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 <cstdio>
int ans[505][505];
int main()
{
 int k;
 scanf("%d",&k);
 if(k==1)
 {
  puts("1");
  puts("1");
  return 0;
 }
 int n=(k+1)/2;
 if(n%2)n++;
 printf("%d\n",n);
 for(int i=0;i<n;i++)
  for(int j=0;j<n;j++)
   ans[i][j]=n*(i%2)+(i+j)%n+1;
 for(int c=2*n;c>k;c--)
  for(int i=1;i<n;i+=2)
   for(int j=0;j<n;j++)
    if(ans[i][j]==c)ans[i][j]-=n;
 for(int i=0;i<n;i++)
 {
  for(int j=0;j<n;j++)
   printf("%d ",ans[i][j]);
  puts("");
 }
 return 0;
}