Triangles from Five Sticks

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Time limit2sMemory limit512 MB

Summary

Given five distinct stick lengths, count how many 3-stick subsets can form a triangle with positive area.

Level: Easy2 of 10
Topics: Brute force, Geometry, Implementation
Solved: No attempts yet

Problem

Vera has five sticks, and no two of them have the same length. The lengths are $l_1, l_2, l_3, l_4, l_5$ . Vera may pick any three of them and use the three sticks as the sides of a triangle. The sticks cannot be bent or cut, and the triangle must have positive area.

How many different triangles can Vera make?

Input

The first line contains the integers $l_1, l_2, l_3, l_4, l_5$ separated by spaces. ( $1 \le l_i \le 1000$ )

Output

Print the number of ways to form a triangle as a single integer on one line.

Hint

In the first example the three triangles come from the lengths 2, 3, 4 and 2, 4, 5 and 3, 4, 5.

Examples3

Example 1
Input
```
1 2 3 4 5
```
Expected output
```
3
```
Example 2
Input
```
1 2 4 8 16
```
Expected output
```
0
```
Example 3
Input
```
100 101 102 103 104
```
Expected output
```
10
```