Generalized chess knight P22796

Let us define an $(a, b)$ knight as a piece that moves by jumping $a$ cells in one direction and $b$ cells in the other direction, where the possible directions are horizontal and vertical. For instance, the traditional chess knight is a $(1, 2)$ knight.

Given an $n \times m$ board with obstacles, an initial position $(i_1, j_1)$, a final position $(i_2, j_2)$, and the pair $(a, b)$, can you tell if an $(a, b)$ knight initially located at $(i_1, j_1)$ can reach $(i_2, j_2)$ in two or less steps? The knight can never leave the board, nor visit any obstacles.

Input

Input consists of several cases, each with $n$ and $m$, followed by the board ($n$ lines with $m$ characters each, where an ‘X’ indicates an obstacle and a ‘.’ indicates a free cell), followed by $i_1$, $j_1$, $i_2$, $j_2$, $a$ and $b$. Assume that $n$ and $m$ are between 1 and 42, that $(i_1, j_1)$ and $(i_2, j_2)$ are free positions inside the board, and $1 \le a < b \le 5$. The upper-left position is $(0, 0)$.

Output

For every case, print “yes” or “no” depending on whether the goal position is reachable from the initial position in two or less steps.