Problem:
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.

Sample Input 1

5
4 4 9 7 5

Sample Output 1

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).

Sample Input 2

6
4 5 4 3 3 5

Sample Output 2

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.

Sample Input 3

10
9 4 6 1 9 6 10 6 6 8

Sample Output 3

39

Sample Input 4

2
1 1

Sample Output 4

0

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

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Runtime Error)

program make_triangle
      integer :: n
      integer,allocatable :: l(:)
      integer :: i, j, k
      integer :: t(3)
      integer :: ans = 0

      read *, n
      allocate(l(n))
      do i = 1, n
        read *, l(i)
      end do

      do i = 1, n-1
        do j = i + 1, n
          if(l(i) .gt. l(j))then
            k = t(i)
            t(i) = t(j)
            t(j) = k
          end if
        end do
      end do

      do i  = 1, n
        do j = i+1, n
          do k = j+1, n
            if(t(k) /= t(j) .and. t(i) /= t(j) .and. t(i) + t(j) > t(k)) then
              ans = ans + 1
            end if
          end do
        end do
      end do
      print *, ans
end program