Problem:
Score : 1000 points

Problem Statement

For an n \times n grid, let (r, c) denote the square at the (r+1)-th row from the top and the (c+1)-th column from the left.
A good coloring of this grid using K colors is a coloring that satisfies the following:

Each square is painted in one of the K colors.

Each of the K colors is used for some squares.

Let us number the K colors 1, 2, ..., K. For any colors i and j (1 \leq i \leq K, 1 \leq j \leq K), every square in Color i has the same number of adjacent squares in Color j. Here, the squares adjacent to square (r, c) are ((r-1)\; mod\; n, c), ((r+1)\; mod\; n, c), (r, (c-1)\; mod\; n) and (r, (c+1)\; mod\; n) (if the same square appears multiple times among these four, the square is counted that number of times).

Given K, choose n between 1 and 500 (inclusive) freely and construct a good coloring of an n \times n grid using K colors.
It can be proved that this is always possible under the constraints of this problem,

Constraints

1 \leq K \leq 1000

Input

Input is given from Standard Input in the following format:

K

Output

Output should be in the following format:

n
c_{0,0} c_{0,1} ... c_{0,n-1}
c_{1,0} c_{1,1} ... c_{1,n-1}
:
c_{n-1,0} c_{n-1,1} ... c_{n-1,n-1}

n should represent the size of the grid, and 1 \leq n \leq 500 must hold.
c_{r,c} should be an integer such that 1 \leq c_{r,c} \leq K and represent the color for the square (r, c).

Sample Input 1

2

Sample Output 1

3
1 1 1
1 1 1
2 2 2

Every square in Color 1 has three adjacent squares in Color 1 and one adjacent square in Color 2.

Every square in Color 2 has two adjacent squares in Color 1 and two adjacent squares in Color 2.

Output such as the following will be judged incorrect:

2
1 2
2 2

3
1 1 1
1 1 1
1 1 1

Sample Input 2

9

Sample Output 2

3
1 2 3
4 5 6
7 8 9

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

#include <bits/stdc++.h>
#define ll long long
using namespace std;

int main() {
  int k;
  cin>>k;
  if(k<=500){
    cout<<k<<endl;
    for(int i=1;i<=k;i++){
      for(int j=0;j<k;j++){
        cout<<i<<" ";
      }
      cout<<endl;
    }
    return 0;
  }
  cout<<((k+3)/4)*2<<endl;
  int z=((k+3)/4)*2;
  if(k%4==1){
    k++;
    int vec[z][z];
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        if(i==0){
          vec[j][i]=j+1;
        }
        if(i==1){
          vec[j][i]=vec[j][i-1]+k/2;
          if(vec[j][i]>k){
            vec[j][i]-=vec[j][i-1];
          }
        }
        if(i>1){
          if(i%2==0){
            vec[j][i]=vec[j][i-2]+z-2;
            if(vec[j][i]>k/2+1){
              vec[j][i]-=k/2+1;
            }
          }
          else{
            vec[j][i]=vec[j][i-1]+k/2;
            if(vec[j][i]>k){
              vec[j][i]-=vec[j][i-1];
            }
          }
        }
      }
    }
    for(int i=0;i<z;i++){
      if(vec[i][i]==1){
        vec[i][i]=vec[1][1];
      }
    }
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        cout<<vec[i][j]-1<<" ";
      }
      cout<<endl;
    }
    return 0;
  }
  if(k%4==2){
    int vec[z][z];
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        if(i==0){
          vec[j][i]=j+1;
        }
        if(i==1){
          vec[j][i]=vec[j][i-1]+k/2;
          if(vec[j][i]>k){
            vec[j][i]-=vec[j][i-1];
          }
        }
        if(i>1){
          if(i%2==0){
            vec[j][i]=vec[j][i-2]+z-2;
            if(vec[j][i]>k/2+1){
              vec[j][i]-=k/2+1;
            }
          }
          else{
            vec[j][i]=vec[j][i-1]+k/2;
            if(vec[j][i]>k){
              vec[j][i]-=vec[j][i-1];
            }
          }
        }
      }
    }
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        cout<<vec[i][j]<<" ";
      }
      cout<<endl;
    }
    return 0;
  }
  if(k%4==3){
    k++;
    int vec[z][z];
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        if(i==0){
          vec[j][i]=j+1;
        }
        if(i==1){
          vec[j][i]=vec[j][i-1]+k-1;
          if(vec[j][i]>k){
            vec[j][i]-=k/2;
          }
        }
        if(i>1){
          if(i%2==0){
            vec[j][i]=vec[j][i-2]+k/2-2;
            if(vec[j][i]>k/2){
              vec[j][i]-=k/2;
            }
          }
          else{
            vec[j][i]=vec[j][i-2]+k/2-2;
            if(vec[j][i]>k){
              vec[j][i]-=k/2;
            }
          }
        }
      }
    }
    for(int i=0;i<z;i++){
      if(vec[i][i]==1){
        vec[i][i]=vec[1][1];
      }
    }
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        cout<<vec[i][j]-1<<" ";
      }
      cout<<endl;
    }
    return 0;
  }
  ///////////
  if(k%4==0){
    int vec[z][z];
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        if(i==0){
          vec[j][i]=j+1;
        }
        if(i==1){
          vec[j][i]=vec[j][i-1]+k-1;
          if(vec[j][i]>k){
            vec[j][i]-=k/2;
          }
        }
        if(i>1){
          if(i%2==0){
            vec[j][i]=vec[j][i-2]+k/2-2;
            if(vec[j][i]>k/2){
              vec[j][i]-=k/2;
            }
          }
          else{
            vec[j][i]=vec[j][i-2]+k/2-2;
            if(vec[j][i]>k){
              vec[j][i]-=k/2;
            }
          }
        }
      }
    }
    for(int i=0;i<z;i++){
      for(int j=0;j<z;j++){
        cout<<vec[i][j]<<" ";
      }
      cout<<endl;
    }
  } 
}