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).



Sample input:
3
2 3 4


Sample output:
13

Submission status: Time Limit Exceeded

Solution code:
def kouyaku(a,b):
    aa = max(a,b)
    bb = min(a,b)
    if bb == 0:
        return aa
    else:
        return kouyaku(bb,aa%bb)

def power(a, b):
	if b == 0:
		return 1
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007
 
def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

primes = 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7849,97859,97861,97871,97879,97883,97919,97927,97931,97943,97961,97967,97973,97987,98009,98011,98017,98041,98047,98057,98081,98101,98123,98129,98143,98179,98207,98213,98221,98227,98251,98257,98269,98297,98299,98317,98321,98323,98327,98347,98369,98377,98387,98389,98407,98411,98419,98429,98443,98453,98459,98467,98473,98479,98491,98507,98519,98533,98543,98561,98563,98573,98597,98621,98627,98639,98641,98663,98669,98689,98711,98713,98717,98729,98731,98737,98773,98779,98801,98807,98809,98837,98849,98867,98869,98873,98887,98893,98897,98899,98909,98911,98927,98929,98939,98947,98953,98963,98981,98993,98999,99013,99017,99023,99041,99053,99079,99083,99089,99103,99109,99119,99131,99133,99137,99139,99149,99173,99181,99191,99223,99233,99241,99251,99257,99259,99277,99289,99317,99347,99349,99367,99371,99377,99391,99397,99401,99409,99431,99439,99469,99487,99497,99523,99527,99529,99551,99559,99563,99571,99577,99581,99607,99611,99623,99643,99661,99667,99679,99689,99707,99709,99713,99719,99721,99733,99761,99767,99787,99793,99809,99817,99823,99829,99833,99839,99859,99871,99877,99881,99901,99907,99923,99929,99961,99971,99989,99991]

pset = set(primes)
pd = {}
for i in range(len(primes)):
	pd[primes[i]] = i
MOD = 10**9+7
N = int(input())
A = [int(i) for i in input().split()]
K = [0]*len(primes)
for i in range(N):
	a = A[i]
	for i in range(len(primes)):
		if a in pset:
			K[pd[a]] = max(K[pd[a]], 1)
			break
		elif a == 1:
			break
		else:
			p = primes[i]
			cou = 0
			while a%p==0:
				a = a//p
				cou += 1
			K[i] = max(cou, K[i])
kv = 1
for i in range(len(primes)):
	kv *= power(primes[i], K[i])
	kv %= MOD
ans = 0
for i in range(N):
	ans += divide(kv, A[i])
	ans %= MOD
print(ans)