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 $$$998\,244\,353$$$.

$$$^{\text{∗}}$$$$$$\operatorname{MEX}$$$ of a collection of integers $$$c_1, c_2, \ldots, c_k$$$ is defined as the smallest non-negative integer $$$x$$$ that does not occur in the collection $$$c$$$. For example, $$$\operatorname{MEX}([0,1,2,2]) = 3$$$ and $$$\operatorname{MEX}([1,2,2]) = 0$$$

$$$^{\text{†}}$$$A sequence $$$x$$$ is a subsequence of a sequence $$$y$$$ if $$$x$$$ can be obtained from $$$y$$$ by deleting several (possibly, zero or all) elements.

Input

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 $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \leq a_i \lt n$$$) — 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

For each test case, output the answer, modulo $$$998\,244\,353$$$.

Note

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 $$$3$$$.

The answer for the first testcase is $$$1+1+2+2+2+3=11$$$.

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

MEXimize the Score

Examples