Problem: 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).

Examples

Input

2


Output

3
1 1 1
1 1 1
2 2 2


Input

9


Output

3
1 2 3
4 5 6
7 8 9

Solution (in JAVA):

Solution:
import java.util.*;
public class Main {
	public static void main(String args[]) {
		Scanner sc =new Scanner(System.in);
		int k = sc.nextInt();
		if(k == 1) {
			System.out.println(1);
			System.out.print(1);
			return;
		}
		int n = 2 * ((k+3)/4);
		int curt = n*2 - k;
		int[][] mat = new int[n][n];
		for(int r=0; r<n; r++) {
			for(int c=0; c<n;c++) {
				if(r%2 == 1 && (r+c)%n < n -curt) {
					mat[r][c] = n + (r+c)%n;
					mat[r][c]++;
				} else {
					mat[r][c] = (r+c)%n;
					mat[r][c]++;
				}
			}
		}
		int rr = 1;
		System.out.println(n);
		for(int[] row: mat) {
			int cc = 1;
			for(int x : row) {
				System.out.print(x);
				if(cc <n) 
					System.out.print(" ");
				cc++;
			}
			if(rr < n)
				System.out.println("");
			rr++;
		}
	}
}