```go
package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const MOD = 998244353
const MAX_VAL = 1000000

var fact []int64

func power(a, b int64) int64 {
	res := int64(1)
	for b > 0 {
		if b&1 == 1 {
			res = (res * a) % MOD
		}
		a = (a * a) % MOD
		b >>= 1
	}
	return res
}

func inverse(n int64) int64 {
	return power(n, MOD-2)
}

func initFact(n int) {
	fact = make([]int64, n+1)
	fact[0] = 1
	for i := 1; i <= n; i++ {
		fact[i] = (fact[i-1] * int64(i)) % MOD
	}
}

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)

	if !scanner.Scan() {
		return
	}
	n, _ := strconv.Atoi(scanner.Text())

	counts := make(map[int]int)
	for i := 0; i < 2*n; i++ {
		scanner.Scan()
		val, _ := strconv.Atoi(scanner.Text())
		counts[val]++
	}

	isPrime := make([]bool, MAX_VAL+1)
	for i := 2; i <= MAX_VAL; i++ {
		isPrime[i] = true
	}
	for i := 2; i*i <= MAX_VAL; i++ {
		if isPrime[i] {
			for j := i * i; j <= MAX_VAL; j += i {
				isPrime[j] = false
			}
		}
	}

	initFact(2 * n)

	denom := int64(1)
	for _, cnt := range counts {
		denom = (denom * fact[cnt]) % MOD
	}

	baseFactor := (fact[n] * inverse(denom)) % MOD

	dp := make([]int64, n+1)
	dp[0] = 1

	for val, cnt := range counts {
		if isPrime[val] {
			c := int64(cnt)
			for j := n; j >= 1; j-- {
				dp[j] = (dp[j] + dp[j-1]*c) % MOD
			}
		}
	}

	fmt.Println((baseFactor * dp[n]) % MOD)
}
```