Given is a sequence of $N$ integers: $A = (A_1, A_2, \dots, A_N)$.

Find the number of (not necessarily contiguous) subsequences $A'=(A'_1,A'_2,\ldots,A'_k)$ of length at least $2$ that satisfy the following condition:

-   $A'_1 \leq A'_k$.

Since the count can be enormous, print it modulo $998244353$.

Here, two subsequences are distinguished when they originate from different sets of indices, even if they are the same as sequences.

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```

Print the number of (not necessarily contiguous) subsequences $A'=(A'_1,A'_2,\ldots,A'_k)$ of length at least $2$ that satisfy the condition in Problem Statement.

-   $2 \leq N \leq 3 \times 10^5$
-   $1 \leq A_i \leq 10^9$
-   All values in input are integers.

3

A=(1,2,1) has four (not necessarily contiguous) subsequences of length at least 2: (1,2), (1,1), (2,1), (1,2,1).

Three of them, (1,2), (1,1), (1,2,1), satisfy the condition in Problem Statement.

4

Note that two subsequences are distinguished when they originate from different sets of indices, even if they are the same as sequences.

In this Sample, there are four subsequences, (1,2), (1,2), (2,2), (1,2,2), that satisfy the condition.

0

There may be no subsequence that satisfies the condition.