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

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

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

见题面 Input 部分

见题面 Output 部分

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 $0$.