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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace abc070_c
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = GetInt();
            var TL = new List<long>();

            for(int i = 0; i < N; i++) 
                TL.Add(GetLong());

            var r = Lcm(TL[0], TL[1]);

            for (int i = 2; i < N; i++) 
                r = Lcm(r, TL[i]);

            Console.WriteLine(r);
        }

        public static string GetStr() => Console.ReadLine();
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static decimal GetDecimal() => decimal.Parse(Console.ReadLine());

        public static List<string> GetStrList() => Console.ReadLine().Split(' ').ToList();
        public static List<int> GetIntList() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
        public static List<long> GetLongList() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
        public static List<double> GetDoubleList() => Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToList();
        public static List<decimal> GetDecimalList() => Console.ReadLine().Split(' ').Select(x => decimal.Parse(x)).ToList();

        /// <summary>
        /// 最小公倍数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static long Lcm(long a, long b)
        {
            return a / Gcd(a, b) * b;
        }

        /// <summary>
        /// 互いに素
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static bool Coprime(long a, long b)
        {
            return Gcd(a, b) == 1;
        }

        /// <summary>
        /// 最小公約数：ユークリッドの互除法 
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static long Gcd(long a, long b)
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }
    }
}