Many Medians

AtCoder

IDarc095_a

Time2000ms

Memory256MB

Difficulty—

When $l$ is an odd number, the median of $l$ numbers $a_1, a_2, ..., a_l$ is the $(\frac{l+1}{2})$\-th largest value among $a_1, a_2, ..., a_l$. You are given $N$ numbers $X_1, X_2, ..., X_N$, where $N$ is an even number. For each $i = 1, 2, ..., N$, let the median of $X_1, X_2, ..., X_N$ excluding $X_i$, that is, the median of $X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N$ be $B_i$. Find $B_i$ for each $i = 1, 2, ..., N$. ## Constraints * $2 \leq N \leq 200000$ * $N$ is even. * $1 \leq X_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $X_2$ ... $X_N$ [samples]

Samples

Input #1

4
2 4 4 3

Output #1

4
3
3
4

*   Since the median of $X_2, X_3, X_4$ is $4$, $B_1 = 4$.
*   Since the median of $X_1, X_3, X_4$ is $3$, $B_2 = 3$.
*   Since the median of $X_1, X_2, X_4$ is $3$, $B_3 = 3$.
*   Since the median of $X_1, X_2, X_3$ is $4$, $B_4 = 4$.

Input #2

2
1 2

Output #2

2
1

Input #3

6
5 5 4 4 3 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Many Medians",
    "description": {
      "content": "When $l$ is an odd number, the median of $l$ numbers $a_1, a_2, ..., a_l$ is the $(\\frac{l+1}{2})$\\-th largest value among $a_1, a_2, ..., a_l$. You are given $N$ numbers $X_1, X_2, ..., X_N$, where $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc095_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "When $l$ is an odd number, the median of $l$ numbers $a_1, a_2, ..., a_l$ is the $(\\frac{l+1}{2})$\\-th largest value among $a_1, a_2, ..., a_l$.\nYou are given $N$ numbers $X_1, X_2, ..., X_N$, where $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments