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()

s = 0

ma = L[N-1]
for j in range(N-2):
    ja = L[j]
    for k in range(j+1,N-1):
        ka = L[k]
        # L[i] < L[j]+L[k] となる L[i]の数を求める
        key = ja + ka
        l = k + 1
        r = N - 1
        while r - l > 1:
            m = l + (r - l) // 2
            if L[m] < key:
                l = m
            else:
                r = m
        kka = L[k+1]
        if kka < key <= ma:
            s += l-k
        elif key <= kka:
            s += 0
        else:
            s += N-k-1

print(s)