Dear Explorer,

Eric is stuck in a 3D maze arranged as an n × n × n cube. Each cell is either a wall 'X' or an empty space '.'. From any empty cell, movement is allowed only to the six face-adjacent neighbors (no diagonals).

Some empty cells allow Eric to reach the outside of the cube via a path of empty cells that touches any outer face of the cube; others are enclosed by walls and cannot reach the outside. Your task is to count how many empty cells have a path to the outside.

Input Format

• Line 1: An integer n (1 ≤ n), the side length of the cube.
• Next n lines: The i-th line (0-indexed) encodes the i-th layer of the cube as a flat string of length n² consisting only of 'X' and '.'. This string is the layer in row-major order: for row j = 0..n-1 and column k = 0..n-1, character at index j·n + k corresponds to cell (layer i, row j, column k).

Output Format

• Single integer: the number of empty cells '.' that have a path through empty cells to any empty cell on the outer surface of the cube.

Notes & Clarifications

• Movement is allowed only between face-adjacent empty cells (±x, ±y, ±z); diagonal moves are not allowed.
• An empty cell on the outer surface is itself considered to “reach the outside”.
• There are no spaces in the layer strings; each layer line is exactly n² characters long.

Example 1 Input

2
....
..X.

Example 1 Output

7

Explanation: The cube is 2×2×2. All empty cells except the single interior-blocked cell are connected to the surface.

Example 2 Input

3
XXXX.XXXX
XXXX.XXXX
XXXX.XXXX

Example 2 Output

3

Explanation: A vertical tunnel of 3 empty cells connects top to bottom; only those 3 cells reach the outside.

Example 3 Input

3
X.X.X.X.X
.X.X.X.X.
X.X.X.X.X

Example 3 Output

12