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: Accepted)

from collections import Counter
N = int(input())
L = Counter(int(i) for i in input().split())
maxL = max(L)
key = sorted(L.keys())
val = [L[i] for i in range(1, max(L) + 1)]
acc = [0] * (len(val) + 1)
for i in range(len(val)):
    acc[i + 1] = acc[i] + val[i]
cnt = 0
for a in key:
    cnt += L[a] * (L[a] - 1) * (L[a] - 2) // 6
    cnt += max(acc[min(2 * a - 1, maxL)] - acc[a], 0) * L[a] * (L[a] - 1) // 2
for i in range(len(key) - 1):
    for j in range(i + 1, len(key)):
        a, b = key[i], key[j]
        cnt += L[a] * L[b] * (L[b] - 1) // 2
for i in range(len(key) - 2):
    for j in range(i + 1, len(key) - 1):
        a, b = key[i], key[j]
        cnt += max(acc[min(a + b - 1, maxL)] - acc[b], 0) * L[a] * L[b]
print(cnt)