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)

import sys
sys.setrecursionlimit(2000000)

from fractions import gcd
def lcm(a):
    x = a[0]
    for i in range(1, len(a)):
        x = (x * a[i]) // gcd(x, a[i])
    return x


mod = 1000000007

def mul(a, b):
    return ((a % mod) * (b % mod)) % mod

def power(x, y):
    if   y == 0     : return 1
    elif y == 1     : return x % mod
    elif y % 2 == 0 : return power(x, y/2)**2 % mod
    else            : return power(x, y/2)**2 * x % mod

def div(a, b):
    return mul(a, power(b, mod-2))




n=int(input())
aa=[]
aa=list(map(int,input().split()))
# for i in range(n):
#     aa.append(randint(1,10**6))

bb=lcm(aa)
mod=10**9+7
ans=0
for i in range(n):
    ccc=div(bb,aa[i])
    ans=int((ccc%mod+ans%mod)%mod)
print(int(ans))