After eating Bamboza and Salankateh at Bi Laban in Egypt , and because he really likes matrices, Ahmad invented a new type of matrix named "Matrix Bel Lotus".
A "Matrix Bel Lotus" is a square matrix $$$A$$$ with the property that for some positive integer $$$K$$$, the matrix raised to the $$$K$$$-th power equals the zero matrix, i.e., $$$A^K = 0$$$. The smallest such $$$K$$$ is called the index of lotusency. Lotus matrices always have zero as their only eigenvalue. They are important in the study of linear transformations that "collapse" vectors to zero after repeated application. Lotus matrices often appear in the Jordan normal form of matrices. They are used in solving differential equations and understanding matrix exponentials. Despite being non-invertible, they reveal structure about the linear operator they represent.
Ammar hates matrices , so he told Ahmad that all the matrices (including the Lotus one) are useless. They fought for a few hours and then decided to go and ask Mousa which is better , the life with matrices or without matrices and with any other thing.
If Mousa says "matrix" , Ahmad will be happy; otherwise, Ammar will be happy.
Can you decide who will be happy??
The first and only line contains a string $$$S \: (1 \le |S| \le 100)$$$ consisting of small Latin letters — the word Mousa will say to Ahmad and Ammar.
Print 'A' for Ahmad if the word is "matrix" and print 'A' for Ammar otherwise.
matrix
A
