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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {
	public static long l=0,l2=0;
	public static void main(String[] args) throws IOException {
		l = System.currentTimeMillis();
		new Main().exec();
		l2 = System.currentTimeMillis();
		
	}

	public void exec() throws IOException {
		InputUtil in = new InputUtil();
		PrintWriter out = new PrintWriter(System.out);
		int N = (int)in.nextInt();
		long[] T= in.nextLong(new long[N],N);
		out.println(getLcm(T));
		out.flush();
	}
	private long gcd(long a, long b){
		return b == 0 ? a : gcd(b, a % b);
	}
	private long lcm(long a, long b){
		return a / gcd(a, b) * b;
	}
//	private long getGcd(long a, long b){
//		if(a<b)
//			return getGcd(b,a);
//		long tmp = 0;
//		while (a%b!=0) {
//			tmp = b;
//			b = a%b;
//			a = tmp;
//		}
//		return b;
//	}
//	
//	private long getLcm(long a, long b){
//		if(a<b)
//			return getLcm(b,a);
//		long gcd = getGcd(a,b);
//		return (a/gcd)*b;
//	}
	
	private long getLcm(long[] T) {
		long ans = 0;
		for(int i=1; i<T.length; i++) {
			ans = lcm((ans == 0)?T[i-1]:ans,T[i]);
		}
		return ans;
	}
}




class InputUtil {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public int nextInt() throws NumberFormatException, IOException{
    	return Integer.parseInt(br.readLine());
    }
    
    public long[] nextLong(long[] a, int num) throws NumberFormatException, IOException{
        int i=0;
        while(i<num) {
            for(String s: br.readLine().split(" ")){
            	if(i<num) {
                    a[i++] = Long.parseLong(s);
            	}
            }
        }
        return a;
    }

}