D. Attraction Theorytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputTaylor Swift - Love Story (Taylor's Version)⠀There are $$$n$$$ people in positions $$$p_1, p_2, \ldots, p_n$$$ on a one-dimensional coordinate axis. Initially, $$$p_i = i$$$ for each $$$1 \leq i \leq n$$$.You can introduce an attraction at some integer coordinate $$$x$$$ ($$$1 \le x \le n$$$), and then all the people will move closer to the attraction to look at it.Formally, if you put an attraction in position $$$x$$$ ($$$1 \le x \le n$$$), the following changes happen for each person $$$i$$$ ($$$1 \le i \le n$$$): if $$$p_i = x$$$, no change; if $$$p_i < x$$$, the person moves in the positive direction, and $$$p_i$$$ is incremented by $$$1$$$; if $$$p_i > x$$$, the person moves in the negative direction, and $$$p_i$$$ is decremented by $$$1$$$. You can put attractions any finite number of times, and in any order you want.It can be proven that all positions of a person always stays within the range $$$[1, n]$$$, i.e. $$$1 \le p_i \le n$$$ at all times.Each position $$$x$$$ ($$$1 \le x \le n$$$), has a value $$$a_x$$$ associated with it. The score of a position array $$$[p_1, p_2, \ldots, p_n]$$$, denoted by $$$score(p)$$$, is $$$\sum_{i = 1}^{n} a_{p_i}$$$, i.e. your score increases by $$$a_x$$$ for every person standing at $$$x$$$ in the end.Over all possible distinct position arrays $$$p$$$ that are possible with placing attractions, find the sum of $$$score(p)$$$. Since the answer may be large, print it modulo $$$998\,244\,353$$$.InputEach 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 $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).The second line of each test case contains $$$n$$$ integers — $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$)It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.OutputFor each test case, output a single line containing an integer: the sum of $$$score(p)$$$ over all possible distinct position arrays $$$p$$$ that are possible with placing attractions, modulo $$$998\,244\,353$$$.ExampleInput71125 1031 1 141 1 1 1410 2 9 751000000000 1000000000 1000000000 1000000000 10000000008100 2 34 59 34 27 5 6Output145247248033357293069365NoteIn the first test case, the only possible result is that person $$$1$$$ stays at $$$1$$$. The score of that is $$$a_1 = 1$$$.In the second test case, the following position arrays $$$[p_1, p_2]$$$ are possible: $$$[1, 2]$$$, score $$$15$$$; $$$[1, 1]$$$, score $$$10$$$; $$$[2, 2]$$$, score $$$20$$$. The sum of scores is $$$15 + 10 + 20 = 45$$$.In the third test case, the following position arrays $$$[p_1, p_2, p_3]$$$ are possible: $$$[1, 1, 1]$$$; $$$[1, 1, 2]$$$; $$$[1, 2, 2]$$$; $$$[1, 2, 3]$$$; $$$[2, 2, 2]$$$; $$$[2, 2, 3]$$$; $$$[2, 3, 3]$$$; $$$[3, 3, 3]$$$. Each has a score of $$$3$$$, and thus the total sum is $$$24$$$.