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!