프로그램 명: coci_iks
제한시간: 1 초

[요약] N개의 수가 주어진다.

당신은 주어진 수 중 두 수 A, B를 선택하고 A의 소인수 X를 정해서 A를 A/X로 바꾸고 B를 BX로 바꾸는 작업을 할 수 있다. 몇 번의 작업 후 N개의 수의 최대공약수로 가능한 최댓값을 구하고, 이 때 필요한 최소 작업의 수를 구한다.

1번째 예제에서
4 4 1 -> 4 2 2로 바꾸면 1번의 작업으로 최대공약수가 2가 된다


Mirkos great grandmother Katica is an avid mathematician. She likes to torment Mirko with math games. This time she wrote down a sequence of numbers on a piece of paper and told Mirko he may do the following:

Mirko may perform this operation as many times he wants. His goal is to obtain the maximum possible score, because he gets candy from his great grandmother if he does so. The score for one sequence is the greatest common divisor of all the numbers in the sequence.

He is not very good at this, and he likes his candy so he has asked you to help him. Write a program that will calculate the maximum possible score. Since you are such a nice guy, you should also print the smallest number of times Mirko must perform the operation to obtain the maximum possible score.

입력

출력

The one and only line of output should contain two integers. The first integer is the maximal possible score Mirko can obtain. The second integer is the smallest number of operations Mirko needs to perform to obtain it.

입출력 예

입력

3
4 4 1

출력

2 1

입력

3
8 24 9

출력

12 3

입력

5
4 5 6 7 8

출력

2 2
출처:coci 2009-2010 contest4 3/6
번역:functionx

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