Alice lives on a flat planet that can be modeled as a square grid of size n×nn×n , with rows and columns enumerated from 11 to nn . We represent the cell at the intersection of row rr and column cc with ordered pair (r,c)(r,c) . Each cell in the grid is either land or water.
An example planet with n=5n=5 . It also appears in the first sample test.
Alice resides in land cell (r1,c1)(r1,c1) . She wishes to travel to land cell (r2,c2)(r2,c2) . At any moment, she may move to one of the cells adjacent to where she is—in one of the four directions (i.e., up, down, left, or right).
Unfortunately, Alice cannot swim, and there is no viable transportation means other than by foot (i.e., she can walk only on land). As a result, Alice's trip may be impossible.
To help Alice, you plan to create at most one tunnel