10782: ABC143 - D - Triangles
[Creator : ]
Description
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.
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:
```
$N$
$L_1$ $L_2$ $...$ $L_N$
```
```
$N$
$L_1$ $L_2$ $...$ $L_N$
```
Output
Print the number of different triangles that can be formed.
Constraints
- All values in input are integers.
- $3 \leq N \leq 2 \times 10^3$
- $1 \leq L_i \leq 10^3$
- $3 \leq N \leq 2 \times 10^3$
- $1 \leq L_i \leq 10^3$
Sample 1 Input
4
3 4 2 1
Sample 1 Output
1
Only one triangle can be formed: the triangle formed by the first, second, and third sticks.
Sample 2 Input
3
1 1000 1
Sample 2 Output
0
No triangles can be formed.
Sample 3 Input
7
218 786 704 233 645 728 389
Sample 3 Output
23