{ "data": { "question": { "questionId": "1279", "questionFrontendId": "1175", "boundTopicId": null, "title": "Prime Arrangements", "titleSlug": "prime-arrangements", "content": "

Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)

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(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)

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

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Example 1:

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\nInput: n = 5\nOutput: 12\nExplanation: 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
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Example 2:

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\nInput: n = 100\nOutput: 682289015\n
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Constraints:

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Compiled with clang 11 using the latest C++ 20 standard.

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Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

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Most standard library headers are already included automatically for your convenience.

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OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

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Most standard library headers are already included automatically for your convenience.

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Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

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Python 2.7.12.

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Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

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For Map/TreeMap data structure, you may use sortedcontainers library.

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Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

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Compiled with gcc 8.2 using the gnu11 standard.

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C# 10 with .NET 6 runtime

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Node.js 16.13.2.

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Ruby 3.1

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Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

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Swift 5.5.2.

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Go 1.21

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Python 3.10.

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Scala 2.13.7.

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Kotlin 1.9.0.

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Rust 1.58.1

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PHP 8.1.

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With bcmath module

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TypeScript 5.1.6, Node.js 16.13.2.

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Dart 2.17.3

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