Suppose we partition the elements of an array $$$b$$$ into any number $$$k$$$ of non-empty multisets $$$S_1, S_2, \ldots, S_k$$$, where $$$k$$$ is an arbitrary positive integer. Define the score of $$$b$$$ as the maximum value of $$$\operatorname{MEX}(S_1)$$$$$$^{\text{∗}}$$$$$$ + \operatorname{MEX}(S_2) + \ldots + \operatorname{MEX}(S_k)$$$ over all possible partitions of $$$b$$$ for any integer $$$k$$$.

Envy is given an array $$$a$$$ of size $$$n$$$. Since he knows that calculating the score of $$$a$$$ is too easy for you, he instead asks you to calculate the sum of scores of all $$$2^n - 1$$$ non-empty subsequences of $$$a$$$.$$$^{\text{†}}$$$ Since this answer may be large, please output it modulo $$$998\,244\,353$$$.

Input format:
The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the length of $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \leq a_i < n$$$) — the elements of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output the answer, modulo $$$998\,244\,353$$$.
Example Input 0:
4
3
0 0 1
4
0 0 1 1
5
0 0 1 2 2
4
1 1 1 1

Example Output 0:
11
26
53
0

Notes:
In the first testcase, we must consider seven subsequences:

- $$$[0]$$$: The score is $$$1$$$.
- $$$[0]$$$: The score is $$$1$$$.
- $$$[1]$$$: The score is $$$0$$$.
- $$$[0,0]$$$: The score is $$$2$$$.
- $$$[0,1]$$$: The score is $$$2$$$.
- $$$[0,1]$$$: The score is $$$2$$$.
- $$$[0,0,1]$$$: The score is $$$3$$$.

In the last testcase, all subsequences have a score of $$$0$$$.

Example input:
4
3
0 0 1
4
0 0 1 1
5
0 0 1 2 2
4
1 1 1 1


Example output:
11
26
53
0