Problem:
Score : 300 points

Problem Statement

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

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample 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.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4

Solution in JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)


'use strict'

let L = []
let R = []
const merge = (A, left, mid, right) => {
  let n1 = mid - left
  let n2 = right - mid
  for (let i = 0; i < n1; i++) L[i] = A[left + i]
  for (let i = 0; i < n2; i++) R[i] = A[mid + i]
  L[n1] = R[n2] = Infinity
  let i = 0
  let j = 0
  let k = 0
  for (let k = left; k < right; k++) {
    if (L[i] <= R[j]) {
      A[k] = L[i++]
    } else {
      A[k] = R[j++]
    }
  }
}
const mergeSort = (A, left, right) => {
  if (left + 1 < right) {
    let mid = (left + right) >> 1
    mergeSort(A, left, mid)
    mergeSort(A, mid, right)
    merge(A, left, mid, right)
  }
}

function main(input) {
  input = input.split(/\n|\s/).map(v => ~~v)
  const n = input.shift()
  const arr = input //.slice(1, n + 1)
  let sorted = arr.slice(0)
  mergeSort(sorted, 0, n)

  const mid = sorted[n / 2]
  const mid2 = sorted[n / 2 - 1]

  for (let i = 0; i < n; i++) {
    if (arr[i] < mid) {
      console.log(mid)
    } else {
      console.log(mid2)
    }
  }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'))