Contest Duration: - (local time) (100 minutes) Back to Home
D - Triangles /

Time Limit: 2 sec / Memory Limit: 1024 MB

• a < b + c
• b < c + a
• c < a + b

### 制約

• 入力は全て整数
• 3 ≤ N ≤ 2 \times 10^3
• 1 \leq L_i \leq 10^3

### 入力

N
L_1 L_2 ... L_N


### 入力例 1

4
3 4 2 1


### 出力例 1

1


### 入力例 2

3
1 1000 1


### 出力例 2

0


### 入力例 3

7
218 786 704 233 645 728 389


### 出力例 3

23


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