6175번 - Cow Travelling

Searching for the very best grass, the cows are travelling about the pasture which is represented as a grid with N rows and M columns (2 <= N <= 100; 2 <= M <= 100). Keen observer Farmer John has recorded Bessie's position as (R1, C1) at a certain time and then as (R2, C2) exactly T (0 < T <= 15) seconds later. He's not sure if she passed through (R2, C2) before T seconds, but he knows she is there at time T.

FJ wants a program that uses this information to calculate an integer S that is the number of ways a cow can go from (R1, C1) to (R2, C2) exactly in T seconds. Every second, a cow can travel from any position to a vertically or horizontally neighboring position in the pasture each second (no resting for the cows). Of course, the pasture has trees through which no cow can travel.

Given a map with '.'s for open pasture space and '*' for trees, calculate the number of possible ways to travel from (R1, C1) to (R2, C2) in T seconds.

• Line 1: Three space-separated integers: N, M, and T
• Lines 2..N+1: Line i+1 describes row i of the pasture with exactly M characters that are each '.' or '*'
• Line N+2: Four space-separated integers: R1, C1, R2, and C2.

Line 1: A single line with the integer S described above.

The pasture is 4 rows by 5 colum. The cow travels from row 1, column 3 to row 1, column 5, which takes exactly 6 seconds.

There is only one way from (1,3) to (1,5) in exactly 6 seconds (and it is the obvious one that travels around the two trees).