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: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
using namespace std;
#define REP(i, n) for(int i=0; i<(int)(n); i++)
typedef long long int lli;
const lli inf = 1e18;

int main(){
    int n;
    cin >> n;
    
    if(n<=500){
        cout << n << endl;
        for(int i=0; i<n; i++){
            for(int j=0; j<n; j++){
                cout << (i+j)%n +1 << " ";
            }
            cout << endl;
        }
    }else{
        int m = (n+1)/2;
        bool add = false;
        if(m%2 == 1){
            m++;
            add = true;
        }
        cout << m << endl;
        for(int i=0; i<m; i++){
            for(int j=0; j<m; j++){
                int c = (i+j)%m +1;
                if(!add){
                    if(i%2==0 && !(n%2!=0 && c==m)) c+=m;
                }else{
                    if(i%2==0 && !((n%2!=0 && c==m) || (c==m-1 || c==m-2))) c+=m;
                }
                cout << c << " ";
            }
            cout << endl;
        }
    }
    return 0;
}