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)

lines = []
while line = gets
    lines << line.chomp.split(' ').map(&:to_i)
end

N = lines[0][0]
Mod = 10 ** 9 + 7
a = []
for i in 1..N do
  a.push(lines[1][i-1])
end

prime = []
for i in 2..1000 do
  pri = true
  for j in 2..35 do
    if j < i and i % j == 0 then
      pri = false
      break
    end
  end
  if pri then
    prime.push(i)
  end
end

s = 1
while s <= prime.length do
  dvd = true
  for j in 1..N do
    if a[j-1] % prime[s-1] != 0 then
      dvd = false
      break
    end
  end
  if dvd == true then
    for j in 1..N do
      a[j-1] /= prime[s-1]
    end
  else
    s += 1
  end
end

mlp = 1
for i in 1..N do
  mlp *= a[i-1]
end

b = []
for i in 1..N do
  b[i-1] = mlp / a[i-1]
end
    
s = 1
while s <= prime.length do
  dvd = true
  for j in 1..N do
    if b[j-1] % prime[s-1] != 0 then
      dvd = false
      break
    end
  end
  if dvd == true then
    for j in 1..N do
      b[j-1] /= prime[s-1]
    end
  else
    s += 1
  end
end
    
answer = 0
for i in 1..N do
  answer += b[i-1]
end
    
print answer % Mod