Problem:
Score : 1000 points

Problem Statement

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).

Sample Input 1

2

Sample Output 1

3
1 1 1
1 1 1
2 2 2

Every square in Color 1 has three adjacent squares in Color 1 and one adjacent square in Color 2.

Every square in Color 2 has two adjacent squares in Color 1 and two adjacent squares in Color 2.

Output such as the following will be judged incorrect:

2
1 2
2 2

3
1 1 1
1 1 1
1 1 1

Sample Input 2

9

Sample Output 2

3
1 2 3
4 5 6
7 8 9

Solution in Python (3.4.3) (judge verdict: Runtime Error)

K  = int(input())
n = 0
n1 = 0
n2 = 0
n3 = 0
n4 = 0
n5 = 0


#Kが500以下の場合、斜め作戦にする
if K <= 500:
   n = K
   mat = [[0 for n1 in range(K)] for n2 in range(K)]
   for n1 in range(K):
      for n2 in range(K-n1):
         mat[n1][n1+n2] = n2+1
   for n1 in range(K):
      for n2 in range(n1):
         mat[n1][n2] = K+n2-n1+1

#Kが500以上の場合、斜めに1マスずつしのびこませる   
else:
   n = 500
   mat = [[0 for n1 in range(500)] for n2 in range(500)]
   for n1 in range(500):
      for n2 in range(500-n1):
         mat[n1][n1+n2] = n2+1
   for n1 in range(500):
      for n2 in range(n1):
         mat[n1][n2] = 500+n2-n1+1










#行列の出力かんがえとく 
print(n)
out = ""
for n1 in range(K):
   out = ""   
   for n2 in range(K):
      out = out + " " + str(mat[n1][n2])
   print(out)