<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 = 1000000007;
    long long rec(long long pick,long long deliv,int &n,vector<vector<int>>&dp){
        if(deliv==n)return 1;
        if(dp[pick][deliv]!=-1) return dp[pick][deliv];
        if(pick==deliv){
            return dp[pick][deliv]= (long long)((n-pick)*rec(pick+1,deliv,n,dp))%mod;
        }
        else{
            long long ans1=0,ans2=0;
            if(pick<n){
                ans1= (long long)((n-pick)*rec(pick+1,deliv,n,dp))%mod;
            }
                ans2= (long long)((pick-deliv)*rec(pick,deliv+1,n,dp))%mod;
                return  dp[pick][deliv]=(ans1+ans2)%mod;;
        }
    }
    int countOrders(int n) {
        vector<vector<int>>dp(n+1,vector<int>(n+1,-1));
        return rec(0,0,n,dp);
    }
};
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