Triangles

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.

Constraints

Print the number of different triangles that can be formed.

Input

Input is given from Standard Input in the following format:

N L_1 L_2 ... L_N

Examples

Input

4 3 4 2 1

Output

1

Input

3 1 1000 1

Output

0

Input

7 218 786 704 233 645 728 389

Output

23

inputFormat

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.

Constraints

Print the number of different triangles that can be formed.

Input

Input is given from Standard Input in the following format:

N L_1 L_2 ... L_N

Examples

Input

4 3 4 2 1

outputFormat

Output

1

Input

3 1 1000 1

Output

0

Input

7 218 786 704 233 645 728 389

Output

23

样例

4
3 4 2 1

1