FOJ1091 Zig-Zag Lines

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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

Sample Output

这题看了N久，还是没找到递推关系，不过看了某大牛的的递推思想的确是妙：先将Z线斜线段看成直线处理，生成的区域数目H（n）,H(1)=6;H(n+1)=H(n)+)+(3n+1)*2+(3n+3)，（3n+1）是每条新增的平行线把前H（n）个区域划分的增加的数目，这时区域里直线的数目=3n+2,最后一条斜线使得区域增加的数目=3n+3。Z中斜线是线段的M（n）,M(n)=G(n)-4n,因为，每个Z有两个角，如果斜线是直线，把每个角都补上对角，发现区域里会多出2*2*n块。

M（n+1）=M（n）+9n+1.

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