Description

Given a sequence of length $n$, ${a_1,a_2,\cdots,a_n}$, in each operation you may choose an interval $[l, r]$ and either add $1$ to every number in this interval or subtract $1$ from every number in this interval.

What is the minimum number of operations needed to make all numbers in the sequence equal, and under this minimum, how many different final sequences are possible?

Input Format

The first line contains a positive integer $n$. Then $n$ lines follow; the integer on the $(i+1)$-th line is $a_i$.

Output Format

Output the minimum number of operations on the first line. Output the number of possible final sequences on the second line.

4
1
1
2
2

1
2

Hint

Constraints: For $100\%$ of the testdata, $n \le 100000$, $0 \le a_i \le 2^{31}$.

Translated by ChatGPT 5