```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)

    n = len(trip_days)
    dp = [float('inf')] * (n + 1)
    dp[0] = 0
    prev_purchase = [-1] * (n + 1)

    for i in range(1, n + 1):
        for cover in passes:
            span = cover["span"]
            cost = cover["cost"]
            if i - span >= 0 and dp[i - span] + cost < dp[i]:
                dp[i] = dp[i - span] + cost
                prev_purchase[i] = i - span

    total_cost = dp[n]
    purchases = []
    while n > 0:
        start_day = prev_purchase[n]
        span = trip_days[start_day:].index(trip_days[n - 1]) + 1
        purchases.append([trip_days[start_day], span])
        n -= span

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