```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": []}
    
    trip_days.sort()
    min_cost = float('inf')
    best_purchases = []
    
    for start_day in trip_days:
        for span in range(1, len(trip_days) - start_day + 1):
            total_cost = 0
            for cover in passes:
                if start_day + cover["span"] - 1 <= len(trip_days) - 1:
                    total_cost += cover["cost"]
            if total_cost < min_cost:
                min_cost = total_cost
                best_purchases = [(start_day, span)]
            elif total_cost == min_cost:
                best_purchases.append((start_day, span))
    
    return {"total": min_cost, "purchases": best_purchases}
```