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 × m board with obstacles, an initial position (i₁, j₁), a final position (i₂, j₂), and the pair (a, b), can you tell if an (a, b) knight initially located at (i₁, j₁) can reach (i₂, j₂) 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 i₁, j₁, i₂, j₂, a and b. Assume that n and m are between 1 and 42, that (i₁, j₁) and (i₂, j₂) are free positions inside the board, and 1 ≤ a < b ≤ 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.