Problem Statement

There is a rooted tree with $N$ vertices called Vertex $1$, $2$, $\ldots$, $N$, rooted at Vertex $1$.

We performed a depth-first search starting at the root and obtained a preorder traversal of the tree: $P_1, P_2, \ldots, P_N$. During the search, when the current vertex had multiple children, we chose the unvisited vertex with the smallest index.

What is a preorder traversal? We start at the root and repeat the following procedure to list the vertices of the tree. If the current vertex $u$ is not recorded yet, record it. Then, if $u$ has an unvisited vertex, go to that vertex. Otherwise, terminate if $u$ is the root, and go to the parent of $u$ if it is not. The list of vertices in the order they are recorded here is the preorder traversal of the tree.

Find the number of rooted trees consistent with the preorder traversal, modulo $998244353$. Two rooted trees (with $N$ vertices and rooted at Vertex $1$) are considered different when there is a non-root vertex whose parent is different in the two trees.

Constraints

• $2 \leq N \leq 500$
• $1 \leq P_i\leq N$
• $P_1=1$
• All $P_i$ are distinct.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print the number of rooted trees consistent with the preorder traversal, modulo $998244353$.