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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import sys
input = sys.stdin.readline

def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    mod=10**9+7
    from collections import defaultdict
    #nの素因数分解，[[a1,b1],[a2,b2]...]   aがb個,ddで
    def factorization(n):
        flag=0
        if n==1:
            return [0,1]
        dd = defaultdict(int)
        temp = n
        for i in range(2, int(-(-n**0.5//1))+1):
            if temp%i==0:
                cnt=0
                while temp%i==0:
                    cnt+=1
                    temp //= i
                dd[i]=cnt
                flag=1

        if temp!=1:
            dd[temp]=1
            flag=1

        if flag==0:
            dd[n]=1

        return dd
    
    lcm_dd = defaultdict(int)
    
    N=I()
    A=LI()
    L=[]
    for i in range(N):
        a=A[i]
        dd=factorization(a)
        for k,v in dd.items():
            p,cnt=k,v
            lcm_dd[p]=max(lcm_dd[p],cnt)
            
    lcm=1
    for k,v in lcm_dd.items():
        temp=pow(k,v,mod)
        lcm=(lcm*temp)%mod
        
    ans=0
    for i in range(N):
        temp=(lcm*pow(A[i],mod-2,mod))%mod
        ans=ans+temp
        
    print(ans%mod)
        
    


main()