<p>A transaction is possibly invalid if:</p>

<ul>
	<li>the amount exceeds <code>$1000</code>, or;</li>
	<li>if it occurs within (and including) <code>60</code> minutes of another transaction with the <strong>same name</strong> in a <strong>different city</strong>.</li>
</ul>

<p>You are given an array of strings <code>transaction</code> where <code>transactions[i]</code> consists of comma-separated values representing the name, time (in minutes), amount, and city of the transaction.</p>

<p>Return a list of <code>transactions</code> that are possibly invalid. You may return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> transactions = [&quot;alice,20,800,mtv&quot;,&quot;alice,50,100,beijing&quot;]
<strong>Output:</strong> [&quot;alice,20,800,mtv&quot;,&quot;alice,50,100,beijing&quot;]
<strong>Explanation:</strong> The first transaction is invalid because the second transaction occurs within a difference of 60 minutes, have the same name and is in a different city. Similarly the second one is invalid too.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> transactions = [&quot;alice,20,800,mtv&quot;,&quot;alice,50,1200,mtv&quot;]
<strong>Output:</strong> [&quot;alice,50,1200,mtv&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> transactions = [&quot;alice,20,800,mtv&quot;,&quot;bob,50,1200,mtv&quot;]
<strong>Output:</strong> [&quot;bob,50,1200,mtv&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>transactions.length &lt;= 1000</code></li>
	<li>Each <code>transactions[i]</code> takes the form <code>&quot;{name},{time},{amount},{city}&quot;</code></li>
	<li>Each <code>{name}</code> and <code>{city}</code> consist of lowercase English letters, and have lengths between <code>1</code> and <code>10</code>.</li>
	<li>Each <code>{time}</code> consist of digits, and represent an integer between <code>0</code> and <code>1000</code>.</li>
	<li>Each <code>{amount}</code> consist of digits, and represent an integer between <code>0</code> and <code>2000</code>.</li>
</ul>

class Solution:
    def invalidTransactions(self, transactions):
        from collections import defaultdict

        # Define a Transaction class to hold transaction details
        class Transaction:
            def __init__(self, index, name, time, amount, city, transaction_string):
                self.index = index
                self.name = name
                self.time = int(time)
                self.amount = int(amount)
                self.city = city
                self.transaction_string = transaction_string

        # List to hold all transactions
        transaction_list = []
        # List to hold indices of invalid transactions
        invalid_indices = set()
        # Mapping from name to list of transactions
        name_to_transactions = defaultdict(list)

        # Step 1: Parse transactions and check for amount > 1000
        for index, transaction_string in enumerate(transactions):
            name, time, amount, city = transaction_string.split(',')
            transaction = Transaction(index, name, time, amount, city, transaction_string)
            transaction_list.append(transaction)
            name_to_transactions[name].append(transaction)
            # Check if amount exceeds 1000
            if transaction.amount > 1000:
                invalid_indices.add(index)

        # Step 2: Check for invalid transactions based on time and city
        for name in name_to_transactions:
            # Get the list of transactions for this name
            transactions_list = name_to_transactions[name]
            n = len(transactions_list)
            # Compare each transaction with every other transaction for this name
            for i in range(n):
                t1 = transactions_list[i]
                for j in range(n):
                    if i == j:
                        continue
                    t2 = transactions_list[j]
                    # Check if transactions are within 60 minutes and different cities
                    if abs(t1.time - t2.time) <= 60 and t1.city != t2.city:
                        invalid_indices.add(t1.index)
                        invalid_indices.add(t2.index)

        # Return the list of invalid transactions based on indices
        result = [transactions[i] for i in invalid_indices]
        return result

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