<p>Given <code>n</code> orders, each order consists of a pickup and a delivery service.</p>

<p>Count all valid pickup/delivery possible sequences such that delivery(i) is always after of&nbsp;pickup(i).&nbsp;</p>

<p>Since the answer&nbsp;may be too large,&nbsp;return it modulo&nbsp;10^9 + 7.</p>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> Unique order (P1, D1), Delivery 1 always is after of Pickup 1.
</pre>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 6
<strong>Explanation:</strong> All possible orders: 
(P1,P2,D1,D2), (P1,P2,D2,D1), (P1,D1,P2,D2), (P2,P1,D1,D2), (P2,P1,D2,D1) and (P2,D2,P1,D1).
This is an invalid order (P1,D2,P2,D1) because Pickup 2 is after of Delivery 2.
</pre>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 90
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
</ul>

class Solution:
    def __init__(self):
        self.mod = 1000000007

    def countOrders(self, n: int) -> int:
        orderJobsRemaining = n
        deliveryJobsRemaining = n
        visited = {}

        return self.calculateNumPickupAndDeliveryOptions(orderJobsRemaining, deliveryJobsRemaining, visited)

    def calculateNumPickupAndDeliveryOptions(self, orderJobsRemaining, deliveryJobsRemaining, visited):
        if orderJobsRemaining == 0 and deliveryJobsRemaining == 0:
            return 1

        # deliveryJobsRemaining < orderJobsRemaining means there are more active deliver jobs picked up than there are active order jobs picked up
        if orderJobsRemaining < 0 or deliveryJobsRemaining < 0 or deliveryJobsRemaining < orderJobsRemaining:
            return 0

        if (orderJobsRemaining, deliveryJobsRemaining) in visited:
            return visited[(orderJobsRemaining, deliveryJobsRemaining)]

        # if we pick up an order, we have N ways for current job and then for next thing, we have N - 1
        ans = orderJobsRemaining * self.calculateNumPickupAndDeliveryOptions(orderJobsRemaining - 1, deliveryJobsRemaining, visited)
        ans = ans % self.mod
        
        # active deliveries
        ans += (deliveryJobsRemaining - orderJobsRemaining) * self.calculateNumPickupAndDeliveryOptions(orderJobsRemaining, deliveryJobsRemaining - 1, visited)
        ans = ans % self.mod

        visited[(orderJobsRemaining, deliveryJobsRemaining)] = ans

        return ans
41200