There is a grid with r rows and c columns, where the square on the i -th row and j -th column has an integer a_{i, j} written on it. Initially, all elements are set to 0 . We are allowed to do the following operation: You want to form grid b by doing the above operations a finite number of times. However, some elements of b are missing and are replaced with '?' instead. Let k be the number of '?' characters. Among all the 2^k ways of filling up the grid b by replacing each '?' with '0' or '1', count the number of grids, that can be formed by doing the above operation a finite number of times, starting from the grid filled with 0 . As this number can be large, output it modulo 998244353 . The first line contains two integers r and c ( 1 <= r, c <= 2000 ) -- the number of rows and columns of the grid respectively. The i -th of the next r lines contain c characters b_{i, 1}, b_{i, 2}, ldots, b_{i, c} ( b_{i, j} in {0, 1, ? } ). Print a single integer representing the number of ways to fill up grid b modulo 998244353 . In the first test case, the only way to fill in the texttt{?} s is to fill it in as such: This can be accomplished by doing a single operation by choosing (i,j)=(2,2) . In the second test case, it can be shown that there is no sequence of operations that can produce that grid.