Problem Statement

Happy New Year!

While making a kadomatsu to decorate the entrance, I noticed something.

Suppose $N$ bamboo poles are arranged at random, and let their heights be $A_i$ respectively.
When taking out $3$ consecutive poles without changing their order, I became curious how many of these combinations form a "kadomatsu sequence".

A kadomatsu is apparently something where "among the $3$ chosen bamboo poles, the $2$nd in descending order of length is positioned on the left or right side". Here,
one that additionally satisfies the condition "the $3$ lengths are all different" is called a "kadomatsu sequence".

Given the heights of the $N$ bamboo poles, find the number of combinations that form a "kadomatsu sequence".

Input

$N$
$A_1\ A_2 \dots A_N$

All inputs are given as integers.
$3\le N \le 100=10^2$
$1\le A_i \le 100=10^2,1\le i \le N$

Output

Output the number of combinations that form a kadomatsu sequence. Print a newline at the end.

Sample

Sample 1

Input

5
1 3 4 1 2

Output

2

$[3,4,1]$ and $[4,1,2]$ are kadomatsu sequences.
Note that $[3,4,2]$ and the like are not consecutive.

5
1 4 2 4 1

2

5
1 4 1 5 2

2