題意：

給定一個長度為2n的數組，將數組分成兩個長度為n的數組p,q，將p從小到大排序，將q從大到小排序，對于每種分法，f(p,q)=${\sum }_{i=1}^n$|xi?yi|.求總和

題目：

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)=${\sum }_{i=1}^n$|xi?yi|

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≤150000).

The second line contains 2n integers a1,a2,…,a2n (1≤ai≤109) — 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:

p=[1], q=[4], then x=[1], y=[4], f(p,q)=|1?4|=3;
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:

p=[2,1], q=[2,1] (elements with indices 1 and 2 in the original array are selected in the subsequence p);
p=[2,2], q=[1,1];
p=[2,1], q=[1,2] (elements with indices 1 and 4 are selected in the subsequence p);
p=[1,2], q=[2,1];
p=[1,1], q=[2,2];
p=[2,1], q=[2,1] (elements with indices 3 and 4 are selected in the subsequence p).

分析：

1.考慮將a先從小到大排序后，可以分成前后兩塊,其中因為p，q的長度是固定的n。
2.求和是每個對應值差的絕對值。可以看作任意兩個值交換集合，因為得到差值的絕對值相同，這里順序對結果沒有影響。
3.前面對a排序，所以對于每種方案，一定是右塊的數去減左塊的數，其值和為ans；
4.而所有的排列總數是$C_m^n$（m=2*n），所以總的答案ans=ans $\times C_m^n$
5.由于是大數需要求余，$C_m^n$=$\frac{m!}{n!(m?n)!}$,只需拆開來算時求$n！\times$$(m?n)!$的逆元即可，又n==m-n,只需求 $n!$的逆元即可，即根據費馬小定理和快速冪求$n{!}^{mod?2}$.

AC代碼：

#include<bits/stdc++.h> using namespace std; #define mod 998244353 typedef long long ll; const int M=3e5+5; int n,m; ll ans,num,a,b,dp[M]; ll dfs(ll x,int y){ll ans=1;while(y){if(y&1) ans=ans*x%mod;y>>=1;x=x*x%mod;}return ans; } int main(){cin>>n;m=n<<1;for(int i=0;i<m;i++)cin>>dp[i];sort(dp,dp+m);for(int i=0;i<n;i++)ans=(ans+dp[n+i]-dp[i])%mod;a=b=1;for(int i=2;i<=m;i++){b=b*i%mod;if(i==n)a=b;}num=dfs(a,mod-2);ans=ans*b%mod*num%mod*num%mod;cout<<ans<<endl;return 0; }

總結

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