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)

def gcd(a, b)
  a,b = b, a % b while b > 0
  a
end

# 最小公倍数
def lcm(a,b)
  a * b / gcd(a,b)
end


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


MOD = 10**9+7
ans = 0
tmp = 0

num = []

n.times do |i|
  num << A[i] % MOD
  if i == 0
    tmp = num[i]
  else
    tmp = lcm(tmp, num[i])
  end
end

n.times do |i|
  ans += tmp/num[i] % MOD
end

p ans % MOD