<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>

typedef long long ll;
ll zz = 1e9 + 7;

ll modadd(ll a, ll b){
    return ((a % zz) + (b % zz)) % zz;
}

ll modmul(ll a, ll b){
    return ((a % zz) * (b % zz)) % zz;
}

ll modexp(ll a, ll b){
    if(b == 0) return 1 % zz;
    if(b % 2 == 0){
        ll u = modexp(a, b / 2);
        return modmul(u, u);
    }
    else return modmul(a, modexp(a, b - 1));
}

// if zz is prime
ll modinv(ll b){
    return modexp(b, zz - 2);
}

ll moddiv(ll a, ll b){
    return modmul(a, modinv(b));
}

ll fact[100005];

void factcalc(){
    fact[0] = 1;
    for(ll i = 1; i < 100005; i++){
        fact[i] = modmul(fact[i - 1], i);
    }
}

ll modncr(ll n, ll r){
    if(n < r) return 0;
    if(r == 0) return 1;
    
    return modmul(modmul(fact[n], modinv(fact[r])), modinv(fact[n - r]));
}

ll modnpr(ll n, ll r){
    if(n < r) return 0;
    if(r == 0) return 1;
    return modmul(fact[n], modinv(fact[n - r]));
}








class Solution {
public:
    int countOrders(int n) {
        factcalc();
        // cout<<modncr(10,3)<<"\n";
        int ans=1;
        for(int i=1;i<=n;i++)ans=modmul(ans,modncr(2*i,2));
        return ans;
    }
};
8200