```python
def stamp_table(dies: list) -> dict:
    table = {}
    for fragment, price in dies:
        if not isinstance(fragment, str) or not fragment:
            raise ValueError("a die fragment must be a non-empty string")
        if isinstance(price, bool) or not isinstance(price, int) or price <= 0:
            raise ValueError("a die price must be a positive integer")
        if fragment in table:
            raise ValueError("die listed twice: " + fragment)
        table[fragment] = price
    return table


def stamp_cover(label: str, dies: list) -> int:
    if not isinstance(label, str) or not label:
        raise ValueError("a label must be a non-empty string")
    if not label:
        return 0
    if len(label) == 1:
        return stamp_table(dies)[label]
    min_price = float('inf')
    for fragment in label:
        if fragment in stamp_table(dies):
            min_price = min(min_price, stamp_table(dies)[fragment] + stamp_cover(label.replace(fragment, '', 1), dies))
    return min_price
```