<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 {
public:
    int MOD = 1e9 + 7;
    
    int countOrders(int n) {
        vector<vector<long>> dp (n + 1, vector<long>(n + 1, 0));

        for (int unpicked = 0; unpicked <= n; unpicked++) {
            for (int undelivered = unpicked; undelivered <= n; undelivered++) {
                // If all orders are picked and delivered then,
                // for remaining '0' orders we have only one way.
                if (unpicked == 0 && undelivered == 0) {
                    dp[unpicked][undelivered] = 1;
                    continue;
                }
                
                // There are some unpicked elements left. 
                // We have choice to pick any one of those orders.
                if (unpicked > 0) {
                    dp[unpicked][undelivered] += unpicked * dp[unpicked - 1][undelivered];
                }
                dp[unpicked][undelivered] %= MOD;
                
                // Number of deliveries done is less than picked orders.
                // We have choice to deliver any one of (undelivered - unpicked) orders. 
                if (undelivered > unpicked) {
                    dp[unpicked][undelivered] += (undelivered - unpicked) * dp[unpicked][undelivered - 1];
                }
                dp[unpicked][undelivered] %= MOD;
            }
        }
        
        return dp[n][n];
    }
};
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