```python
"""The cheapest set of travel passes covering every trip day."""


def _validate_plan(trip_days, passes):
    for day in trip_days:
        if isinstance(day, bool) or not isinstance(day, int) or day < 1:
            raise ValueError("trip days must be positive integers")
    for earlier, later in zip(trip_days, trip_days[1:]):
        if later <= earlier:
            raise ValueError("trip days must be strictly increasing")
    if not passes:
        raise ValueError("at least one pass kind is required")
    for cover in passes:
        span = cover["span"]
        cost = cover["cost"]
        if isinstance(span, bool) or not isinstance(span, int) or span < 1:
            raise ValueError("pass span must be a positive integer")
        if isinstance(cost, bool) or not isinstance(cost, int) or cost < 0:
            raise ValueError("pass cost must be a non-negative integer")


def cheapest_pass_plan(trip_days: list, passes: list) -> dict:
    _validate_plan(trip_days, passes)
    # TODO: find the cheapest combination of passes covering every trip
    # day and reconstruct its purchases in increasing start-day order.
    if not trip_days:
        return {"total": 0, "purchases": []}
    
    total_cost = 0
    purchases = []
    current_pass_index = 0
    
    for trip_day in sorted(trip_days):
        while current_pass_index < len(passes) and passes[current_pass_index]["span"] <= trip_day:
            span = passes[current_pass_index]["span"]
            cost = passes[current_pass_index]["cost"]
            if total_cost + cost > trip_day:
                break
            total_cost += cost
            purchases.append([trip_day, span])
            current_pass_index += 1
    
    return {"total": total_cost, "purchases": purchases}
```