Pashmak and Flowers

题意翻译

Pashmak 想要给 Parmida一对花。有n朵花在花园里，每朵花都有一个魅力值bi，Pashmak想要两朵魅力值相差最大的花，问有多少种方案？ 输入格式 首先输入n (2<= n <= 2*10^5)。 接下来一行有n个空格隔开的整数b1, b2, …, bn (1 <= bi <= 10 ^ 9). 输出格式 输出最大差异和方案数，中间用空格隔开

题目描述

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 $ b_{i} $ . 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.

输入输出格式

输入格式

The first line of the input contains $ n $ $ (2<=n<=2·10^{5}) $ . In the next line there are $ n $ space-separated integers $ b_{1} $ , $ b_{2} $ , ..., $ b_{n} $ $ (1<=b_{i}<=10^{9}) $ .

输出格式

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

输入输出样例

输入样例 #1

2
1 2

输出样例 #1

1 1

输入样例 #2

3
1 4 5

输出样例 #2

4 1

输入样例 #3

5
3 1 2 3 1

输出样例 #3

2 4

说明

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.