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 employee 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 this:

         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,

      first rotation           second rotation            third rotation           fourth rotation
         Ameen                     Ameen                     Ameen                     Ameen
         7 4 1                     9 8 7                     3 6 9                     1 2 3
  Sameh  8 5 2  Shafeek     Sameh  6 5 4  Shafeek     Sameh  2 5 8  Shafeek     Sameh  4 5 6  Shafeek
         9 6 3                     3 2 1                     1 4 7                     7 8 9
         Atef                      Atef                      Atef                      Atef

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 ≤ 10⁹).

Output

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

Example

Input:
3 4

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

Input:
4 3

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