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"
	"log"
	"os"
	"strconv"
)

func main() {
	scanner := Scanner()
	n := ReadInt(scanner)

	// ans := make(map[int]int, n)
	nMax := 10 * 10 * 10 * 10
	ans := make([]int, nMax+1)
	// count := 0

	for x := 1; x*x <= n; x++ {
		for y := 1; y*y <= n; y++ {
			for z := 1; z*z <= n; z++ {
				result := x*x + y*y + z*z + x*y + y*z + z*x
				if result < nMax {
					// fmt.Println(x, y, z, x*x+y*y+z*z+x*y+y*z+z*x)
					ans[result-1]++
				} else {
					break
				}
			}
		}
	}

	for i := 0; i < n; i++ {
		fmt.Println(ans[i])
	}
}

func Scanner() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	return scanner
}

func ReadInt(scanner *bufio.Scanner) int {
	var t string

	if scanner.Scan() {
		t = scanner.Text()
	}

	n, err := strconv.Atoi(t)
	if err != nil {
		log.Fatal(err)
	}

	return n

}