{"raw_statement":[{"iden":"problem statement","content":"There is a square grid with $N$ rows and $M$ columns. Each square contains an integer: $0$ or $1$. The square at the $i$\\-th row from the top and the $j$\\-th column from the left contains $a_{ij}$.\nAmong the $2^{N+M}$ possible pairs of a subset $A$ of the rows and a subset $B$ of the columns, find the number of the pairs that satisfy the following condition, modulo $998244353$:\n\n*   The sum of the $|A||B|$ numbers contained in the intersection of the rows belonging to $A$ and the columns belonging to $B$, is odd."},{"iden":"constraints","content":"*   $1 \\leq N,M \\leq 300$\n*   $0 \\leq a_{i,j} \\leq 1(1\\leq i\\leq N,1\\leq j\\leq M)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$a_{11}$ $...$ $a_{1M}$\n$:$\n$a_{N1}$ $...$ $a_{NM}$"},{"iden":"sample input 1","content":"2 2\n0 1\n1 0"},{"iden":"sample output 1","content":"6\n\nFor example, if $A$ consists of the first row and $B$ consists of both columns, the sum of the numbers contained in the intersection is $0+1=1$."},{"iden":"sample input 2","content":"2 3\n0 0 0\n0 1 0"},{"iden":"sample output 2","content":"8"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}