```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)
    total = 0
    purchases = []
    covered_until = 0

    for day in trip_days:
        if day > covered_until:
            min_cost = float('inf')
            best_pass = None
            for pass_ in passes:
                if day >= pass_["span"]:
                    cost = pass_["cost"]
                    if cost < min_cost:
                        min_cost = cost
                        best_pass = pass_
            if best_pass is None:
                raise ValueError("no valid pass found to cover trip day")
            total += best_pass["cost"]
            purchases.append([day, best_pass["span"]])
            covered_until = day + best_pass["span"] - 1

    return {"total": total, "purchases": purchases}
```