sum += ri%la[i]
end
puts sum