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

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            "title": "Prime Arrangements",
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            "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",
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                    "code": "class Solution(object):\n    def numPrimeArrangements(self, n):\n        \"\"\"\n        :type n: int\n        :rtype: int\n        \"\"\"\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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