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 <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

int n, m;

int main() {
#ifdef isLOCAL
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif 

    cin >> m, n = (m - 1 >> 2) + 1 << 1;
    if (m <= 500) {
        cout << m << endl;
        for (int i = 1; i <= m; ++i)
            for (int j = 1; j <= m; ++j)
                printf("%d%c", (i + j - 2) % m + 1, " \n"[j == m]);
        return 0;
    }
    cout << n << endl;
    for (int i = 1; i <= n; ++i)
        for (int j = 1; j <= n; ++j) {
            int tmp = (i + j - 2) % n + 1;
            if (i % 2 == 0 && tmp + n <= m) tmp += n;
            printf("%d%c", tmp, " \n"[j == n]);
        }
    return 0;
}