n people gathered to hold a jury meeting of the upcoming competition, the i-th member of the jury came up with a_i tasks, which they want to share with each other.

First, the jury decides on the order which they will follow while describing the tasks. Let that be a permutation p of numbers from 1 to n (an array of size n where each integer from 1 to n occurs exactly once).

Then the discussion goes as follows:

  * If a jury member p_1 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
  * If a jury member p_2 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
  * ... 
  * If a jury member p_n has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
  * If there are still members with tasks left, then the process repeats from the start. Otherwise, the discussion ends. 



A permutation p is nice if none of the jury members tell two or more of their own tasks in a row. 

Count the number of nice permutations. The answer may be really large, so print it modulo 998 244 353.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of the test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — number of jury members.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the number of problems that the i-th member of the jury came up with.

The sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, print one integer — the number of nice permutations, taken modulo 998 244 353.

Example

Input


4
2
1 2
3
5 5 5
4
1 3 3 7
6
3 4 2 1 3 3


Output


1
6
0
540

Note

Explanation of the first test case from the example:

There are two possible permutations, p = [1, 2] and p = [2, 1]. For p = [1, 2], the process is the following:

  1. the first jury member tells a task; 
  2. the second jury member tells a task; 
  3. the first jury member doesn't have any tasks left to tell, so they are skipped; 
  4. the second jury member tells a task. 



So, the second jury member has told two tasks in a row (in succession), so the permutation is not nice.

For p = [2, 1], the process is the following:

  1. the second jury member tells a task; 
  2. the first jury member tells a task; 
  3. the second jury member tells a task. 



So, this permutation is nice.
import java.util.*;

import java.io.*;

public class cf {
    static Reader sc = new Reader();
    static PrintWriter out = new PrintWriter(System.out);
    static long mod = (long) 1e9 + 7;

    public static void main(String[] args) {
        int tc = sc.ni();
        long mod= 998244353;
        long[] fact=new long[200001];
        fact[0]=1;
        for(int i=1;i<=200000;i++){
            fact[i]=((long)fact[i-1]*i)%mod;
        }
        
        while (tc-- > 0) {
            int n=sc.ni();
            int[] arr=sc.nai(n);
            sort(arr);
            if(arr[n-1]-arr[n-2]>1){
                out.println(0);
            }else if(arr[n-1]==arr[n-2]){
                out.println(fact[n]);
            }else{
                int freq=0;
                int idx=n-2;
                while(idx>=0 && arr[idx]==arr[n-2]){
                    freq++;
                    idx--;
                }
                long res=fact[n],curr=0;
                for(int i=0;i<n;i++){
                    long calc=ncr(i,freq,fact,mod);
                    curr=(curr+calc)%mod;
                }
                curr = (curr * fact[freq]) % mod;
                curr = (curr * fact[n - freq-1]) % mod;
                res=(res-curr+mod)%mod;
                out.println(res);
            }
        }
        out.close();

    }

    static long ncr(int i,int j,long[] fact,long mod){
        if(i<j) return 0;
        if(i==j) return 1;
        long res=(fact[i-j]*fact[j])%mod;
        return (fact[i]*modInverse(res,mod))%mod;
    }

    static long modInverse(long a, long m) {
        if (m == 1)
            return -1;
        if (gcd(a, m) != 1)
            return -1;
        long[] g = gcdExtended(a, m);
        long ans = (g[0] + m) % m;
        return ans;
    }

    // result contains {x,y,gcd}
    static long[] gcdExtended(long a, long b) {
        if (b == 0) {
            return new long[] { 1, 0, a };
        }
        long[] sa = gcdExtended(b, a % b);
        // x0=y1,y0=x1-y1*(a/b);
        long x0 = sa[1];
        long y0 = sa[0] - (sa[1] * (a / b));
        return new long[] { x0, y0, sa[2] };
    }
    

    public static long pow(long a, long b, long m) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 0) {
            return pow((a * a) % m, b / 2, m) % m;
        } else {
            return (a * pow((a * a) % m, b / 2, m)) % m;
        }
    }

    // snippets

    static class Pair implements Comparable<Pair> {
        int x;
        int y;

        Pair(int x, int y) {
            this.x = x;
            this.y = y;

        }

        @Override
        public int compareTo(Pair o) {
            if (this.x > o.x)
                return 1;
            else if (this.x < o.x)
                return -1;
            else {
                if (this.y > o.y)
                    return 1;
                else if (this.y < o.y)
                    return -1;
                else
                    return 0;
            }
        }

        public int hashCode() {
            int ans = 1;
            ans = x * 31 + y * 13;
            return ans;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null) {
                return false;
            }
            if (this.getClass() != o.getClass()) {
                return false;
            }
            Pair other = (Pair) o;
            if (this.x == other.x && this.y == other.y) {
                return true;
            }
            return false;
        }

    }

    static void add_map(HashMap<Integer, Integer> map, int v) {
        if (!map.containsKey(v)) {
            map.put(v, 1);
        } else {
            map.put(v, map.get(v) + 1);
        }
    }

    static void remove_map(HashMap<Integer, Integer> map, int v) {
        if (map.containsKey(v)) {
            map.put(v, map.get(v) - 1);
            if (map.get(v) == 0)
                map.remove(v);
        }
    }

    static int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static void sort(int[] arr) {
        // shuffle
        Random rand = new Random();
        for (int i = 0; i < arr.length; i++) {
            int j = rand.nextInt(i + 1);
            int tmp = arr[i];
            arr[i] = arr[j];
            arr[j] = tmp;
        }
        Arrays.sort(arr);
    }

    static void sort(long[] arr) {
        // shuffle
        Random rand = new Random();
        for (int i = 0; i < arr.length; i++) {
            int j = rand.nextInt(i + 1);
            long tmp = arr[i];
            arr[i] = arr[j];
            arr[j] = tmp;
        }
        Arrays.sort(arr);
    }

    static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        double sq = Math.sqrt(n);

        for (int i = 5; i <= sq; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        double sq = Math.sqrt(n);

        for (int i = 5; i <= sq; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static void print_arr(int A[]) {
        for (int i : A) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    static void print_arr(long A[]) {
        for (long i : A) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    static void print_arr(char A[]) {
        for (char i : A) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    static int min(int a, int b) {
        return Math.min(a, b);
    }

    static int min(int a, int b, int c) {
        return Math.min(a, Math.min(b, c));
    }

    static int min(int a, int b, int c, int d) {
        return Math.min(a, Math.min(b, Math.min(c, d)));
    }

    static int max(int a, int b) {
        return Math.max(a, b);
    }

    static int max(int a, int b, int c) {
        return Math.max(a, Math.max(b, c));
    }

    static int max(int a, int b, int c, int d) {
        return Math.max(a, Math.max(b, Math.max(c, d)));
    }

    static long min(long a, long b) {
        return Math.min(a, b);
    }

    static long min(long a, long b, long c) {
        return Math.min(a, Math.min(b, c));
    }

    static long min(long a, long b, long c, long d) {
        return Math.min(a, Math.min(b, Math.min(c, d)));
    }

    static long max(long a, long b) {
        return Math.max(a, b);
    }

    static long max(long a, long b, long c) {
        return Math.max(a, Math.max(b, c));
    }

    static long max(long a, long b, long c, long d) {
        return Math.max(a, Math.max(b, Math.max(c, d)));
    }

    static int max(int A[]) {
        int max = Integer.MIN_VALUE;
        for (int i = 0; i < A.length; i++) {
            max = Math.max(max, A[i]);
        }
        return max;
    }

    static int min(int A[]) {
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < A.length; i++) {
            min = Math.min(min, A[i]);
        }
        return min;
    }

    static long max(long A[]) {
        long max = Long.MIN_VALUE;
        for (int i = 0; i < A.length; i++) {
            max = Math.max(max, A[i]);
        }
        return max;
    }

    static long min(long A[]) {
        long min = Long.MAX_VALUE;
        for (int i = 0; i < A.length; i++) {
            min = Math.min(min, A[i]);
        }
        return min;
    }

    static long sum(int A[]) {
        long sum = 0;
        for (int i : A) {
            sum += i;
        }
        return sum;
    }

    static long sum(long A[]) {
        long sum = 0;
        for (long i : A) {
            sum += i;
        }
        return sum;
    }

    static ArrayList<Integer> sieve(int n) {
        ArrayList<Integer> primes = new ArrayList<>();
        boolean[] isPrime = new boolean[n];
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (isPrime[i]) {
                for (int j = i * i; j < n; j += i) {
                    isPrime[j] = false;
                }
            }
        }
        for (int i = 2; i < n; i++) {
            if (isPrime[i])
                primes.add(i);
        }
        return primes;
    }

    static class Reader {
        BufferedReader br;
        StringTokenizer st;

        Reader() {
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        }

        Reader(File f) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(f));
            st = new StringTokenizer("");
        }

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                }
            return st.nextToken();
        }

        int ni() {
            return Integer.parseInt(next());
        }

        long nl() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] nai(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = ni();
            return a;
        }

        long[] nal(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nl();
            return a;
        }
    }

}