Sandpile Tray

Drop grains of sand one at a time onto a tray with drains, and report every avalanche and how many grains the tray loses.

The tray is a grid. Each cell of tray is a digit 0 to 3, the number of grains lying there, or #, a drain. Grains that reach a drain disappear.

A grain is dropped at each position of drops, in order ([row, col], counted from 0 at the top left). Dropping a grain adds 1 to that cell, then the tray settles before the next drop:

• Whenever a non-drain cell holds 4 or more grains, it topples: it loses 4 grains and each of its four neighbours (up, down, left, right) receives 1. A grain sent beyond the edge of the grid is lost, and a grain sent onto a drain is lost. A cell that still holds 4 or more grains after toppling topples again.
• Toppling continues until every non-drain cell holds at most 3 grains. (The final result does not depend on the order in which you topple cells.)
• A grain dropped directly onto a drain is lost at once and nothing topples.

For each drop, record the avalanche as [topples, cells]: the total number of topples that happened during that settling (a cell that toppled three times counts three), and the number of different cells that toppled at least once. A drop that causes no topple records [0, 0].

Input: tray, a list of equal-length strings of digits 0-3 and #; drops, a list of [row, col] positions inside the grid.

Output: a list [final_tray, avalanches, lost]: the tray after all drops in the same string format (drains stay #), the list of [topples, cells] pairs, one per drop, and lost, the total number of grains lost over all the drops, through the edges and into drains (including grains dropped directly on drains).