Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)
(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.)
Since the answer may be large, return the answer modulo 10^9 + 7.
Example 1:
Input: n = 5
Output: 12
Explanation: 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.
Example 2:
Input: n = 100
Output: 682289015
Constraints:
-
1 <= n <= 100
SOLUTION:
import math
class Solution:
def isPrime(self, n):
if n <= 1:
return False
if n == 2:
return True
if n % 2 == 0:
return False
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
return False
return True
def factorial(self, n):
if n <= 1:
return 1
return n * self.factorial(n - 1)
def numPrimeArrangements(self, n: int) -> int:
numPrimes = 0
for i in range(1, n + 1):
if self.isPrime(i):
numPrimes += 1
return (self.factorial(numPrimes) * self.factorial(n - numPrimes)) % (10 ** 9 + 7)
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