SAMER08F - Feynman

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Richard Phillips Feynman was a well known American physicist and a recipient of the Nobel Prize in Physics. He worked in theoretical physics and also pioneered the field of quantum computing. He visited South America for ten months, giving lectures and enjoying life in the tropics. He is also known for his books "Surely You're Joking, Mr. Feynman!" and "What Do You Care What Other People Think?", which include some of his adventures below the equator.

His life-long addiction was solving and making puzzles, locks, and cyphers. Recently, an old farmer in South America, who was a host to the young physicist in 1949, found some papers and notes that is believed to have belonged to Feynman. Among notes about mesons and electromagnetism, there was a napkin where he wrote a simple puzzle: "how many different squares are there in a grid of N ×N squares?".

In the same napkin there was a drawing which is reproduced below, showing that, for N=2, the answer is 5.

subir imagenes

Input

The input contains several test cases. Each test case is composed of a single line, containing only one integer N, representing the number of squares in each side of the grid (1 ≤ N ≤ 100).

The end of input is indicated by a line containing only one zero.

Output

For each test case in the input, your program must print a single line, containing the number of different squares for the corresponding input.

Example

Input:
2
1
8
0


Output:
5
1
204


hide comments
rrm_2016: 2016-10-12 16:01:13

Please read the input format...made me submit 1 wrong solution

teracoder: 2016-10-11 10:33:09

I wish I had seen the weird input pattern earlier, so 2 tries...

quvi: 2016-09-16 16:18:51

AC in first go! Interesting one. Use mathematical logic and observe the pattern :D

suraj_: 2016-08-16 22:42:33

qed

young_padawan: 2016-07-19 09:36:46

me too @zakir_0

eminemvarun: 2016-07-15 18:56:32

Is answer to 3, fourteen?

saurabh412: 2016-07-15 04:47:28

AC in One Go :)

true_coder: 2016-06-09 15:36:01

an easy dp problem for beginners (although easily solved straight forwardly)

Last edit: 2016-06-09 15:37:17
code0monkey1: 2016-06-01 12:04:24

hint : hope you know your summation formulas !! ;)

chakkriii: 2016-05-11 18:24:23

find logic , it will be mathematical formula


Added by:Diego Satoba
Date:2008-11-23
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:ASM64 C C++ 4.3.2 CPP FORTRAN JAVA PAS-GPC PAS-FPC
Resource:South American Regional Contests 2008