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.

Input

Input is given from Standard Input in the following format:
N
L_1 L_2 ... L_N

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Constraints

• All values in input are integers.
• $3 \leq N \leq 2 \times 10^3$
• $1 \leq L_i \leq 10^3$

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

见题面 Input 部分

见题面 Output 部分