Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Data.Array.IO
main = do
  n <- readLn :: IO Int
  let as = flip
        map
        [(x, y, z) | x <- [1 .. 100], y <- [1 .. 100], z <- [1 .. 100], x+y+z <= 110]
        $ \(x, y, z) -> x ^ 2 + y ^ 2 + z ^ 2 + x * y + y * z + z * x
  ar <- newArray (1,n) 0 :: IO (IOUArray Int Int)
  flip mapM_ as $ write n ar
  flip mapM_ [1..n] $ \i -> print =<< readArray ar i
  where
      write n ar i | i <= n = writeArray ar i =<< (+1) <$> (readArray ar i)
              | otherwise = return ()