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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

	public void Proc()
	{

        int clockCount = int.Parse(Reader.ReadLine());

        long[] inpt = new long[clockCount];
        for (int i = 0; i < clockCount; i++) {
            inpt[i] = long.Parse(Reader.ReadLine());            
        }

        if(clockCount == 1) {
            Console.WriteLine(inpt[0]);
            return;
        }
        long tmp = inpt[0];
        for (int i = 1; i < clockCount; i++) {
            tmp = GetKoubai(tmp, inpt[i]);
        }
        Console.WriteLine(tmp);
    }


    private long GetKoubai(long num1, long num2) {
        if(num1%num2==0) {
            return num1;
        }
        long kouyaku = GetKouyaku(num1, num2);

        long tmp1 = num1 / kouyaku;
        long tmp2 = num2 / kouyaku;
        return tmp1 * tmp2 * kouyaku;
    }

    private long GetKouyaku(long num1, long num2) {
        if(num1%num2==0) {
            return num2;
        }
        return GetKouyaku(num2, num1 % num2);
    }


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"



5
2
5
10
1000000000000000000
1000000000000000000


";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}