===== 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:
    seen_ids = set()
    payments = {}
    balances = {}
    rejected = []

    for tx in transactions:
        tx_id = tx["id"]
        tx_type = tx["type"]
        account = tx["account"]
        amount = tx["amount"]

        if tx_id in seen_ids:
            rejected.append((tx_id, "duplicate"))
            continue

        seen_ids.add(tx_id)

        if amount <= 0:
            rejected.append((tx_id, "invalid_amount"))
            continue

        if tx_type == "payment":
            balances[account] = balances.get(account, 0) + amount
            payments[tx_id] = {
                "account": account,
                "amount": amount,
                "refunded": 0,
            }
        else:
            refers_to = tx["refers_to"]

            if refers_to not in payments:
                rejected.append((tx_id, "unknown_payment"))
                continue

            payment = payments[refers_to]

            if account != payment["account"]:
                rejected.append((tx_id, "account_mismatch"))
                continue

            if payment["refunded"] + amount > payment["amount"]:
                rejected.append((tx_id, "over_refund"))
                continue

            payment["refunded"] += amount
            balances[account] -= amount

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