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 = list(map(int, input().split()))
L.sort()

ans = 0
flag = 0
ma = 2

for left1 in range(N-2):
    for left2 in range(left1+1, N-1):
        ma = left2 +1
        for right in range(max(ma, left2+1), N):
            a = L[right] - ( L[left1] + L[left2])
            if a < 0:
                flag = 1
                if right == N-1:
                    ans += right - left2
                    break
            if a >= 0:
                ma = right - 1
                if flag == 1:
                    ans += right - left2 - 1
                    flag = 0
                break
print(ans)