Given is a sequence of $N$ integers: $A=(A_1,A_2,\ldots,A_N)$. 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: - $A_1' \le A_k'$. 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: > $N$\ > $A_1 \quad A_2 \quad \cdots \quad A_N$ #### Constraints - $2 \le N \le 3 \times 10^5$ - $1 \le A_i \le 10^9$ - All values in input are integers.

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.

***For Sample #1:*** $A=(1,2,1)$ 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. ***For Sample #2:*** 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. ***For Sample #3:*** There may be no subsequence that satisfies the condition. ***For Sample #4:*** Print the answer modulo $998244353$.

AtCoder [ABC221E]