You are given an array a of length 2n. Consider a partition of array a into two subsequences p and q of length n each (each element of array a should be in exactly one subsequence: either in p or in q).

Let's sort p in non-decreasing order, and q in non-increasing order, we can denote the sorted versions by x and y, respectively. Then the cost of a partition is defined as f(p, q) = ∑_{i = 1}^n |x_i - y_i|.

Find the sum of f(p, q) over all correct partitions of array a. Since the answer might be too big, print its remainder modulo 998244353.

Input

The first line contains a single integer n (1 ≤ n ≤ 150 000).

The second line contains 2n integers a_1, a_2, …, a_{2n} (1 ≤ a_i ≤ 10^9) — elements of array a.

Output

Print one integer — the answer to the problem, modulo 998244353.

Examples

Input


1
1 4


Output


6

Input


2
2 1 2 1


Output


12

Input


3
2 2 2 2 2 2


Output


0

Input


5
13 8 35 94 9284 34 54 69 123 846


Output


2588544

Note

Two partitions of an array are considered different if the sets of indices of elements included in the subsequence p are different.

In the first example, there are two correct partitions of the array a:

  1. p = [1], q = [4], then x = [1], y = [4], f(p, q) = |1 - 4| = 3; 
  2. p = [4], q = [1], then x = [4], y = [1], f(p, q) = |4 - 1| = 3. 



In the second example, there are six valid partitions of the array a: 

  1. p = [2, 1], q = [2, 1] (elements with indices 1 and 2 in the original array are selected in the subsequence p); 
  2. p = [2, 2], q = [1, 1]; 
  3. p = [2, 1], q = [1, 2] (elements with indices 1 and 4 are selected in the subsequence p); 
  4. p = [1, 2], q = [2, 1]; 
  5. p = [1, 1], q = [2, 2]; 
  6. p = [2, 1], q = [2, 1] (elements with indices 3 and 4 are selected in the subsequence p). 
import sys, os, io
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n')
import math,datetime,functools,itertools,operator,bisect,fractions,statistics
from collections import deque,defaultdict,OrderedDict,Counter
from fractions import Fraction
from decimal import Decimal
from sys import stdout
from heapq import heappush, heappop, heapify ,_heapify_max,_heappop_max
N = 300005
 
# array to store inverse of 1 to N 
factorialNumInverse = [None] * (N + 1) 
 
# array to precompute inverse of 1! to N! 
naturalNumInverse = [None] * (N + 1) 
 
# array to store factorial of  
# first N numbers 
fact = [None] * (N + 1) 
 
# Function to precompute inverse of numbers 
def InverseofNumber(p): 
    naturalNumInverse[0] = naturalNumInverse[1] = 1
    for i in range(2, N + 1, 1): 
        naturalNumInverse[i] = (naturalNumInverse[p % i] * 
                                (p - int(p / i)) % p) 
# Function to precompute inverse  
# of factorials 
def InverseofFactorial(p): 
    factorialNumInverse[0] = factorialNumInverse[1] = 1
  
    # precompute inverse of natural numbers 
    for i in range(2, N + 1, 1): 
        factorialNumInverse[i] = (naturalNumInverse[i] * 
                                  factorialNumInverse[i - 1]) % p 
  
# Function to calculate factorial of 1 to N 
def factorial(p): 
    fact[0] = 1
  
    # precompute factorials 
    for i in range(1, N + 1): 
        fact[i] = (fact[i - 1] * i) % p 
  
# Function to return nCr % p in O(1) time 
def Binomial(N, R, p): 
      
    # n C r = n!*inverse(r!)*inverse((n-r)!) 
    ans = ((fact[N] * factorialNumInverse[R])% p * 
                      factorialNumInverse[N - R])% p 
    return ans 


def main():
    mod=998244353
    InverseofNumber(mod)
    InverseofFactorial(mod)
    factorial(mod)
    starttime=datetime.datetime.now()
    if(os.path.exists('input.txt')):
        sys.stdin = open("input.txt","r")
        sys.stdout = open("output.txt","w")
    tc=1
    # zz=0
    for _ in range(tc):
        n=ri()
        a=ria()
        a=sorted(a)
        s1=sum(a[:n])
        s2=sum(a[n:])
        ans=(s2-s1)*(Binomial(2*n,n,mod))  
        print(ans%mod)      
        
        
        
            
            
            
            
            
        
        
        
            
        
        
        
            
        
        
        
        
            
            
        
        
        
        
        
        
        
                
                
                    
        
        
            
            
        
                
            
            
        
        
        
        
                
        
            
        
                
        
        
            
        
       
            

                
        
        
        
   
            
        
        
        
        
            
        
                
        
        
        
            
            
        
        
            
        
        

        
        
            
        
        
            
        
                        

        
        
            
     
        
        
            
        
        
                
            
        
        
        
                
            
        

            
             
        
            
        
        
        
                
        
            
        
        
        
        
                
        
        
            
        
        
        
        
                
        
    #<--Solving Area Ends
    endtime=datetime.datetime.now()
    time=(endtime-starttime).total_seconds()*1000
    if(os.path.exists('input.txt')):
        print("Time:",time,"ms")  
    
                
class FastReader(io.IOBase):
    newlines = 0

    def __init__(self, fd, chunk_size=1024 * 8):
        self._fd = fd
        self._chunk_size = chunk_size
        self.buffer = io.BytesIO()

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self, size=-1):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size if size == -1 else size))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()


class FastWriter(io.IOBase):

    def __init__(self, fd):
        self._fd = fd
        self.buffer = io.BytesIO()
        self.write = self.buffer.write

    def flush(self):
        os.write(self._fd, self.buffer.getvalue())
        self.buffer.truncate(0), self.buffer.seek(0)


class FastStdin(io.IOBase):
    def __init__(self, fd=0):
        self.buffer = FastReader(fd)
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


class FastStdout(io.IOBase):
    def __init__(self, fd=1):
        self.buffer = FastWriter(fd)
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.flush = self.buffer.flush


if __name__ == '__main__':
    sys.stdin = FastStdin()
    sys.stdout = FastStdout()
    main()
    