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)

# -*- coding: utf-8 -*-

n = int(input())
l = [int(i) for i in input().split()]
l.sort()
# print(l)

count = 0
for i in range(n-3):
    for j in range(i+1, n-2):
        # j+1~n-1まで二分探索
        left = j+1
        right = n-1
        # print(left, right)
        while left <= right:
            mid = (left + right) // 2
            if l[i] + l[j] > l[mid] and l[j] + l[mid] > l[i] and l[mid] + l[i] > l[j]:
                left = mid + 1
                satisfied = mid
            else:
                right = mid - 1
        # print(j+1, right)
        count += right - j+1

print(count)