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 CPP):

Solution:
#include<bits/stdc++.h>
#define MN 505
int k,n,col[MN<<1],N,ans[MN][MN];
int main()
{
	scanf("%d",&k);
	n=(k+3)/4*2;
	N=n<<1;
	for(int i=1;i<=N;i++) col[i]=i;
	if(k==1) return 0*printf("1\n1\n");
	if(k%4==3) col[N]=N-1;
	if(k%4==2) col[N]=col[N-1]=N-2,col[N-2]=N-3;
	if(k%4==1) col[N]=col[N-1]=N-3,col[N-2]=col[N-3]=N-4,col[N-4]=N-5;
	for(int i=1;i<=N;i+=2)
	{
		for(int j=0;j<n;j++)
			ans[j][((i>>1)+j)%n]=col[(j&1)?(i+1):i];
	}
	printf("%d\n",n);
	for(int i=0;i<n;i++) {
		for(int j=0;j<n;j++) {
			printf("%d ",ans[i][j]);
		}
		puts("");
	}
}