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: Runtime Error)

import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from fractions import gcd
 
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))
 
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

# from functools import reduce
# from math import gcd as gcd_base  # from fractions import gcd
# gcd = lambda *numbers: reduce(gcd_base, numbers)  # 3 数以上の最大公約数

# lcm_base = lambda x, y: (x * y) // gcd_base(x, y)
# lcm = lambda *numbers: reduce(lcm_base, numbers, 1)  # 3 数以上の最小公倍数
# 最小公倍数
def gcd(a, b):
    if a < b:
        a, b = b, a
    while a % b != 0:
        a, b = b, a % b
    return b


## 最大公約数 
def lcm(a, b):
    y = a*b / gcd(a, b)
    return int(y)

def many_lcm(l):
    for i in range(len(l)-1):
        if i == 0:
            ans = lcm(l[0], l[1])
        else:
            ans = lcm(l[i+1], ans)
    return ans
N = INT()
A = LIST()

lm = many_lcm(A)
# print(l)
B = []
for a in A:
    B.append(lm // a)
print(sum(B) % mod)