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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
# 整数の入力
fscanf(STDIN, "%d", $num);
if($num == 1) {
  fscanf(STDIN, "%d", $num);
  echo $num;
  return;
}

for($i=0;$i<$num;$i++){
	fscanf(STDIN, "%d", $sec[$i]);
}

echo  MathAppend::lcm($sec);


	/**
	 * Class MathAppend
	 * 
	 * 数学的によく使う処理をまとめたクラスです
	 */
	class MathAppend {
	
		/////////////////////////////////////////////////////////////////////////
		//
		// constructor
		//
		/////////////////////////////////////////////////////////////////////////
		
		private function __construct() {
		}
		
		
		
		/////////////////////////////////////////////////////////////////////////
		//
		// public functions
		//
		/////////////////////////////////////////////////////////////////////////
		
		/**
		 * 最大公約数を求めます
		 * 
		 * @param  array $list 比較数値配列
		 * @return int         最大公約数
		 * 
		 * @usage  echo MathAppend::gcd(1071, 1029); // 21
		 */
		public static function gcd(array $list) {
			// validationだけ先に
			$c = count($list);
			if ($c === 0)
				return 0;
			else if ($c === 1)
				return $list[0];
			
			return self::calcGCD($list);
		}
		
		/**
		 * 最小公倍数を求めます
		 * 
		 * @param  array $list 比較数値配列
		 * @return int         最小公倍数
		 * 
		 * @usage  echo MathAppend::lcm(1071, 1029); // 52479
		 */
		public static function lcm(array $list) {
			// validationだけ先に
			$c = count($list);
			if ($c === 0)
				return 0;
			else if ($c === 1)
				return 1;
			
			return self::calcLCM($list);
		}
		
		
		
		/////////////////////////////////////////////////////////////////////////
		//
		// private functions
		//
		/////////////////////////////////////////////////////////////////////////
		
		/**
		 * 最大公約数を求めます(本体)
		 * 
		 * @param  array &$list 比較数値配列
		 * @return int          最大公約数
		 */
		private static function calcGCD(array &$list) {
			$c = count($list);
			
			// ユークリッドの互除法を末尾2要素にかける
			$v = $list[$c - 1] % $list[$c - 2];
			if ($v === 0) {
				if ($c === 2)
					return $list[$c - 2];
				
				// 2要素の最大公約数が決まったら、配列を更新して再帰
				array_pop($list);
				return self::calcGCD($list);
			}
			
			$list[$c - 1] = $list[$c - 2];
			$list[$c - 2] = $v;
			return self::calcGCD($list);
		}
		
		/**
		 * 最小公倍数を求めます(本体)
		 * 
		 * @param  array &$list 比較数値配列
		 * @return int          最小公倍数
		 */
		private static function calcLCM(array &$list) {
			$c = count($list);
			$v = $list[$c - 1] * $list[$c - 2] / self::gcd(array($list[$c - 1], $list[$c - 2]));
			
			if ($c === 2)
				return $v;
			
			$list[$c - 2] = $v;
			array_pop($list);
			return self::calcLCM($list);
		}
	}