Not Median

AtCoder

IDarc173_c

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of integers from $1$ to $N$. For each $i=1,2,\dots,N$, print the minimum value of $r-l+1$ for a pair of integers $(l,r)$ that satisfies all of the following conditions. If no such $(l,r)$ exists, print `-1`. * $1 \leq l \leq i \leq r \leq N$ * $r-l+1$ is odd. * The median of the contiguous subsequence $(P_l,P_{l+1},\dots,P_r)$ of $P$ is **not** $P_i$. Here, the median of $A$ for an integer sequence $A$ of length $L$ (odd) is defined as the $\frac{L+1}{2}$\-th value of the sequence $A'$ obtained by sorting $A$ in ascending order. ## Constraints * $3 \leq N \leq 3 \times 10^5$ * $(P_1,P_2,\dots,P_N)$ is a permutation of integers from $1$ to $N$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\dots$ $P_N$ [samples]

Samples

Input #1

5
1 3 5 4 2

Output #1

3 3 3 5 3

For example, when $i=2$, if we set $(l,r)=(2,4)$, then $r-l+1=3$ is odd, and the median of $(P_2,P_3,P_4)=(3,5,4)$ is $4$, which is not $P_2$, so the conditions are satisfied. Thus, the answer is $3$.
On the other hand, when $i=4$, the median of $(P_l,\dots,P_r)$ for any of $(l,r)=(4,4),(2,4),(3,5)$ is $P_4=4$. If we set $(l,r)=(1,5)$, the median of $(P_1,P_2,P_3,P_4,P_5)=(1,3,5,4,2)$ is $3$, which is not $P_4$, so the conditions are satisfied. Thus, the answer is $5$.

Input #2

3
2 1 3

Output #2

\-1 3 3

When $i=1$, no pair of integers $(l,r)$ satisfies the conditions.

Input #3

14
7 14 6 8 10 2 9 5 4 12 11 3 13 1

Output #3

5 3 3 7 3 3 3 5 3 3 5 3 3 3

API Response (JSON)

{
  "problem": {
    "name": "Not Median",
    "description": {
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of integers from $1$ to $N$. For each $i=1,2,\\dots,N$, print the minimum value of $r-l+1$ for a pair of integers $(l,r)$ that satisfies all of the f",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc173_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of integers from $1$ to $N$.\nFor each $i=1,2,\\dots,N$, print the minimum value of $r-l+1$ for a pair of integers $(l,r)$ that satisfies all of the f...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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