```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)
    if not trip_days:
        return {"total": 0, "purchases": []}
    trips = set(trip_days)
    cheapest = float("inf")
    best_purchases = []
    for start in sorted(trips):
        for pass_kind in passes:
            span = pass_kind["span"]
            cost = pass_kind["cost"]
            end = start + span - 1
            if end < trips:
                purchases = [(start, span)]
                total = cost
                break
            elif start == end:
                purchases = [(start, span)]
                total = cost
                break
            else:
                purchases = [(start, span)]
                total = cost
                while end + 1 in trips:
                    end += 1
                    purchases.append((end, span))
                    total += cost
                if total < cheapest:
                    cheapest = total
                    best_purchases = purchases
    return {"total": cheapest, "purchases": best_purchases}
```