Description: In the easy version, the $$$a_i$$$ are in the range $$$[0, n]$$$; in the hard version, the $$$a_i$$$ are in the range $$$[-1, n]$$$ and the definition of good permutation is slightly different. You can make hacks only if all versions of the problem are solved. You are given an integer $$$n$$$ and an array $$$a_1, a_2, \dots, a_n$$$ of integers in the range $$$[-1, n]$$$. A permutation $$$p_1, p_2, \dots, p_n$$$ of $$$[1, 2, \dots, n]$$$ is good if, for each $$$i$$$, the following condition is true: - if $$$a_i \neq -1$$$, the number of values $$$\leq i$$$ in $$$[p_1, p_2, \dots, p_i]$$$ is exactly $$$a_i$$$. Count the good permutations of $$$[1, 2, \dots, n]$$$, modulo $$$998\,244\,353$$$. Input Format: 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 $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the length of the array $$$a$$$. The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-1 \le a_i \le n$$$), which describe the conditions for a good permutation. 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 a single line containing the number of good permutations, modulo $$$998\,244\,353$$$. Note: In the first test case, all the permutations of length $$$5$$$ are good, so there are $$$120$$$ good permutations. In the second test case, the only good permutation is $$$[1, 2, 3, 4, 5]$$$. In the third test case, there are $$$4$$$ good permutations: $$$[2, 1, 5, 6, 3, 4]$$$, $$$[2, 1, 5, 6, 4, 3]$$$, $$$[2, 1, 6, 5, 3, 4]$$$, $$$[2, 1, 6, 5, 4, 3]$$$. For example, $$$[2, 1, 5, 6, 3, 4]$$$ is good because: - $$$a_1 = 0$$$, and there are $$$0$$$ values $$$\leq 1$$$ in $$$[p_1] = [2]$$$; - $$$a_2 = 2$$$, and there are $$$2$$$ values $$$\leq 2$$$ in $$$[p_1, p_2] = [2, 1]$$$; - $$$a_3 = 2$$$, and there are $$$2$$$ values $$$\leq 3$$$ in $$$[p_1, p_2, p_3] = [2, 1, 5]$$$; - $$$a_4 = 2$$$, and there are $$$2$$$ values $$$\leq 4$$$ in $$$[p_1, p_2, p_3, p_4] = [2, 1, 5, 6]$$$; - $$$a_5 = -1$$$, so there are no restrictions on $$$[p_1, p_2, p_3, p_4, p_5]$$$; - $$$a_6 = -1$$$, so there are no restrictions on $$$[p_1, p_2, p_3, p_4, p_5, p_6]$$$.