Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

$lcdcache = {}
def lcd(s, t)
  return $lcdcache[s][t] if $lcdcache[s] && $lcdcache[s][t]
  a, b = s, t
  while true
    a, b = b, a % b
    if b == 0
      $lcdcache[s] ||= {}
      $lcdcache[s][t] = a
      return a
    end
  end
end

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

N = gets.to_i
as = gets.split(' ').map {|i| i.to_i }
l = 1
as.each {|a|
  l = lcm(l, a)
}

DIV = 10 ** 9 + 7
sum = 0
as.each {|a|
  b = (l / a).to_i
  sum += b
  sum = sum % DIV if sum >= DIV
}
puts sum