Just do it

#include <bits/stdc++.h>
using namespace std;
const int N = 1000;
int perm[N];
int assg[N];
int nc = 1;
long totc = 0;
void f(int lo, int hi) {
    if (hi-lo < 3) {
        for (int i = lo; i < hi; ++i) {
            if (!assg[perm[i]]) assg[perm[i]] = nc++;
        }
        return;
    }
    int mid = (lo+hi)/2;
    if (!assg[perm[lo]]) assg[perm[lo]] = nc++;
    if (!assg[perm[mid]]) assg[perm[mid]] = nc++;
    // if (!assg[perm[hi-1]]) assg[perm[hi-1]] = nc++;
    swap(perm[lo+1], perm[mid]);
    totc += hi-lo-1;
    f(lo+2, hi);
}
// long sim(vector<int> &v, int lo, int hi) {
//     long res = 0;
//     if (hi - lo > 1) {
//         vector<int> pv{v[lo], v[(lo+hi)/2], v[hi-1]};
//         sort(pv.begin(), pv.end());
//         int pivot = pv[1];
//         int a = lo;
//         int b = hi-1;
//         while (true) {
//             while (++res && v[a] < pivot) a += 1;
//             while (++res && v[b] > pivot) b -= 1;
//             if (a >= b) break;
//             swap(v[a], v[b]);
//             a += 1;
//             b -= 1;
//         }
//         res += sim(v, lo, a);
//         res += sim(v, a, hi);
//     }
//     return res;
// }
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        perm[i] = i;
    }
    f(0, n);
    for (int i = 0; i < n; ++i) {
        cout << assg[i] << " ";
    }
    cout << endl;
    // {
    //     cerr << totc << " " << long(n)*n/4 << endl;
    //     vector<int> v;
    //     for (int i = 0; i < n; ++i) {
    //         v.push_back(assg[i]);
    //     }
    //     cout << sim(v, 0, n) << endl;
    // }
}

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