Basics: accounts with validated deposits and withdrawals

Bank-system OAs are mostly about validating first, then changing state. A failed operation must leave everything exactly as it was. Build Accounts with:

• open(account_id) -> bool: create an account with balance 0. Return False (changing nothing) if the id is already taken.
• deposit(account_id, amount) -> int | None: add amount and return the new balance.
• withdraw(account_id, amount) -> int | None: take amount out and return the new balance.
• balance(account_id) -> int | None: the current balance, or None for an unknown account.

deposit and withdraw return None and change nothing when:

• the account doesn't exist,
• amount is not positive (0 or negative),
• (withdraw only) the balance is less than amount. Withdrawing the whole balance is fine.

Amounts are integers.

a = Accounts()
a.open("ann")          # True
a.open("ann")          # False
a.deposit("ann", 100)  # 100
a.withdraw("ann", 30)  # 70
a.withdraw("ann", 80)  # None: not enough money
a.deposit("ann", -5)   # None: amount must be positive
a.deposit("bob", 10)   # None: no such account
a.balance("ann")       # 70