You run a grid of weather monitoring stations, each reporting the rainfall captured at one lattice cell of a continentspan field. Readings shift whenever a sensor is recalibrated, and researchers constantly ask for the total rainfall across a rectangular patch. Because the values change frequently, a one-time prefix table goes stale the moment any sensor is retuned. Design a system that handles both kinds of requests efficiently: refreshing a single cell to a new reading, and summing every cell inside an axis-aligned rectangle. The two operations interleave arbitrarily, so an update can re-run a sensor immediately after a query reports on it.

Implement the Solution class:

• Solution(matrix) initializes the object with the integer matrix.
• sumRegion(row1, col1, row2, col2) returns the sum of the elements of matrix inside the rectangle whose upper-left corner is (row1, col1) and whose lower-right corner is (row2, col2).
• update(row, col, val) makes matrix[row][col] equal to val, and records the change for every subsequent query.

Every update rewrites the cell value for all later calls. Rectangle corners are inclusive on all four sides.