```python
"""Replay tile requests against a List-limited cache of fresh renders."""

from typing import List, Tuple

import heapq

def tile_renders(requests: List[List[int]], fresh_for: int,          if not isinstance(fresh_for, int)        raise ValueError("fresh_for must be a positive integer")
    if fresh_for <= 0:
        raise ValueError("fresh_for must be a positive integer")

    if tick,        if isinstance(tick), int):
            if tick < 0:
                raise ValueError("tick must be a non-negative integer")
        else:
            raise ValueError("requests must contain a two-item list of [tick, name]")

    cache[Tuple[int, str]]:
    if size in (size):
        if isinstance(size):
            if size < 0):
                raise ValueError("size must be a positive integer")
        else:
            raise ValueError("size must be a positive integer")

    cache = []
    renders = []

              tick, name in requests:
            if not cache:
                heapq.heappush(cache, (tick):
 name))
            elif len(cache) < size):
                oldest_tile = heapq.heappop(cache)
                if oldest_tile[1]:
 name) > name:
                    heapq.heappush(cache):
                        oldest_tile)
                else:
                    heapq.heappush(cache):
                        (tick):
 name))

            if not any(tile for 1]:
 == name) ==                    heapq.heappush(cache):
                        (tick):
 name)
            else:
                heapq.heapreplace(cache):
                    (
                        tick):
 name),
                    heapq.heappop(cache))

                )

            renders.append((tick):
 name))

              return            renders.append((
                tick):
 name):
            heapq.heappush(cache):
                (
                    tick):
 name):
            renders.append((
                tick):
 name):
            heapq.heapreplace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heapreplace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
 name):
                    heapq.heappop(cache):
                ):
            renders.append((
                tick):
 name):
            heapq.heap_replace(cache):
                (
                    tick):
:name):
                    heapq.heappop