B - Making Triangle

Score : $200$ points

Problem Statement

We have sticks numbered $1, \cdots, N$. The length of Stick $i$ $(1 \leq i \leq N)$ is $L_i$.

In how many ways can we choose three of the sticks with different lengths that can form a triangle?

That is, find the number of triples of integers $(i, j, k)$ $(1 \leq i < j < k \leq N)$ that satisfy both of the following conditions:

• $L_i$, $L_j$, and $L_k$ are all different.
• There exists a triangle whose sides have lengths $L_i$, $L_j$, and $L_k$.

Constraints

• $1 \leq N \leq 100$
• $1 \leq L_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$L_1$ $L_2$ $\cdots$ $L_N$

Output

Print the number of ways to choose three of the sticks with different lengths that can form a triangle.

5
4 4 9 7 5

5

The following five triples $(i, j, k)$ satisfy the conditions: $(1, 3, 4)$, $(1, 4, 5)$, $(2, 3, 4)$, $(2, 4, 5)$, and $(3, 4, 5)$.

6
4 5 4 3 3 5

8

We have two sticks for each of the lengths $3$, $4$, and $5$. To satisfy the first condition, we have to choose one from each length.

There is a triangle whose sides have lengths $3$, $4$, and $5$, so we have $2 ^ 3 = 8$ triples $(i, j, k)$ that satisfy the conditions.

10
9 4 6 1 9 6 10 6 6 8

39

2
1 1

0

No triple $(i, j, k)$ satisfies $1 \leq i < j < k \leq N$, so we should print $0$.