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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

# E - Flatten

n = int(input())
a = list(map(int, input().split()))
assert len(a) == n

modulus = 10 ** 9 + 7

class factorization:
    def __init__(self, x=1):
        self.vec = {}
        d = 2
        while d <= x:
            if x % d == 0:
                if d not in self.vec:
                    self.vec[d] = 0
                self.vec[d] += 1
                x //= d
            else:
                d += 1

    def add(self, x):
        for i in x.vec:
            self.vec[i] = max(self.vec[i] if i in self.vec else 0, x.vec[i])
        return self

    def subtract(self, x):
        for i in x.vec:
            self.vec[i] -= x.vec[i]
        return self

    def clone(self):
        x = factorization()
        for i in self.vec:
            x.vec[i] = self.vec[i]
        return x

    def value(self):
        p = 1
        for i in self.vec:
            p *= (i ** self.vec[i]) % modulus
        return p

fact = [factorization(x) for x in a]

lcm = factorization()
for f in fact:
    lcm.add(f)

difffact = [lcm.clone().subtract(f) for f in fact]

b = [f.value() for f in difffact]
s = sum(x % modulus for x in b) % modulus
print(s)