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)

from math import sqrt,ceil
from collections import defaultdict

lim = 10**4 + 10

def sieve(N):
    """Dumb sieve of Eratosthemes, O(N*log(log(N)))"""
    b = [True]*(N+1)
    b[0] = False
    b[1] = False

    lim = ceil(sqrt(N))
    i = 2
    while i <= lim:
        if b[i]:
            for n in range(i**2,N+1,i):
                b[n] = False
        i+=1
    
    return [i for i,b in enumerate(b) if b]

P = sieve(lim)

def factor(n):
    """Given prime list, factorize n. Format as dict of factors with counts."""
    if n in P: return {n: 1}

    F = []
    for p in P:
        while n%p == 0:
            n//=p
            F.append(p)
        if n in P:
            F.append(n)
            break
    else:
        if n != 1:
            F.append(n)

    C = {}
    for f in F:
        if f not in C:
            C[f] = 0
        C[f] += 1

    return C

mod = 1000000007

n = int(input())
A = [int(x) for x in input().split()]

D = defaultdict(int)
for a in A:
    for f,cnt in factor(a).items():
        D[f] = max(D[f], cnt)
l = 1
for f,cnt in D.items():
    l = l*pow(f, cnt, mod) % mod

res = sum(l*pow(a, mod-2, mod) for a in A)
print(res % 1000000007)