Problem:
Score : 300 points

Problem Statement

We have N clocks. The hand of the i-th clock (1≤i≤N) rotates through 360° in exactly T_i seconds.

Initially, the hand of every clock stands still, pointing directly upward.

Now, Dolphin starts all the clocks simultaneously.

In how many seconds will the hand of every clock point directly upward again?

Constraints

1≤N≤100

1≤T_i≤10^{18}

All input values are integers.

The correct answer is at most 10^{18} seconds.

Input

Input is given from Standard Input in the following format:

N
T_1
:
T_N

Output

Print the number of seconds after which the hand of every clock point directly upward again.

Sample Input 1

2
2
3

Sample Output 1

6

We have two clocks. The time when the hand of each clock points upward is as follows:

Clock 1: 2, 4, 6, ... seconds after the beginning

Clock 2: 3, 6, 9, ... seconds after the beginning

Therefore, it takes 6 seconds until the hands of both clocks point directly upward.

Sample Input 2

5
2
5
10
1000000000000000000
1000000000000000000

Sample Output 2

1000000000000000000

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
from functools import reduce
import copy
import math
from pprint import pprint
import collections
import bisect


sys.setrecursionlimit(4100000)


def inputs(num_of_input):
    ins = [input() for i in range(num_of_input)]
    return ins


def int_inputs(num_of_input):
    ins = [int(input()) for i in range(num_of_input)]
    return ins


def euqrid(a, b):
    if a > b:
        large = a
        small = b
    else:
        large = b
        small = a

    if small == 0:
        return large
    return euqrid(small, large % small)


def calc_m(numbers):
    if len(numbers) == 1:
        return numbers[0]
    if len(numbers) == 2:
        a = numbers.pop()
        b = numbers.pop()
        e = euqrid(a, b)
        return a * b // e
    a = numbers.pop()
    b = calc_m(numbers)
    e = euqrid(a, b)
    return a * b // e


def solve(inputs):
    clocks = inputs
    return calc_m(clocks)


def string_to_int(string):
    return list(map(int, string.split()))


if __name__ == "__main__":
    N = int(input())
    ret = solve(int_inputs(N))
    print(ret)