Coloring Torus

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

inputFormat

Input

Input is given from Standard Input in the following format:

K

outputFormat

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

样例

9

3
1 2 3
4 5 6
7 8 9

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