1359. Count All Valid Pickup and Delivery Options

https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options

Description

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

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