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 PYTHON3):

Solution:
#!/usr/bin/env python3
import collections
def solve(k):
    if k == 1:
        return 1, [ [ 1 ] ]
    n = (k + 3) // 4 * 2
    f = [ [ None ] * n for _ in range(n) ]
    for y in range(n):
        for x in range(n):
            f[y][x] = (y * n + (x - y) % n) % (2 * n) + 1
            if f[y][x] > n:
                if f[y][x] - n <= 2 * n - k:
                    f[y][x] -= n
                else:
                    f[y][x] -= 2 * n - k
    return n, f

if __name__ == '__main__':
    k = int(input())
    n, f = solve(k)
    print(n)
    for y in range(n):
        print(*f[y])