<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 {
    int MOD = 1e9 + 7;
public:
    int countOrders(int n) {
        long res = 1;
        for (int i = 1; i <= n; ++i) {
            res *= i;
            res *= 2 * i - 1;
            res %= MOD;
        }
        return res;
    }
};

class Solution_TLE {
    // Time: n^2
    // Space: n^2
    int MOD = 1e9 + 7;
    std::vector<std::vector<int>> memo;

    long totalWays(int pickups, int deliveries) {
        if (pickups == 0 && deliveries == 0) {
            return 1;
        }

        if (pickups < 0 || deliveries < 0 || pickups > deliveries) {
            return 0;
        }

        if (memo[pickups][deliveries]) {
            return memo[pickups][deliveries];
        }

        long res = 0;

        res += pickups * totalWays(pickups - 1, deliveries);
        res %= MOD;
        res += (deliveries - pickups) * totalWays(pickups, deliveries - 1);
        res %= MOD;

        return res;
    }

public:
    int countOrders(int n) {
        memo = std::vector<std::vector<int>>(n + 1, std::vector<int>(n + 1, 0));
        return totalWays(n, n);
    }
};
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