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-----
4
3 4 2 1

-----Sample Output-----
1

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

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