Score : 300 points
There are N integers, A_1, A_2, ..., A_N, written on the blackboard.
You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.
Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.
Input is given from Standard Input in the following format:
N A_1 A_2 ... A_N
Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.
3 7 6 8
2
If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.
3 12 15 18
6
2 1000000000 1000000000
1000000000
We can replace an integer with itself.