A11662 | Mystical Mosaic

There is a rectangular grid of $n$ rows of $m$ initially-white cells each.

Arkady performed a certain number (possibly zero) of operations on it. In the $i$ -th operation, a non-empty subset of rows $R_{i}$ and a non-empty subset of columns $C_{i}$ are chosen. For each row $r$ in $R_{i}$ and each column $c$ in $C_{i}$ , the intersection of row $r$ and column $c$ is coloured black.

There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of $(i,j)$ ( $i<j$ ) exists such that  or , where  denotes intersection of sets, and  denotes the empty set.

You are to determine whether a valid sequence of operations exists that produces a given final grid.

The first line contains two space-separated integers $n$ and $m$ $(1<=n,m<=50$ ) — the number of rows and columns of the grid, respectively.

Each of the following $n$ lines contains a string of $m$ characters, each being either '.' (denoting a white cell) or '\#' (denoting a black cell), representing the desired setup.

If the given grid can be achieved by any valid sequence of operations, output "Yes"; otherwise output "No" (both without quotes).

You can print each character in any case (upper or lower).