You are given a permutation $$$p$$$ of length $$$n$$$.

Please count the number of permutations $$$q$$$ of length $$$n$$$ which satisfy the following:

for each $$$1 \le i \lt n$$$, $$$\max(q_1,\ldots,q_i) \neq \max(p_1,\ldots,p_i)$$$.

Since the answer may be large, output the answer modulo $$$998\,244\,353$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$). It is guaranteed that $$$p$$$ is a permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print a single integer — the answer modulo $$$998\,244\,353$$$.

Note

In the first test case, $$$p = [2, 1]$$$. The only suitable $$$q$$$ is $$$[1, 2]$$$. Indeed, we need to satisfy the inequality $$$q_1 \neq p_1$$$. It only holds for $$$q = [1, 2]$$$.

In the second test case, $$$p = [1, 2, 3]$$$. So $$$q$$$ has to satisfy two inequalities: $$$q_1 \neq p_1$$$ and $$$\max(q_1, q_2) \neq \max(1, 2) = 2$$$. One can prove that this only holds for the following $$$3$$$ permutations:

$$$q = [2, 3, 1]$$$: in this case $$$q_1 = 2 \neq 1$$$ and $$$\max(q_1, q_2) = 3 \neq 2$$$;
$$$q = [3, 1, 2]$$$: in this case $$$q_1 = 3 \neq 1$$$ and $$$\max(q_1, q_2) = 3 \neq 2$$$;
$$$q = [3, 2, 1]$$$: in this case $$$q_1 = 3 \neq 1$$$ and $$$\max(q_1, q_2) = 3 \neq 2$$$.

Yet Yet Another Permutation Problem

Examples