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)

import sys, math
def input():
    return sys.stdin.readline()[:-1]
from itertools import permutations, combinations
from collections import defaultdict, Counter
from math import factorial
from fractions import gcd
div = 10**9 + 7

sys.setrecursionlimit(10**7)
N = int(input())
A = list(map(int, input().split()))
sA = list(set(A))

val = 1
def lcm(a, b):
    ret = gcd(a, b)
    ret = a*b//ret
    return ret

val = sA[0]
for a in sA[1:]:
    val = lcm(val, a)

B = [val//a for a in A]
sumB = sum(B)
sumB %= div

print(sumB)