Score : $600$ points
Given is a sequence $A$ of $N$ numbers.
There are $2^{N-1}$ ways to divide $A$ into non-empty contiguous subsequences $B_1,B_2,\ldots,B_k$. Find the value below for each of those ways, and print the sum, modulo $998244353$, of those values.
Here, for a sequence $B_i=(B_{i,1},B_{i,2},\ldots,B_{i,j})$, $\max(B_i)$ and $\min(B_i)$ are defined to be the maximum and minimum values of an element of $B_i$, respectively.
Input is given from Standard Input in the following format:
$N$ $A_1$ $A_2$ $\ldots$ $A_N$
Print the sum, modulo $998244353$, of the values found.
3 1 2 3
2
There are $4$ ways to divide $A=(1,2,3)$ into non-empty contiguous subsequences, as follows.
$\prod_{i=1}^{k} (\max(B_i)-\min(B_i))$ for these divisions are $0$, $0$, $0$, $2$, respectively. The sum of them, $2$, should be printed.
4 1 10 1 10
90
10 699498050 759726383 769395239 707559733 72435093 537050110 880264078 699299140 418322627 134917794
877646588
Be sure to print the sum modulo $998244353$.