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: Accepted)

package main

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

func main() {
	N := getStdinInt()
	fInit(N)
	for i := 1; i <= N; i++ {
		fmt.Printf("%d\n", f(i))
	}
}

var fAns []int

func fInit(n int) {
	fAns = make([]int, n+1)
	nsqrt := int(math.Sqrt(float64(n)))
	for x := 1; x < nsqrt; x++ {
		for y := 1; y < nsqrt; y++ {
			for z := 1; z < nsqrt; z++ {
				ans := x*x + y*y + z*z + x*y + y*z + z*x
				if ans <= n {
					fAns[ans]++
				}
			}
		}
	}
}

func f(n int) int {
	return fAns[n]
}

var sc = bufio.NewReaderSize(os.Stdin, 1024*1024*10)

func getStdin() string {
	return readLine()
}
func getStdinInt() int {
	str := getStdin()
	rtn, _ := strconv.Atoi(str)
	return rtn
}
func getStdinInt2() (int, int) {
	list := getStdinIntArr()
	return list[0], list[1]
}
func getStdinInt3() (int, int, int) {
	list := getStdinIntArr()
	return list[0], list[1], list[2]
}
func getStdinInt64() int64 {
	str := getStdin()
	rtn, _ := strconv.ParseInt(str, 10, 64)
	return rtn
}
func getStdinInt64_2() (int64, int64) {
	list := getStdinIntArr64()
	return list[0], list[1]
}
func getStdinInt64_3() (int64, int64, int64) {
	list := getStdinIntArr64()
	return list[0], list[1], list[2]
}
func getStdinIntArr() []int {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.Atoi(val)
	}
	return rtn
}
func getStdinIntArr64() []int64 {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int64, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.ParseInt(val, 10, 64)
	}
	return rtn
}
func readLine() string {
	buf := make([]byte, 0, 0)
	for {
		l, p, _ := sc.ReadLine()
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}