leetcode-problemset/leetcode-cn/originData/prime-arrangements.json

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        "question": {
            "questionId": "1279",
            "questionFrontendId": "1175",
            "categoryTitle": "Algorithms",
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            "title": "Prime Arrangements",
            "titleSlug": "prime-arrangements",
            "content": "<p>Return the number of permutations of 1 to <code>n</code> so that prime numbers are at prime indices (1-indexed.)</p>\n\n<p><em>(Recall that an integer&nbsp;is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers&nbsp;both smaller than it.)</em></p>\n\n<p>Since the answer may be large, return the answer <strong>modulo <code>10^9 + 7</code></strong>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 100\n<strong>Output:</strong> 682289015\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "质数排列",
            "translatedContent": "<p>请你帮忙给从 <code>1</code> 到 <code>n</code>&nbsp;的数设计排列方案，使得所有的「质数」都应该被放在「质数索引」（索引从 1 开始）上；你需要返回可能的方案总数。</p>\n\n<p>让我们一起来回顾一下「质数」：质数一定是大于 1 的，并且不能用两个小于它的正整数的乘积来表示。</p>\n\n<p>由于答案可能会很大，所以请你返回答案 <strong>模 mod&nbsp;<code>10^9 + 7</code></strong>&nbsp;之后的结果即可。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>n = 5\n<strong>输出：</strong>12\n<strong>解释：</strong>举个例子，[1,2,5,4,3] 是一个有效的排列，但 [5,2,3,4,1] 不是，因为在第二种情况里质数 5 被错误地放在索引为 1 的位置上。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>n = 100\n<strong>输出：</strong>682289015\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 100</code></li>\n</ul>\n",
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            "hints": [
                "Solve the problem for prime numbers and composite numbers separately.",
                "Multiply the number of permutations of prime numbers over prime indices with the number of permutations of composite numbers over composite indices.",
                "The number of permutations equals the factorial."
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