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)

def func():
    N = int(input())
    li = sorted(list(map(int, input().split())))
    r = 0
    i, j, k = -1,-1,-1
    for n1 in li:
        i += 1;
        if i + 3 == N:
            if li[i] + li[i + 1] > li[i + 2]:
                r += 1
            return r
        j = i
        for n2 in li:
            j += 1;
            k = j

            if j + 2 > N:
                break
            for n3 in li:
                k += 1;
                if k + 1 > N:
                    break
                if li[i] + li[j] > li[k]:
                    r += 1
                else:
                    break
print(func())