Problem Statement

There are $N$ points numbered $1,2, \dots, N$ on the $2$-dimensional plane. The coordinates of point $i$ are $(i,Y_i)$. In this problem, it is guaranteed that $Y=(Y_1,Y_2,\dots ,Y_N)$ is a permutation of $(1,2, \dots ,N)$.

Find the sum of the areas of bounding boxes for all subsets $S$ of $\lbrace \texttt{point}\,1,\texttt{point}\,2,\dots ,\texttt{point}\,N \rbrace$ with at least $2$ elements, modulo $998244353$.

The bounding box for $S$ refers to the minimum area rectangle with sides parallel to the $x$-axis that contains all points in $S$ inside or on the boundary.

Constraints

• $2 \le N \le 2 \times 10^5$
• $Y$ is a permutation of $(1,2, \dots ,N)$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
Y_1 Y_2 \ldots Y_N

Output

Output the sum, modulo $998244353$, of the areas of bounding boxes.