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: Time Limit Exceeded)

import math
mod=10**9 + 7
N=10**6+1
inv_t=[0]+[1]
for i in range(2,N):
    inv_t+=[inv_t[mod%i]*(mod-int(mod/i))%mod]
n=int(input())
A=list(map(int,input().split()))
l=[0]*10**6
for a in A:
    for i in range(2,int(math.sqrt(a))+1):
        c=0
        while a%i==0:
            c+=1
            a//=i
        l[i]=max(l[i],c)
    if a!=1:
        l[a]=max(l[a],1)
lcm=1
for i in range(10**6):
    if l[i]!=0:
        lcm=(lcm*(i**l[i]))%mod
ans=0
for a in A:
    ans=(ans+lcm*inv_t[a])%mod
print(ans)