Jack and Jill went up the hill. Jack proposed Jill after reaching at the top of the hill. Jill gave Jack 'N' numbers and asked him to choose a pair of numbers such that their absolute difference is minimum. She also asked him to choose a pair of numbers such that their absolute difference is maximum. Jill wondered just finding maximum and minimum values is mainstream and it will be a cakewalk for Jack, instead she asked him to find number of pairs which have minimum absolute difference and number of pairs which have maximum absolute difference.

Jill will accept Jack's proposal only if he can answer her question correctly. Jack does not know programming. Fortunately Jack had his laptop with him, fully charged and with good internet connection. He mailed you the numbers and asked you to mail him the answers back, as you are known to be a good programmer. Now it's your turn to help him.

Input

First line contains a positive integer 'N'. Next line contains 'N' non-negative integers 'a[i]' separated by a single space.

Output

Print the number of pairs having minimum and maximum difference separated by a single space.

Constraints

1 ≤ N ≤ 10⁵

0 ≤ a[i] ≤ 10¹⁵

Sample

Input:
5
5 12 8 1 35

Output:
1 1

Explanation

It's optimal to choose the pair (5, 8) for the minimum difference. So only 1 pair.

It's optimal to choose the pair (1, 35) for the maximum difference. Here also only 1 pair.