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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
)

func main() {
	read := bufio.NewReader(os.Stdin)
	write := bufio.NewWriter(os.Stdout)
	defer write.Flush()
	var n int
	fmt.Fscan(read, &n)
	for i := 1; i <= n; i++ {
		sum := 0
		lim := int(math.Sqrt(float64(i+1)/2) + 1)
		for x := 1; x <= lim; x++ {
			for y := 1; y <= lim; y++ {
				xpy := (x + y) * (x + y)
				for z := 1; z <= lim; z++ {
					ypz := (y + z) * (y + z)
					zpx := (z + x) * (z + x)
					if xpy+ypz+zpx == 2*i {
						sum++
					}
				}
			}
		}
		fmt.Fprintln(write, sum)
	}
}