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: Accepted)

import Control.Applicative
import Control.Monad
import Data.Vector.Unboxed.Mutable (IOVector, STVector)
import qualified Data.Vector.Unboxed.Mutable as VM

main :: IO ()
main = readLn >>= solve

solve :: Int -> IO ()
solve n = do
  let ls = takeWhile ((< n) .(^2)) [1..]
  v <- VM.replicate (n + 1) 0 :: IO (IOVector Int)
  forM_ ls $ \x -> do
    forM_ ls $ \y -> do
      forM_ ls $ \z -> do
        let m = x * x + y * y + z * z + x * y + y * z + z * x
        when (m <= n) $ do
          VM.modify v (+1) m
  forM_ [1 .. n] $ \i -> do
    c <- VM.read v i
    print c