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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())
l = [int(c) for c in input().split()]
l.sort()
def bin_search(l, r, f):
    while r - l > 1:
        c = (l + r) // 2
        if f(c):
            r = c
        else:
            l = c
    return r

llen = len(l)
ans = 0
for i in range(llen):
    a = l[i]
    for j in range(i + 1, llen):
        b = l[j]
        s = a + b
        upper = bin_search(j, n, lambda x: l[x] >= s)
        #print(i, j, upper)
        ans += upper - (j + 1)
print(ans)