Problem:
Score : 1100 points

Problem Statement

You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

1 \leq a_{i,j} \leq 10^{15}

a_{i,j} are pairwise distinct integers.

There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:

N

Output

Print your solution in the following format:

a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Sample Input 1

2

Sample Output 1

4 7
23 10

For any two elements x and y that are vertically or horizontally adjacent, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always 3.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

    #include <iostream>
    #include <stdio.h>
    #include <string>
    #include <math.h>
    #include<algorithm>
    #include <numeric>
    using namespace std;
 
    int main(){
      long long N;
      cin >> N;
      long long a[N+1][N+1]={};
      a[1][1]=2;
      for(int i=1;i<N;i++){
       a[i+1][1]=4*i-1;
        a[1][i+1]=4*i+1;
      }
      for(int i=2;i<=N;i++){
       for(int j=2;j<=N;j++){
        a[i][j]=(a[i-1][j])*(a[i][j-1])+1; 
       }
      }
      for(int i=1;i<=N;i++){
       for(int j=1;j<=N;j++){
        cout << a[i][j];
         if(j==N){
          cout << endl; 
         }else{
          cout << ' '; 
         }
       }
      }
      return 0;}