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diff --git a/leetcode-cn/originData/beautiful-towers-i.json b/leetcode-cn/originData/beautiful-towers-i.json
new file mode 100644
index 00000000..127d0808
--- /dev/null
+++ b/leetcode-cn/originData/beautiful-towers-i.json
@@ -0,0 +1,165 @@
+{
+ "data": {
+ "question": {
+ "questionId": "3114",
+ "questionFrontendId": "100049",
+ "categoryTitle": "Algorithms",
+ "boundTopicId": 2453610,
+ "title": "Beautiful Towers I",
+ "titleSlug": "beautiful-towers-i",
+ "content": "
You are given a 0-indexed array maxHeights of n integers.
\n\nYou are tasked with building n towers in the coordinate line. The ith tower is built at coordinate i and has a height of heights[i].
\n\nA configuration of towers is beautiful if the following conditions hold:
\n\n\n\t1 <= heights[i] <= maxHeights[i]heights is a mountain array.
\n\nArray heights is a mountain if there exists an index i such that:
\n\n\n\t- For all
0 < j <= i, heights[j - 1] <= heights[j] \n\t- For all
i <= k < n - 1, heights[k + 1] <= heights[k] \n
\n\nReturn the maximum possible sum of heights of a beautiful configuration of towers.
\n\n
\nExample 1:
\n\n\nInput: maxHeights = [5,3,4,1,1]\nOutput: 13\nExplanation: One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i] \n- heights is a mountain of peak i = 0.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 13.
\n\nExample 2:
\n\n\nInput: maxHeights = [6,5,3,9,2,7]\nOutput: 22\nExplanation: One beautiful configuration with a maximum sum is heights = [3,3,3,9,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 3.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 22.
\n\nExample 3:
\n\n\nInput: maxHeights = [3,2,5,5,2,3]\nOutput: 18\nExplanation: One beautiful configuration with a maximum sum is heights = [2,2,5,5,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 2. \nNote that, for this configuration, i = 3 can also be considered a peak.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 18.\n
\n\n
\nConstraints:
\n\n\n\t1 <= n == maxHeights <= 1031 <= maxHeights[i] <= 109
\n",
+ "translatedTitle": "美丽塔 I",
+ "translatedContent": "给你一个长度为 n 下标从 0 开始的整数数组 maxHeights 。
\n\n你的任务是在坐标轴上建 n 座塔。第 i 座塔的下标为 i ，高度为 heights[i] 。
\n\n如果以下条件满足，我们称这些塔是 美丽 的：
\n\n\n\t1 <= heights[i] <= maxHeights[i]heights 是一个 山状 数组。
\n\n如果存在下标 i 满足以下条件，那么我们称数组 heights 是一个 山状 数组：
\n\n\n\t- 对于所有
0 < j <= i ，都有 heights[j - 1] <= heights[j] \n\t- 对于所有
i <= k < n - 1 ，都有 heights[k + 1] <= heights[k] \n
\n\n请你返回满足 美丽塔 要求的方案中，高度和的最大值 。
\n\n
\n\n示例 1：
\n\n\n输入：maxHeights = [5,3,4,1,1]\n输出：13\n解释：和最大的美丽塔方案为 heights = [5,3,3,1,1] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i] \n- heights 是个山状数组，峰值在 i = 0 处。\n13 是所有美丽塔方案中的最大高度和。
\n\n示例 2：
\n\n\n输入：maxHeights = [6,5,3,9,2,7]\n输出：22\n解释： 和最大的美丽塔方案为 heights = [3,3,3,9,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，峰值在 i = 3 处。\n22 是所有美丽塔方案中的最大高度和。
\n\n示例 3：
\n\n\n输入：maxHeights = [3,2,5,5,2,3]\n输出：18\n解释：和最大的美丽塔方案为 heights = [2,2,5,5,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，最大值在 i = 2 处。\n注意，在这个方案中，i = 3 也是一个峰值。\n18 是所有美丽塔方案中的最大高度和。\n
\n\n
\n\n提示：
\n\n\n\t1 <= n == maxHeights <= 1031 <= maxHeights[i] <= 109
\n",
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+ "hints": [
+ "Try all the possible indices i as the peak.",
+ "If i is the peak, start from heights[i] = maxHeights[i], and heights[j] = max(maxHeights[j], heights[j + 1]) for 0 <= j < i ",
+ "If i is the peak, start from heights[i] = maxHeights[i], and heights[j] = max(maxHeights[j], heights[j - 1]) for i < j < heights.size()"
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diff --git a/leetcode-cn/originData/beautiful-towers-ii.json b/leetcode-cn/originData/beautiful-towers-ii.json
new file mode 100644
index 00000000..b53f09af
--- /dev/null
+++ b/leetcode-cn/originData/beautiful-towers-ii.json
@@ -0,0 +1,167 @@
+{
+ "data": {
+ "question": {
+ "questionId": "3113",
+ "questionFrontendId": "100048",
+ "categoryTitle": "Algorithms",
+ "boundTopicId": 2453609,
+ "title": "Beautiful Towers II",
+ "titleSlug": "beautiful-towers-ii",
+ "content": "
You are given a 0-indexed array maxHeights of n integers.
\n\nYou are tasked with building n towers in the coordinate line. The ith tower is built at coordinate i and has a height of heights[i].
\n\nA configuration of towers is beautiful if the following conditions hold:
\n\n\n\t1 <= heights[i] <= maxHeights[i]heights is a mountain array.
\n\nArray heights is a mountain if there exists an index i such that:
\n\n\n\t- For all
0 < j <= i, heights[j - 1] <= heights[j] \n\t- For all
i <= k < n - 1, heights[k + 1] <= heights[k] \n
\n\nReturn the maximum possible sum of heights of a beautiful configuration of towers.
\n\n
\nExample 1:
\n\n\nInput: maxHeights = [5,3,4,1,1]\nOutput: 13\nExplanation: One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i] \n- heights is a mountain of peak i = 0.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 13.
\n\nExample 2:
\n\n\nInput: maxHeights = [6,5,3,9,2,7]\nOutput: 22\nExplanation: One beautiful configuration with a maximum sum is heights = [3,3,3,9,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 3.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 22.
\n\nExample 3:
\n\n\nInput: maxHeights = [3,2,5,5,2,3]\nOutput: 18\nExplanation: One beautiful configuration with a maximum sum is heights = [2,2,5,5,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 2. \nNote that, for this configuration, i = 3 can also be considered a peak.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 18.\n
\n\n
\nConstraints:
\n\n\n\t1 <= n == maxHeights <= 1051 <= maxHeights[i] <= 109
\n",
+ "translatedTitle": "美丽塔 II",
+ "translatedContent": "给你一个长度为 n 下标从 0 开始的整数数组 maxHeights 。
\n\n你的任务是在坐标轴上建 n 座塔。第 i 座塔的下标为 i ，高度为 heights[i] 。
\n\n如果以下条件满足，我们称这些塔是 美丽 的：
\n\n\n\t1 <= heights[i] <= maxHeights[i]heights 是一个 山状 数组。
\n\n如果存在下标 i 满足以下条件，那么我们称数组 heights 是一个 山状 数组：
\n\n\n\t- 对于所有
0 < j <= i ，都有 heights[j - 1] <= heights[j] \n\t- 对于所有
i <= k < n - 1 ，都有 heights[k + 1] <= heights[k] \n
\n\n请你返回满足 美丽塔 要求的方案中，高度和的最大值 。
\n\n
\n\n示例 1：
\n\n\n输入：maxHeights = [5,3,4,1,1]\n输出：13\n解释：和最大的美丽塔方案为 heights = [5,3,3,1,1] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i] \n- heights 是个山状数组，峰值在 i = 0 处。\n13 是所有美丽塔方案中的最大高度和。
\n\n示例 2：
\n\n\n输入：maxHeights = [6,5,3,9,2,7]\n输出：22\n解释： 和最大的美丽塔方案为 heights = [3,3,3,9,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，峰值在 i = 3 处。\n22 是所有美丽塔方案中的最大高度和。
\n\n示例 3：
\n\n\n输入：maxHeights = [3,2,5,5,2,3]\n输出：18\n解释：和最大的美丽塔方案为 heights = [2,2,5,5,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，最大值在 i = 2 处。\n注意，在这个方案中，i = 3 也是一个峰值。\n18 是所有美丽塔方案中的最大高度和。\n
\n\n
\n\n提示：
\n\n\n\t1 <= n == maxHeights <= 1051 <= maxHeights[i] <= 109
\n",
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diff --git a/leetcode-cn/originData/count-valid-paths-in-a-tree.json b/leetcode-cn/originData/count-valid-paths-in-a-tree.json
new file mode 100644
index 00000000..886c22f0
--- /dev/null
+++ b/leetcode-cn/originData/count-valid-paths-in-a-tree.json
@@ -0,0 +1,168 @@
+{
+ "data": {
+ "question": {
+ "questionId": "3112",
+ "questionFrontendId": "100047",
+ "categoryTitle": "Algorithms",
+ "boundTopicId": 2453611,
+ "title": "Count Valid Paths in a Tree",
+ "titleSlug": "count-valid-paths-in-a-tree",
+ "content": "
There is an undirected tree with n nodes labeled from 1 to n. You are given the integer n and a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.
\n\nReturn the number of valid paths in the tree.
\n\nA path (a, b) is valid if there exists exactly one prime number among the node labels in the path from a to b.
\n\nNote that:
\n\n\n\t- The path
(a, b) is a sequence of distinct nodes starting with node a and ending with node b such that every two adjacent nodes in the sequence share an edge in the tree. \n\t- Path
(a, b) and path (b, a) are considered the same and counted only once. \n
\n\n
\nExample 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2023/08/27/example1.png\")
\n\nInput: n = 5, edges = [[1,2],[1,3],[2,4],[2,5]]\nOutput: 4\nExplanation: The pairs with exactly one prime number on the path between them are: \n- (1, 2) since the path from 1 to 2 contains prime number 2. \n- (1, 3) since the path from 1 to 3 contains prime number 3.\n- (1, 4) since the path from 1 to 4 contains prime number 2.\n- (2, 4) since the path from 2 to 4 contains prime number 2.\nIt can be shown that there are only 4 valid paths.\n
\n\nExample 2:
\n![\"\"](\"https://assets.leetcode.com/uploads/2023/08/27/example2.png\")
\n\nInput: n = 6, edges = [[1,2],[1,3],[2,4],[3,5],[3,6]]\nOutput: 6\nExplanation: The pairs with exactly one prime number on the path between them are: \n- (1, 2) since the path from 1 to 2 contains prime number 2.\n- (1, 3) since the path from 1 to 3 contains prime number 3.\n- (1, 4) since the path from 1 to 4 contains prime number 2.\n- (1, 6) since the path from 1 to 6 contains prime number 3.\n- (2, 4) since the path from 2 to 4 contains prime number 2.\n- (3, 6) since the path from 3 to 6 contains prime number 3.\nIt can be shown that there are only 6 valid paths.\n
\n\n
\nConstraints:
\n\n\n\t1 <= n <= 105edges.length == n - 1edges[i].length == 21 <= ui, vi <= n- The input is generated such that
edges represent a valid tree. \n
\n",
+ "translatedTitle": "统计树中的合法路径数目",
+ "translatedContent": "给你一棵 n 个节点的无向树，节点编号为 1 到 n 。给你一个整数 n 和一个长度为 n - 1 的二维整数数组 edges ，其中 edges[i] = [ui, vi] 表示节点 ui 和 vi 在树中有一条边。
\n\n请你返回树中的 合法路径数目 。
\n\n如果在节点 a 到节点 b 之间 恰好有一个 节点的编号是质数，那么我们称路径 (a, b) 是 合法的 。
\n\n注意：
\n\n\n\t- 路径
(a, b) 指的是一条从节点 a 开始到节点 b 结束的一个节点序列，序列中的节点 互不相同 ，且相邻节点之间在树上有一条边。 \n\t- 路径
(a, b) 和路径 (b, a) 视为 同一条 路径，且只计入答案 一次 。 \n
\n\n
\n\n示例 1：
\n\n
\n\n\n输入：n = 5, edges = [[1,2],[1,3],[2,4],[2,5]]\n输出：4\n解释：恰好有一个质数编号的节点路径有：\n- (1, 2) 因为路径 1 到 2 只包含一个质数 2 。\n- (1, 3) 因为路径 1 到 3 只包含一个质数 3 。\n- (1, 4) 因为路径 1 到 4 只包含一个质数 2 。\n- (2, 4) 因为路径 2 到 4 只包含一个质数 2 。\n只有 4 条合法路径。\n
\n\n示例 2：
\n\n
\n\n\n输入：n = 6, edges = [[1,2],[1,3],[2,4],[3,5],[3,6]]\n输出：6\n解释：恰好有一个质数编号的节点路径有：\n- (1, 2) 因为路径 1 到 2 只包含一个质数 2 。\n- (1, 3) 因为路径 1 到 3 只包含一个质数 3 。\n- (1, 4) 因为路径 1 到 4 只包含一个质数 2 。\n- (1, 6) 因为路径 1 到 6 只包含一个质数 3 。\n- (2, 4) 因为路径 2 到 4 只包含一个质数 2 。\n- (3, 6) 因为路径 3 到 6 只包含一个质数 3 。\n只有 6 条合法路径。\n
\n\n
\n\n提示：
\n\n\n\t1 <= n <= 105edges.length == n - 1edges[i].length == 21 <= ui, vi <= n- 输入保证
edges 形成一棵合法的树。 \n
\n",
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+ },
+ {
+ "lang": "Ruby",
+ "langSlug": "ruby",
+ "code": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @return {Integer}\ndef count_paths(n, edges)\n\nend",
+ "__typename": "CodeSnippetNode"
+ },
+ {
+ "lang": "Scala",
+ "langSlug": "scala",
+ "code": "object Solution {\n def countPaths(n: Int, edges: Array[Array[Int]]): Long = {\n\n }\n}",
+ "__typename": "CodeSnippetNode"
+ },
+ {
+ "lang": "Rust",
+ "langSlug": "rust",
+ "code": "impl Solution {\n pub fn count_paths(n: i32, edges: Vec>) -> i64 {\n\n }\n}",
+ "__typename": "CodeSnippetNode"
+ },
+ {
+ "lang": "Racket",
+ "langSlug": "racket",
+ "code": "(define/contract (count-paths n edges)\n (-> exact-integer? (listof (listof exact-integer?)) exact-integer?)\n )",
+ "__typename": "CodeSnippetNode"
+ },
+ {
+ "lang": "Erlang",
+ "langSlug": "erlang",
+ "code": "-spec count_paths(N :: integer(), Edges :: [[integer()]]) -> integer().\ncount_paths(N, Edges) ->\n .",
+ "__typename": "CodeSnippetNode"
+ },
+ {
+ "lang": "Elixir",
+ "langSlug": "elixir",
+ "code": "defmodule Solution do\n @spec count_paths(n :: integer, edges :: [[integer]]) :: integer\n def count_paths(n, edges) do\n \n end\nend",
+ "__typename": "CodeSnippetNode"
+ }
+ ],
+ "stats": "{\"totalAccepted\": \"1.1K\", \"totalSubmission\": \"4.4K\", \"totalAcceptedRaw\": 1070, \"totalSubmissionRaw\": 4391, \"acRate\": \"24.4%\"}",
+ "hints": [
+ "Use the sieve of Eratosthenes to find all prime numbers in the range [1, n].****",
+ "Root the tree at any node.",
+ "Let dp[i][0] = the number of vertical paths starting from i containing no prime nodes , and dp[i][1] = the number of vertical paths starting from i containing one prime node .",
+ "If i is not prime, dp[i][0] = sum(dp[child][0]) + 1, and dp[i][1] = sum(dp[child][1]) for each child of i in the rooted tree.",
+ "If i is prime, dp[i][0] = 0, and dp[i][1] = sum(dp[child][0]) + 1 for each child of i in the rooted tree.",
+ "For each node i, and using the computed dp matrix, count the number of unordered pairs (a,b) such that lca(a,b) = i, and there exists exactly one prime number on the path from a to b."
+ ],
+ "solution": null,
+ "status": null,
+ "sampleTestCase": "5\n[[1,2],[1,3],[2,4],[2,5]]",
+ "metaData": "{\n \"name\": \"countPaths\",\n \"params\": [\n {\n \"name\": \"n\",\n \"type\": \"integer\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"edges\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}",
+ "judgerAvailable": true,
+ "judgeType": "large",
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+ "enableRunCode": true,
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