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 sys
input=sys.stdin.readline

MOD=10**9+7
kl = [0]*(10**6+1)

            
def main():
    N=int(input())
    A=list(map(int,input().split()))
    if N==1:
        print(1)
        exit()
    for j in range(N):
        n=A[j]
        for i in range(2,int((n)**0.5)+1):
            if n%i==0:
                cnt=0
                while(n%i==0):
                    n//=i
                    cnt+=1
                if kl[i]<cnt:
                    kl[i]=cnt
        if n!=1:
            if kl[n]<1:
                kl[n]=1
                
    lcm=1
    for i in range(2,10**6+1):
        lcm*=pow(i, kl[i], MOD)

    modsum=0
    for i in range(N):
        modsum+=pow(A[i],MOD-2,MOD)

    ans = lcm*modsum%MOD
    print(ans)
    
    
    
if __name__=="__main__":
    main()