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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Random;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author keyurjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class TaskC {
        static final int MOD = 998244353;
        static final int N = (int) (2e5 + 5);
        static final int[] factorial = new int[N];
        static final int[] ifactorial = new int[N];

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            init();
            int n = in.readInt();
            int[] arr = in.readIntArray(n);
            Sorting.shuffleAndSort(arr);

            if (arr[n - 1] > arr[n - 2] + 1) {
                out.printLine(0);
            } else if (arr[n - 1] == arr[n - 2]) {
                out.printLine(factorial[n]);
            } else {
                int totalPermutations = factorial[n];
                int invalidPermutations = 0;
                int countPenultimate = 0;
                for (int i : arr) {
                    if (i == arr[n - 1] - 1) {
                        countPenultimate++;
                    }
                }
                for (int i = countPenultimate; i < n; i++) {
                    int right = n - i - 1;
                    int left = i;
                    if (left < countPenultimate) continue;
                    int elementsRemaining = n - 1 - countPenultimate;
                    int elementsNeeded = left - countPenultimate;
                    int leftPermutations = multiplySafe(nCr(elementsRemaining, elementsNeeded), factorial[left]);
                    int rightPermuations = factorial[right];
                    invalidPermutations = (int) ((1L * invalidPermutations + multiplySafe(leftPermutations, rightPermuations)) % MOD);
                }
                int validPermutations = (totalPermutations - invalidPermutations) % MOD;
                if (validPermutations < 0) validPermutations += MOD;
                out.printLine(validPermutations);
            }
        }

        private int nCr(int n, int r) {
            int numerator = factorial[n];
            int denominator = multiplySafe(ifactorial[n - r], ifactorial[r]);
            return multiplySafe(numerator, denominator);
        }

        private int modPow(int a, int b) {
            int ans = 1;
            while (b > 0) {
                if ((b & 1) == 1) {
                    ans = multiplySafe(ans, a);
                }
                a = multiplySafe(a, a);
                b >>= 1;
            }
            return ans;
        }

        private void init() {
            if (factorial[0] == 0) {
                factorial[0] = 1;
                ifactorial[0] = 1;
                for (int i = 1; i < N; i++) {
                    factorial[i] = multiplySafe(factorial[i - 1], i);
                    ifactorial[i] = modPow(factorial[i], MOD - 2);
                }
            }
        }

        private int multiplySafe(int a, int b) {
            return (int) ((1L * a * b) % MOD);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static class Sorting {
        public static void shuffleAndSort(int[] arr) {
            shuffleArray(arr);
            Arrays.sort(arr);
        }

        public static void shuffleArray(int[] arr) {
            int n = arr.length;
            Random rnd = new Random();
            for (int i = 0; i < n; ++i) {
                int tmp = arr[i];
                int randomPos = i + rnd.nextInt(n - i);
                arr[i] = arr[randomPos];
                arr[randomPos] = tmp;
            }
        }

    }
}

