Problem:
Score : 1100 points

Problem Statement

You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

1 \leq a_{i,j} \leq 10^{15}

a_{i,j} are pairwise distinct integers.

There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:

N

Output

Print your solution in the following format:

a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Sample Input 1

2

Sample Output 1

4 7
23 10

For any two elements x and y that are vertically or horizontally adjacent, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always 3.

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n = nn = gets.to_i
prime=[2, 3, 5, 7,11,13,17,19,23,29,31,37,41]
pp = prime.inject(:*)/41/37/31;

l = 42
r = 41 + n
res =[]
while ( nn > 0)
  res << (l..r).map{|x| pp*x}
  nn-=1
  l += n
  r += n
end
puts res.map{|x|x*" "}