Makes And The Product

题意翻译

给你 $n$ 个数 $a[1...n]$ 问你满足 $a[i]\times a[j]\times a[k]$ 的值最小，且 $i<j<k$ 的有序对有几个？

题目描述

After returning from the army Makes received a gift — an array $ a $ consisting of $ n $ positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a particular question: how many triples of indices $ (i, j, k) $ ( $ i&lt;j&lt;k $ ), such that $ a_{i}·a_{j}·a_{k} $ is minimum possible, are there in the array? Help him with it!

输入输出格式

输入格式

The first line of input contains a positive integer number $ n (3<=n<=10^{5}) $ — the number of elements in array $ a $ . The second line contains $ n $ positive integer numbers $ a_{i} (1<=a_{i}<=10^{9}) $ — the elements of a given array.

输出格式

Print one number — the quantity of triples $ (i, j, k) $ such that $ i, j $ and $ k $ are pairwise distinct and $ a_{i}·a_{j}·a_{k} $ is minimum possible.

输入输出样例

输入样例 #1

4
1 1 1 1

输出样例 #1

4

输入样例 #2

5
1 3 2 3 4

输出样例 #2

2

输入样例 #3

6
1 3 3 1 3 2

输出样例 #3

1

说明

In the first example Makes always chooses three ones out of four, and the number of ways to choose them is $ 4 $ . In the second example a triple of numbers $ (1,2,3) $ is chosen (numbers, not indices). Since there are two ways to choose an element $ 3 $ , then the answer is $ 2 $ . In the third example a triple of numbers $ (1,1,2) $ is chosen, and there's only one way to choose indices.