Treasure Hunt

2000ms

524288K

Description:

Define the beauty value of a sequence $$$b_1,b_2,\ldots,b_c$$$ as the maximum value of $$$\sum\limits_{i=1}^{q}b_i + \sum\limits_{i=s}^{t}b_i$$$, where $$$q$$$, $$$s$$$, $$$t$$$ are all integers and $$$s > q$$$ or $$$t\leq q$$$. Note that $$$b_i = 0$$$ when $$$i<1$$$ or $$$i>c$$$, $$$\sum\limits_{i=s}^{t}b_i = 0$$$ when $$$s>t$$$.

For example, when $$$b = [-1,-2,-3]$$$, we may have $$$q = 0$$$, $$$s = 3$$$, $$$t = 2$$$ so the beauty value is $$$0 + 0 = 0$$$. And when $$$b = [-1,2,-3]$$$, we have $$$q = s = t = 2$$$ so the beauty value is $$$1 + 2 = 3$$$.

You are given a sequence $$$a$$$ of length $$$n$$$, determine the sum of the beauty value of all non-empty subsegments $$$a_l,a_{l+1},\ldots,a_r$$$ ($$$1\leq l\leq r\leq n$$$) of the sequence $$$a$$$.

Print the answer modulo $$$998\,244\,353$$$.

Input:

Each test contains multiple test cases. The first line contains an integer $$$T$$$ ($$$1 \le T \le 10^4$$$) — the number of test cases.

The first line contains an integer $$$n$$$ ($$$1\le n\le 10^6$$$) — the length of $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$-10^6 \leq a_i \leq 10^6$$$) — the given sequence.

It's guaranteed that the sum of $$$n$$$ does not exceed $$$10^6$$$.

Output:

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

Sample Input:

4
7
80 59 100 -52 -86 -62 75
8
-48 -14 -26 43 -41 34 13 55
1
74
20
56 -60 62 13 88 -48 64 36 -10 19 94 25 -69 88 87 79 -70 74 -26 59

Sample Output:

Note:

In the second test case, for the subsequence $$$[-26,43,-41,34,13]$$$, when $$$q=5$$$, $$$s=2$$$, $$$t=5$$$, $$$\sum\limits_{i=1}^{q}b_i + \sum\limits_{i=s}^{t}b_i = 23 + 49 = 72$$$.

In the third test case, there is only one non-empty consecutive subsequence $$$[74]$$$. When $$$q=1$$$, $$$s=1$$$, $$$t=1$$$, $$$\sum\limits_{i=1}^{q}b_i + \sum\limits_{i=s}^{t}b_i = 148$$$.

Informação

Provedor Codeforces

Código CF1787I