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 (2.4.0) (judge verdict: Time Limit Exceeded)

MOD = 10**9+7
def fact(n):
    dict = {}
    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
            dict[i] = cnt

    if temp!=1:
        dict[temp] = 1

    if dict=={}:
        dict[n] = 1

    return dict

def lcm(arr):
    # 素因数分解をもとにarr全体のLCMを求める
    lcm = 1
    factor = {}
    for a in arr:
        f = fact(a)
        for k,v in f.items():
            if k in factor:
                tmp = factor[k]
                factor[k] = max(factor[k],v)
                lcm *= pow(k,max(0, v-tmp),MOD)%MOD
            else:
                factor[k] = v
                lcm *= pow(k,v,MOD)%MOD

    return lcm

def main():
    N = int(input())
    A = list(map(int, input().split()))
    # 方針.A全体のlcmをLとすると、ans=Σ(i=[0,N])x/Ai
    ans = 0
    L = lcm(A)
    for a in A:
        ans += (L//a)%MOD
        ans %= MOD
    print(ans)

main()