<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 {
private:
    int MOD = 1e9 + 7;
    vector<vector<int>> memo;
    
    long totalWays(int unpicked, int undelivered) {
        if (unpicked == 0 && undelivered == 0) {
            // We have completed all orders.
            return 1;
        }
        
        if (unpicked < 0 || undelivered < 0 || undelivered < unpicked) {
            // We can't pick or deliver more than N items
            // Number of deliveries can't exceed number of pickups 
            // as we can only deliver after a pickup.
            return 0;
        }
        
        if (memo[unpicked][undelivered]) {
            // Return cached value, if already present. 
            return memo[unpicked][undelivered];
        }
        
        long ans = 0;
        
        // Count all choices of picking up an order.
        ans += unpicked * totalWays(unpicked - 1, undelivered);
        // Handle integer overflow.
        ans %= MOD;
        
        // Count all choices of delivering a picked order.
        ans += (undelivered - unpicked) * totalWays(unpicked, undelivered - 1);
        // Handle integer overflow.
        ans %= MOD;
        
        return memo[unpicked][undelivered] = ans;
    }
    
public:
    int countOrders(int n) {
        memo = vector<vector<int>> (n + 1, vector<int>(n + 1, 0));
        return totalWays(n, n);
    }
};
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