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). 
from sys import stdin
from math import floor
k=int(input())
n=2*k
arr=[int(x) for x in stdin.readline().split()]
arr=sorted(arr)
primes=[]
degrees=[]
degrees1=[]
numbers=[True]*(n+1)
numbers[0]=False
numbers[1]=False
for i in range(2,n+1):
    if numbers[i]==True:
        primes.append(i)
        k=i
        while i*k<=n:
            numbers[i*k]=False
            k=k+1 
for p in primes:
    s=0
    j=1
    while p**j<=n:
        s=s+n//(p**j)
        j=j+1
    degrees.append(s)
k=n//2
for p in primes:
    s=0
    j=1
    while p**j<=k:
        s=s+k//(p**j)
        j=j+1
    degrees1.append(s)
ans=1
for j in range(len(degrees)):
    degrees[j]=degrees[j]-2*degrees1[j]
    for i in range(degrees[j]):
        ans=(ans*primes[j])%998244353
st=sum(arr[:k])%998244353
en=sum(arr[k:])%998244353
su=((en-st)*ans)%998244353
print(su)