Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program triangle
    implicit none
    integer :: n, i, j, k, cnt = 0, t
    integer,allocatable :: l(:)
    read *, n
    allocate(l(n))
    read *, l(1:n)
    do i = 1, n-1
        do j = 1, n
            if(l(i) .gt. l(j))then
                t = l(i)
                l(i) = l(j)
                l(j) = t
            end if
        end do
    end do
    i = 1
    j = 2
    k = 3
    do while(i .le. n-2)
        do while(j .le. n-1)
            do while(k .le. n)
                if(l(i)+l(j) .gt. l(k) .and. l(j)+l(k) .gt. l(i) .and. l(k)+l(i) .gt. l(j))then
                    cnt = cnt+n-k+1
                    k = k + 1
                end if
            end do
            j = j + 1
        end do
        i = i + 1
    end do
    print *, cnt
end program