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: Runtime Error)

N = int(input())
L = list(map(int, input().split()))
L.sort()
import numpy as np
L = np.array(L)
m = [0] * (L[-1] + 10)
for i in range(L[-1] + 10):
    m[i] = np.count_nonzero(L <= i)
print(L)
print(m)
cnt = 0
for i in range(N):
    for j in range(i + 1, N):
        tot = L[i] + L[j]
        if tot >= len(m) + 1:
            tot = len(m) - 2
        cnt += m[tot + 1] - m[L[j] + 1]
        print(i,j,tot,m[tot + 1],m[L[j] + 1])
print(cnt)