Count the Regions

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

What's the maximum number of regions definable by N zig-zag lines, each of which consists of two parallel infinite half-lines joined by a straight line segment?

Here is an example of 2 zig-zag lines yield 12 regions at the most.


Input

The input consists of a sequence of N (<= 10000), which is the number of the zig-zag lines, one per line.


Output

For each N, you should output the number of the maximum regions.


Sample Input

1
2

Sample Output

2
12

Hint

None

Source

ZOJ Monthly, October 2003

提交代码