Just do it

#include <bits/stdc++.h>
using namespace std;
 
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
 
    int n = 0;
    cin >> n;
 
    vector<int> initial(n);
    iota(initial.begin(), initial.end(), 0);
 
    vector<int> ans(n);
    iota(ans.begin(), ans.end(), n + 1);
 
    int l = 0, r = n;
    int cnt = 0;
 
    bool reversed = false;
    while (l + 1 < r) {
        int m = (l + r) / 2;
 
        if (!reversed) {
             if (ans[initial[l]] > n) {
            ans[initial[l]] = ++cnt;
            }
            if (ans[initial[m]] > n) {
                ans[initial[m]] = ++cnt;
            }
            if (ans[initial[r - 1]] > n) {
                ans[initial[r - 1]] = ++cnt;
            }
 
            swap(initial[l + 1], initial[m]);
            l = l + 2;
            reversed = !reversed;
        } else {
            if (ans[initial[r - 1]] > n) {
                ans[initial[r - 1]] = ++cnt;
            }
            if (ans[initial[m]] > n) {
                ans[initial[m]] = ++cnt;
            }
             if (ans[initial[l]] > n) {
            ans[initial[l]] = ++cnt;
            }
            
            swap(initial[l], initial[r - 1]);
            swap(initial[l + 1], initial[m]);
            l = l + 2;
        }
    }
 
    auto ans1 = ans;
    sort(ans1.begin(), ans1.end());
    for (int i = 0; i < n; ++i)
        ans[i] = lower_bound(ans1.begin(), ans1.end(),  ans[i]) - ans1.begin() + 1;
 
    for (auto x : ans)
        cout << x << " ";
    cout << endl;
 
    
    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED