LEQ

AtCoder

IDabc221_e

Time2000ms

Memory256MB

Difficulty—

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. ## Constraints * $2 \leq N \leq 3 \times 10^5$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3
1 2 1

Output #1

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.

Input #2

3
1 2 2

Output #2

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.

Input #3

3
3 2 1

Output #3

0

There may be no subsequence that satisfies the condition.

Input #4

10
198495780 28463047 859606611 212983738 946249513 789612890 782044670 700201033 367981604 302538501

Output #4

API Response (JSON)

{
  "problem": {
    "name": "LEQ",
    "description": {
      "content": "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 fol",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc221_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence of $N$ integers: $A = (A_1, A_2, \\dots, A_N)$.\nFind the number of (not necessarily contiguous) subsequences $A'=(A'_1,A'_2,\\ldots,A'_k)$ of length at least $2$ that satisfy the fol...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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