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
from collections import deque, Counter, defaultdict

input = sys.stdin.readline
MOD = (10**9+7)

def factorization(n):
    arr = []
    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
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr


def pow_k1(x, n):
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2
    return K * x


def pow_k(x, n):
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2
        x%=MOD
    return K * x


def main():
    n = int(input())
    al = list(map(int, input().split())) 
    lcm_dic = defaultdict(int)
    # lcm_dic = {}
    # al_facs = []
    for a in al:
        fac = factorization(a)
        # a_fac_dic = {}
        for f in fac:
            # lcm_dic.setdefault(f[0],0)
            lcm_dic[f[0]] = max(f[1], lcm_dic[f[0]])
            # a_fac_dic[f[0]] = f[1]
        # al_facs.append(a_fac_dic)


    lcm = 1
    for prime, cnt in lcm_dic.items():
        lcm *= pow_k1(prime,cnt)

    
    ans = 0
    for a in al:
        ans += lcm//a
        if ans >= MOD: ans%=MOD
    # ans%=MOD


    # ans = 0
    # for al_f in al_facs:
    #     curr_val = 1
    #     for prime, cnt in lcm_dic.items():
    #         if prime in al_f:
    #             curr_val *= pow_k(prime,(cnt-al_f[prime]))
    #             curr_val%=MOD
    #         else:
    #             curr_val *= pow_k(prime,cnt)
    #             curr_val%=MOD
    #     ans += curr_val
    #     ans %= MOD
    print(ans)


if __name__ == "__main__":
    main()