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 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
import math
from collections import deque

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()


def make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]


# Nの素因数分解を辞書で返す
def prime_fact(n):
    root = int(math.sqrt(n))
    prime_dict = {}
    for i in range(2, root+1):
        cnt = 0
        for j in range(root+1):
            if n % i == 0 and n != 0:
                cnt += 1
                n = n // i
            else:
                break
        if cnt:
            prime_dict[i] = cnt
    if n != 1:
        prime_dict[n] = 1
    return prime_dict


def main():
    N = NI()
    A = NLI()
    L = {}
    B = [0] * N
    primes_a = {}
    for a in A:
        prime_a = prime_fact(a)
        primes_a[a] = prime_a
        for p, n in prime_a.items():
            L.setdefault(p, 0)
            L[p] = max(L[p], n)
    for i, a in enumerate(A):
        b = 1
        for p, n in L.items():
            primes_a[a].setdefault(p, 0)
            b *= pow(p, (n - primes_a[a][p]), MOD)
        B[i] = b
    print(sum(B) % MOD)



if __name__ == "__main__":
    main()