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)

#E
def Primefact(n):
    Dic={}
    for i in range(2,int(pow(n,0.5))+1):
        if n%i==0:
            Dic[i]=0
            while True:
                n/=i
                Dic[i]+=1
                if n%i!=0:
                    break
        if n==1:
            break
    if n!=1:
        Dic[int(n)]=1
    return Dic

from math import gcd
N=int(input())
A=list(map(int,input().split()))
mod=10**9+7

Prime={}
for i in range(N):
    D=Primefact(A[i])
    for key,v in D.items():
        if key in list(Prime.keys()):
            Prime[key]=max(Prime[key],v)
        else:
            Prime[key]=v
ans=0
for i in range(N):
    B=1
    D=Primefact(A[i])
    for key,v in Prime.items():
        if key in list(D.keys()):
            v-=D[key]
        B*=key**v
        B%=mod
    ans+=B
    ans%=mod
print(ans)