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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N = int(input())
L = sorted(list(map(int, input().split())))
ans = 0

def nibunki_left(L, s, f, p):
	cent = (f-s)//2 + s
	if s == f:
		return s
	elif s+1 == f:
		if L[s] > p:
			return s
		else:
			return f

	if L[cent] <= p:
		return nibunki_left(L, cent, f, p)
	else:
		return nibunki_left(L, s, cent, p)

def nibunki_right(L, s, f, p):
	cent = (f-s)//2 + s
	if s == f:
		return f
	elif s+1 == f:
		if L[f] < p:
			return f
		else:
			return s

	if L[cent] < p:
		return nibunki_right(L, cent, f, p)
	else:
		return nibunki_right(L, s, cent, p)



ans = 0

for a in range(N-2):
	for b in range(a+1, N-1):
		l = max(L[a] - L[b], L[b] - L[a])
		r = L[a] + L[b]

		l_ind = nibunki_left(L, 0, N-1, l)
		r_ind = nibunki_right(L, 0, N-1, r)

		if l_ind <= b and r_ind <= b:
			continue
		elif l_ind <= b and r_ind > b:
			ans += r_ind - b
		elif l_ind > b and r_ind > b:
			ans += r_ind - l_ind + 1


print(ans)