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)

import bisect
n = int(input())
l = list(map(int, input().split()))
l.sort()
#print(l)
ans = 0
for x in range(n - 1):
    for y in range(x + 1, n):
        lx = l[x]
        ly = l[y]
        s = lx + ly
        pl = bisect.bisect_left(l, s)
        pr = bisect.bisect_right(l, s)
        c = l[y + 1:pr]
        #print("x:{} y:{}, lx:{}, ly:{} pl:{}, pr:{}, c:{}".format(x, y, lx, ly, pl, pr, c))
        for lz in c:
            if lx + ly > lz:
                if lx + lz > ly:
                    if ly + lz > lx:
                        #print("{} {} {}".format(lx, ly, lz))
                        ans += 1
print(ans)