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: Runtime Error)

MOD=10**9+7
def factorization(n):
    arr=[]
    tmp=n
    for i in range(2,int(n**0.5)+1):
        if(tmp%i==0):
            cnt=0
            while tmp%i==0:
                cnt+=1
                tmp//=i
            arr.append([i,cnt])
    if(not arr):
        arr.append([1,1])
    if(tmp!=1):
        arr.append([tmp,1])
    return arr
def moddiv(a,m):
    return pow(a,m-2,m)
N=int(input())
A=list(map(int,input().split()))
cnt=[0]*1001
for i in range(N):
    arr=factorization(A[i])
    for a,b in arr:
        cnt[a]=max(cnt[a],b)
g=1;res=0
for i in range(1001):
    g=g*(i**cnt[i])%MOD
for i in range(N):
    res=(res+g*moddiv(A[i],MOD))%MOD
print(res)