Problem Description

Find the maximum sum of any rectangular submatrix in a 3D matrix. Consider all possible 3D rectangular regions and return the maximum sum.

Input Format

First line: x y z (dimensions). Next x*y lines: z space-separated integers for each layer.

Output Format

Maximum sum of any 3D rectangular submatrix.

Constraints

• 1 ≤ x, y, z ≤ 20

• -100 ≤ matrix elements ≤ 100

• Consider all possible 3D rectangular regions

• Submatrix can be any size from 1×1×1 to x×y×z

• Use efficient algorithm for large search space

Sample Input/Output

Explanation

Maximum sum submatrix includes elements that sum to maximum value across all possible 3D rectangular regions.