Sailing

Anthony named his boat the Invincible and sails her in a regatta in the waters south of Singapore. Relative to the wind, the Invincible travels in only three ways.

The wind always blows from the top of the grid to the bottom. A close haul therefore reaches the neighboring waypoint diagonally above, a beam reach the one to the left or to the right, and a broad reach the one diagonally below.

Each point of sail comes in two versions: the starboard tack, with the wind on the right (the three directions heading left), and the port tack, with the wind on the left (the three directions heading right). That gives six possible directions.

No sailing boat can go directly into the wind for a longer period (the no-go zone), and Anthony's sailing skills do not allow him to go directly away from the wind (running).

Anthony enters waypoints into his GPS device as a square grid. At each waypoint he changes direction at most once, then sails on to the next waypoint. Within the same tack he switches from close haul to beam reach, from beam reach to close haul, from beam reach to broad reach and from broad reach to beam reach, all without any loss of speed. He cannot jibe, which means switching from broad reach on one tack to broad reach on the other. He can tack, switching from close haul on one tack to close haul on the other, and that maneuver costs 12 minutes because the boat points into the no-go zone and loses speed.

The waters south of Singapore have many parked container ships and tankers. Anthony marks the waypoints that he cannot safely reach because of a parked vessel. He never enters a marked waypoint, but a leg that cuts diagonally between two marked waypoints is not blocked.

At the start Anthony points the Invincible in any one of the six directions and immediately reaches the matching speed.

The first line has the side length $n$ of the square grid ($2 \le n \le 150$).

Each of the next $n$ lines has $n$ characters and describes one row of the grid. The start is S, the finish is F, a waypoint Anthony cannot reach is X, and every other waypoint is W. The grid holds exactly one S and one F.

Print one line with the smallest number of minutes in which Anthony can take the Invincible from the start to the finish. If there is no way for him to reach the finish, print -1 instead.