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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())

def check(a, b, i):
  if (a + 1) * 10 ** i + b - 10 <= N:
    return 10 ** (i - 1)
  else:
    ret = 0
    for j in range(10 ** (i - 1)):
      if a * 10 ** i + j * 10 + a <= N:
        ret += 1
      else:
        return ret
ans = 0
for a in range(1, 10):
  for b in range(1, 10):
    if a == b:
      n = 0
      if a * 10 + b <= N:
        n += 2
      elif a <= N:
        ans += 1
      for i in range(2, 6):
        n += check(a, b, i)
      ans += n ** 2
    else:
      n, m = 0, 0
      if a * 10 + b <= N:
        n += 1
      if b * 10 + a <= N:
        m += 1
      for i in range(2, 6):
        n += check(a, b, i)
        m += check(b, a, i)
      ans += n * m
print(ans)