## 1359. Count All Valid Pickup and Delivery Options

Given `n` orders, each order consist in pickup and delivery services.

Count all valid pickup/delivery possible sequences such that delivery(i) is always after of pickup(i).

Since the answer may be too large, return it modulo 10^9 + 7.

Example 1:

```Input: n = 1
Output: 1
Explanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1.
```

Example 2:

```Input: n = 2
Output: 6
Explanation: 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.
```

Example 3:

```Input: n = 3
Output: 90
```

Constraints:

• `1 <= n <= 500`

## Rust Solution

``````struct Solution;

const MOD: i64 = 1_000_000_007;

impl Solution {
fn count_orders(n: i32) -> i32 {
let n = n as i64;
let mut res: i64 = 1;
for i in 1..=n {
res *= i * 2 - 1;
res %= MOD;
res *= i;
res %= MOD;
}
res as i32
}
}

#[test]
fn test() {
let n = 1;
let res = 1;
assert_eq!(Solution::count_orders(n), res);
let n = 2;
let res = 6;
assert_eq!(Solution::count_orders(n), res);
let n = 3;
let res = 90;
assert_eq!(Solution::count_orders(n), res);
}
``````

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