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: Wrong Answer)

from sys import stdin

def main():
    n = int(input())
    l = list(map(int, input().split()))
    l.sort()
    # print(l)
    ans = 0
    for i in range(len(l)-2):
        first = l[i]
        for j in range(i + 2, len(l)):
            second = l[j]
            s = i + 1
            e = j 
            # print("start",s, e)
            while(True):
                mid = int((s + e) / 2)
                # print("S",s, e, mid)
                
                if s == e:
                    break
                else:
                    if second >= first + l[mid]:
                        if s == mid:
                            s = e
                        else:
                            s = mid
                    else:
                        e = mid
            # print(s)
            ans += j - s
            print("ans", ans)
    print(ans)
if __name__ == '__main__':
    main()