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#F1938. Pashmak and Flowers

    ID: 1944 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 3 上传者: 标签>组合数学模拟排序数学编程与模拟基础难度共享题库Codeforces英文题面题目来源题面语言

Pashmak and Flowers

题目描述

B. Pashmak and Flowers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Pashmak decided to give Parmida a pair of flowers from the garden. There are n flowers in the garden and the i-th of them has a beauty number bi. Parmida is a very strange girl so she doesn't want to have the two most beautiful flowers necessarily. She wants to have those pairs of flowers that their beauty difference is maximal possible!

Your task is to write a program which calculates two things:

  1. The maximum beauty difference of flowers that Pashmak can give to Parmida.
  2. The number of ways that Pashmak can pick the flowers. Two ways are considered different if and only if there is at least one flower that is chosen in the first way and not chosen in the second way.
Input

The first line of the input contains n (2≤n≤2·105). In the next line there are n space-separated integers b1, b2, ..., bn (1≤bi≤109).

Output

The only line of output should contain two integers. The maximum beauty difference and the number of ways this may happen, respectively.

Examples
Input
2
1 2
Output
1 1
Input
3
1 4 5
Output
4 1
Input
5
3 1 2 3 1
Output
2 4
Note

In the third sample the maximum beauty difference is 2 and there are 4 ways to do this:

  1. choosing the first and the second flowers;
  2. choosing the first and the fifth flowers;
  3. choosing the fourth and the second flowers;
  4. choosing the fourth and the fifth flowers.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1518 题。保留原作者与原赛事署名。