Multiple Clocks

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.

Examples

Input

2 2 3

Output

6

Input

5 2 5 10 1000000000000000000 1000000000000000000

Output

1000000000000000000

inputFormat

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

outputFormat

Output

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

Examples

Input

2 2 3

Output

6

Input

5 2 5 10 1000000000000000000 1000000000000000000

Output

1000000000000000000

样例

5
2
5
10
1000000000000000000
1000000000000000000

1000000000000000000