TR-MO 2003 Problem 6

An assignment of either a $0$ or a $1$ to each unit square of an $m$ x $n$ chessboard is called $fair$ if the total numbers of $0$ s and $1$ s are equal. A real number $a$ is called $beautiful$ if there are positive integers $m,n$ and a fair assignment for the $m$ x $n$ chessboard such that for each of the $m$ rows and $n$ columns , the percentage of $1$ s on that row or column is not less than $a$ or greater than $100-a$ . Find the largest beautiful number.