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Grand is one of the best companies every month , The manager  chooses the best employee and rewards him.
this month there are 4 employees do the same effort Sameh , Ameen , Shafeek and Atef but the manager will give reward to one only ,He got a good idea

let's say that the 4 employees will stand in someway like that every employe in one of the four sides east(Sameh) , north(Ameen) , west(Shafik) and south(Atef)
then , there's a square matrix of  width and height N*N among them first element in matrix will start with 1 then next element increase by 1 from left to right and from top
to down until n*n like that

                Ameen
                1 2 3
  Sameh  4 5 6  Shafeek
                7 8 9
                 Atef

then let's rotate the matrix T turns 90 degrees clockwise per turn and the winner is the person who the sum of his side is the greatest 

for example let's say that T=4 and N=3 ,

Atef wins because the sum of his side is 7+8+9=24 and it's the greatest

It's your job now create a program that do this job.

Input

Two integers  the size of the matrix N(3≤N≤25) , and the number of turns (1≤T≤10^9).

Output

The final result of the matrix and the employee who will get the reward (Sameh,Ameen,Shafeek,Atef).

Example

Input:
123 456
555 555
123 594
3 4

Output:
Atef
1 2 3
4 5 6
7 8 9




Input:
123 456
555 555
123 594
4 3

Output:
Shafeek
4 8 12 16
3 7 11 15
2 6 10 14
1 5 9 13