A labyrinth is the rectangular grid, each of the cells of which is either free or wall, and it's possible to move only between free cells sharing a side.
Constantine and Mike are the world leaders of composing the labyrinths. Each of them has just composed one labyrinth of size n × m, and now they are blaming each other for the plagiarism. They consider that the plagiarism takes place if there exists such a path from the upper-left cell to the lower-right cell that is the shortest for both labyrinths. Resolve their conflict and say if the plagiarism took place.
In the first line two integers n and m (1 ≤ n, m ≤ 500) are written — the height and the width of the labyrinths.
In the next n lines the labyrinth composed by Constantine is written. Each of these n lines consists of m characters. Each character is equal either to «_#_», which denotes a wall, or to «_._», which denotes a free cell.
The next line is empty, and in the next n lines the labyrinth composed by Mike is written in the same format. It is guaranteed that the upper-left and the lower-right cells of both labyrinths are free.
Output «_YES_» if there exists such a path from the upper-left to the lower-right cell that is the shortest for both labyrinths. Otherwise output «_NO_».
## Input
In the first line two integers n and m (1 ≤ n, m ≤ 500) are written — the height and the width of the labyrinths.In the next n lines the labyrinth composed by Constantine is written. Each of these n lines consists of m characters. Each character is equal either to «_#_», which denotes a wall, or to «_._», which denotes a free cell.The next line is empty, and in the next n lines the labyrinth composed by Mike is written in the same format. It is guaranteed that the upper-left and the lower-right cells of both labyrinths are free.
## Output
Output «_YES_» if there exists such a path from the upper-left to the lower-right cell that is the shortest for both labyrinths. Otherwise output «_NO_».
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**Definitions**
Let $ n, m \in \mathbb{Z} $ with $ 1 \leq n, m \leq 500 $.
Let $ C = (c_{i,j})_{1 \leq i \leq n, 1 \leq j \leq m} \in \{ \text{`.`}, \text{`#'} \}^{n \times m} $ be Constantine’s labyrinth.
Let $ M = (m_{i,j})_{1 \leq i \leq n, 1 \leq j \leq m} \in \{ \text{`.`}, \text{`#'} \}^{n \times m} $ be Mike’s labyrinth.
Assume $ c_{1,1} = c_{n,m} = \text{`.`} $ and $ m_{1,1} = m_{n,m} = \text{`.`} $.
Let $ G_C = (V_C, E_C) $ be the grid graph of Constantine’s labyrinth:
- $ V_C = \{ (i,j) \mid c_{i,j} = \text{`.`} \} $,
- $ E_C = \{ ((i,j), (i',j')) \mid |i - i'| + |j - j'| = 1 \} $.
Let $ G_M = (V_M, E_M) $ be the grid graph of Mike’s labyrinth, defined analogously.
Let $ d_C(u,v) $ denote the shortest path distance between nodes $ u, v \in V_C $ in $ G_C $, and $ d_M(u,v) $ analogously in $ G_M $.
Let $ s = (1,1) $, $ t = (n,m) $.
**Constraints**
1. $ s, t \in V_C \cap V_M $.
2. Both $ G_C $ and $ G_M $ are connected graphs with $ s, t \in V_C $ and $ s, t \in V_M $.
**Objective**
Determine whether:
$$
\exists \, P \text{ (path from } s \text{ to } t \text{)} \quad \text{such that} \quad |P| = d_C(s,t) = d_M(s,t)
$$
where $ |P| $ is the number of edges in path $ P $, and $ P $ is valid in both labyrinths (i.e., all cells of $ P $ are free in both $ C $ and $ M $).
Equivalently:
Is the set of shortest paths from $ s $ to $ t $ in $ G_C $ intersecting the set of shortest paths from $ s $ to $ t $ in $ G_M $, under the constraint that all cells along the path are free in both labyrinths?
Output "YES" if such a path exists, "NO" otherwise.