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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

/*input
6
*/




import java.math.*;
import java.io.*;
import java.util.*;
public class Main
{
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead;
public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        }
public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        }
public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9');
if (neg) 
                return -ret; 
            return ret; 
        }
public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        }
public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read();
do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9');
if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            }
if (neg) 
                return -ret; 
            return ret; 
        }
private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        }
private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        }
public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 




        
    static Reader sc=new Reader();
    static BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String args[])throws IOException
    {
        /*
         * For integer input: int n=inputInt();
         * For long input: long n=inputLong();
         * For double input: double n=inputDouble();
         * For String input: String s=inputString();
         * Logic goes here
         * For printing without space: print(a+""); where a is a variable of any datatype
         * For printing with space: printSp(a+""); where a is a variable of any datatype
         * For printing with new line: println(a+""); where a is a variable of any datatype
            Scanner in = new Scanner(System.in);
        //all four
         int[] dr = { 1, 0, -1, 0 };
         int[] dc = { 0, 1, 0, -1 };
         */
 	int n=inputInt();


 	int[] a= new int[n+1];
 	
 		int cnt=0;
 		for(int x=1;x<100;x++)
 		{
 			for(int y=1;y<100;y++)
 			{
 				for(int z=1;z<100;z++)
 				{
 					int i=x*x +y*y+z*z+x*z+x*y+y*z;

 					if(i<=n)
 						a[i]++;
 				}
 			}
 		}

 		StringBuilder sb = new StringBuilder();
        for(int i = 1; i <= n; i++){
            sb.append(a[i]).append("\n");
        }
        System.out.println(sb);
 
 	



  





  bw.flush();
  bw.close();

}

static long nCr(long n, long r) 
{ 
    long ans=1;
    if(r>n-r)
    {
    	r=n-r;
    }

    for(long i=1;i<=r;i++)
    {
    	ans*=(n-i+1);
    	ans/=i;

    }

    return ans;
} 
 

  




        public static int modulo(int x,int N)
        {
            return (x % N + N) %N;
        }
        public static long lcm(long a,long b)
        {    
            return a / gcd(a, b) * b;
        }
        public static long gcd(long a,long b)
        {
            if(b==0)
                return a;
            return gcd(b,a%b);
        }

     public static int inputInt()throws IOException
    {
        return sc.nextInt();
    }
    public static long inputLong()throws IOException
    {
        return sc.nextLong();
    }
    public static double inputDouble()throws IOException
    {
        return sc.nextDouble();
    }
    public static String inputString()throws IOException
    {
        return sc.readLine();
    }
    public static void print(String a)throws IOException
    {
        bw.write(a);
    }
    public static void printSp(String a)throws IOException
    {
        bw.write(a+" ");
    }
    public static void println(String a)throws IOException
    {
        bw.write(a+"\n");
    }
}