Problem1597--Makes And The Product

1597: Makes And The Product

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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<j<k), such that ai·aj·ak is minimum possible, are there in the array? Help him with it!

Input

The first line of input contains a positive integer number n(3≤n≤105) − the number of elements in array a. The second line contains n positive integer numbers ai(1≤ai≤109) − the elements of a given array.

Output

Print one number − the quantity of triples (i,j,k) such that i,j and k are pairwise distinct and ai·aj·ak is minimum possible.

Examples
Input
4
1 1 1 1
Output
4
Input
5
1 3 2 3 4
Output
2
Input
6
1 3 3 1 3 2
Output
1
Note

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.

Source/Category

 
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