===== ISTEM =====
Solve the following programming task.

TASK: Payment and Refund Reconciliation

Write a function 'reconcile(transactions)' that processes a list of payment and refund transactions in order and returns a dict with two keys, 'balances' and 'rejected'.

Each transaction is a dict with the keys 'id' (str), 'type' ('payment' or 'refund'), 'account' (str) and 'amount' (int, in cents). A refund also has 'refers_to', the id of the payment it refunds. You can assume every transaction has these keys with these types.

Process the transactions in list order:
- A transaction whose id has already appeared earlier in the list is rejected with reason 'duplicate', whether or not the earlier one was accepted.
- A transaction whose amount is 0 or negative is rejected with reason 'invalid_amount'.
- A refund is rejected with reason 'unknown_payment' if 'refers_to' is not the id of an earlier, accepted payment. This includes ids of refunds, ids of rejected payments, and ids of payments that appear later in the list.
- A refund is rejected with reason 'account_mismatch' if its account differs from the account of the payment it refers to.
- A refund is rejected with reason 'over_refund' if the accepted refunds for that payment, including this one, would add up to more than the payment's amount.
- If more than one reason applies, use the first one in the order listed above.
- An accepted payment adds its amount to its account's balance; an accepted refund subtracts its amount. Rejected transactions change nothing.

Return:
- 'balances': a dict mapping each account that appears in at least one accepted transaction to its final balance in cents. Accounts that appear only in rejected transactions are not included.
- 'rejected': a list of (id, reason) tuples, in the order the rejected transactions appeared.

STARTER CODE (python):
def reconcile(transactions: list) -> dict:
    # Write your code here
    pass


RULES:
- Keep the function name and signature EXACTLY as given.
- Return working code only. No explanations.
- Put the code in a single ``` block.
- Try to solve it first. If you genuinely cannot, write only this single
  line instead of producing faulty code: CANNOT_SOLVE

===== HAM YANIT =====
```python
def reconcile(transactions: list) -> dict:
    balances = {}
    rejected = []
    seen_ids = set()
    accepted_payments = {}  # maps payment id -> (account, amount, refunds_total)
    accepted_refunds_by_payment = {}  # maps payment id -> list of refund ids (for tracking, not strictly needed for amount)

    for txn in transactions:
        txn_id = txn['id']
        txn_type = txn['type']
        account = txn['account']
        amount = txn['amount']

        reason = None

        # Check duplicate
        if txn_id in seen_ids:
            reason = 'duplicate'
        # Check invalid amount
        elif amount <= 0:
            reason = 'invalid_amount'
        else:
            if txn_type == 'payment':
                # Accept the payment
                balances[account] = balances.get(account, 0) + amount
                accepted_payments[txn_id] = {
                    'account': account,
                    'amount': amount,
                    'refunds_total': 0
                }
                accepted_refunds_by_payment[txn_id] = []
            elif txn_type == 'refund':
                refers_to = txn['refers_to']
                # Check unknown payment
                if refers_to not in accepted_payments:
                    reason = 'unknown_payment'
                elif accepted_payments[refers_to]['account'] != account:
                    reason = 'account_mismatch'
                elif accepted_payments[refers_to]['refunds_total'] + amount > accepted_payments[refers_to]['amount']:
                    reason = 'over_refund'
                else:
                    # Accept the refund
                    balances[account] = balances.get(account, 0) - amount
                    accepted_payments[refers_to]['refunds_total'] += amount
                    accepted_refunds_by_payment[refers_to].append(txn_id)

        if reason:
            rejected.append((txn_id, reason))
            seen_ids.add(txn_id)
        else:
            seen_ids.add(txn_id)

    return {'balances': balances, 'rejected': rejected}
```