Second Sum

AtCoder

IDabc140_e

Time2000ms

Memory256MB

Difficulty—

Given is a permutation $P$ of ${1, 2, \ldots, N}$. For a pair $(L, R) (1 \le L \lt R \le N)$, let $X_{L, R}$ be the second largest value among $P_L, P_{L+1}, \ldots, P_R$. Find $\displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}$. ## Constraints * $2 \le N \le 10^5$ * $1 \le P_i \le N$ * $P_i \neq P_j $ $(i \neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\ldots$ $P_N$ [samples]

Samples

Input #1

3
2 3 1

Output #1

5

$X_{1, 2} = 2, X_{1, 3} = 2$, and $X_{2, 3} = 1$, so the sum is $2 + 2 + 1 = 5$.

Input #2

5
1 2 3 4 5

Output #2

Input #3

8
8 2 7 3 4 5 6 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Second Sum",
    "description": {
      "content": "Given is a permutation $P$ of ${1, 2, \\ldots, N}$. For a pair $(L, R) (1 \\le L \\lt R \\le N)$, let $X_{L, R}$ be the second largest value among $P_L, P_{L+1}, \\ldots, P_R$. Find $\\displaystyle \\sum_{L=",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc140_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a permutation $P$ of ${1, 2, \\ldots, N}$.\nFor a pair $(L, R) (1 \\le L \\lt R \\le N)$, let $X_{L, R}$ be the second largest value among $P_L, P_{L+1}, \\ldots, P_R$.\nFind $\\displaystyle \\sum_{L=...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments