Construct Quad Tree

You are given an n x n binary matrix grid, where n is a power of 2. Build and return the root of a quad tree that represents the matrix. Each node represents a square region:

• If every value in the region is the same, the node is a leaf.
• Otherwise, the node is an internal node with exactly four children for the top-left, top-right, bottom-left, and bottom-right quadrants. Each returned node should expose the fields val, isLeaf, topLeft, topRight, bottomLeft, and bottomRight. For this practice environment, use val = false for every non-leaf node so the returned structure is deterministic across languages.

The full grid is not uniform, so the root is an internal node with four leaf children.