{ "data": { "question": { "questionId": "1461", "questionFrontendId": "1359", "categoryTitle": "Algorithms", "boundTopicId": 102335, "title": "Count All Valid Pickup and Delivery Options", "titleSlug": "count-all-valid-pickup-and-delivery-options", "content": "

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

\n\n

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

\n\n

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

\n\n

 

\n

Example 1:

\n\n
\nInput: n = 1\nOutput: 1\nExplanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1.\n
\n\n

Example 2:

\n\n
\nInput: n = 2\nOutput: 6\nExplanation: All possible orders: \n(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).\nThis is an invalid order (P1,D2,P2,D1) because Pickup 2 is after of Delivery 2.\n
\n\n

Example 3:

\n\n
\nInput: n = 3\nOutput: 90\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "有效的快递序列数目", "translatedContent": "

给你 n 笔订单，每笔订单都需要快递服务。

\n\n

请你统计所有有效的 收件/配送 序列的数目，确保第 i 个物品的配送服务 delivery(i) 总是在其收件服务 pickup(i) 之后。

\n\n

由于答案可能很大，请返回答案对 10^9 + 7 取余的结果。

\n\n

 

\n\n

示例 1：

\n\n
输入：n = 1\n输出：1\n解释：只有一种序列 (P1, D1)，物品 1 的配送服务（D1）在物品 1 的收件服务（P1）后。\n
\n\n

示例 2：

\n\n
输入：n = 2\n输出：6\n解释：所有可能的序列包括：\n(P1,P2,D1,D2)，(P1,P2,D2,D1)，(P1,D1,P2,D2)，(P2,P1,D1,D2)，(P2,P1,D2,D1) 和 (P2,D2,P1,D1)。\n(P1,D2,P2,D1) 是一个无效的序列，因为物品 2 的收件服务（P2）不应在物品 2 的配送服务（D2）之后。\n
\n\n

示例 3：

\n\n
输入：n = 3\n输出：90\n
\n\n

 

\n\n

提示：

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