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)

def triangle_search(list,item):
    low = 0
    high = len(list) - 1
    while low <= high:
        mid = (low + high) // 2
        if mid == high:
            return mid
        elif mid == low:
            return mid
        elif list[mid] > item >= list[mid+1]:
            return mid
        elif list[mid + 1] > item:
            low = mid + 1
        else:
            high = mid - 1
    return mid

N = int(input())
L = list(map(int,input().split()))
L.sort()
L.reverse()
ans = 0
for i in range(0,N-2):
    for j in range(i+1,N-1):
        if triangle_search(L,L[i]-L[j]) > j:
            ans = ans + triangle_search(L,L[i]-L[j]) - j 
print(ans)