River Game

Together with an ornithologist friend, you spend hours bird-watching in wetlands, waiting for a rare bird that you want to photograph.

To pass the time, you devised a small game. The wetland is an $N \times N$ grid made of three types of squares: firm ground, wet zone, and protected zone.

Connected wet zone squares form wet areas. A wet area is a maximal set of wet zone squares such that any square of the area can reach any other square of the area through a path of connected wet zone squares. Two squares are connected when they share an edge, so a square not on the border of the grid is connected to 4 other squares. Each wet area must be connected to both the left and right sides of the grid, and it contains no more than $2N$ wet zone squares. Wet zone squares that belong to two different wet areas are always at distance at least 3 from each other, where distance is counted by moving horizontally or vertically on the grid. For example, in the two examples below, the blue squares are at distance 3 from one another.

You and your friend take turns placing a camera on the wetland under these rules:

• The camera must be on a firm ground square.
• The camera must be adjacent to a wet zone square, so that you can take bird photos.
• The camera must not be on a protected zone square.
• There cannot be two cameras on the same square.
• Two cameras adjacent to the same wet area cannot be adjacent to each other. Adjacency means sharing an edge.

The first player who cannot place a camera anymore loses the game.

Assuming both players play optimally, will the first player win or lose?

The input consists of the following lines:

• on the first line, the integer $N$;
• on the next $N$ lines, a string representing a row of the grid: \* represents a wet zone square, . represents a firm ground square, and x represents a protected square.

Print First player will win if the first player wins the game when both players play optimally, or Second player will win otherwise.

The input satisfies $1 \le N \le 10$.