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)

# coding: utf-8
def binary_search(x, L2):
    l, r = 0, len(L2)-1
    mid = (r + l) // 2
    while r - l > 1:
        mid = (r + l) // 2
        if L2[mid] == x:
            return len(L2) - mid
        elif L2[mid] > x:
            l = mid
        elif L2[mid] < x:
            r = mid
    if L2[r] > c:
        return r
    else:
        return l

N = int(input())
L = list(map(int, input().split()))
L.sort()
L = L[::-1]
ans = 0
for i in range(N-2):
    a = L[i]
    for j in range(i+1, N-1):
        b = L[j]
        c = a - b
        r = binary_search(c, L)
        if r > j and L[r] > c:
            ans += r - j
print(ans)