# Complexity of finding choice of entries of matrices

Suppose I have a matrix with entries either $$x$$ or $$y$$, where the number of rows = number of columns = $$n$$. If I want to select/circle $$n$$ entries such that for each row, only exactly one is circled, for each column, also exactly one is circled, and such that all entries circled are only $$x$$ (if such a circling of entries exists), what complexity class does this belong to? Thanks!