#include <bits/stdc++.h>
using namespace std;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
string direc = "RDLU";
const long long MOD2 = (long long)1000000007 * (long long)1000000007;
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 1000000007) {
  x += y;
  if (x >= mod) x -= mod;
  if (x < 0) x += mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 1000000007) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
char S[20][20];
long long dp[(1 << 18) + 135][20], g[20][(1 << 18) + 135];
int cc, cnt[(1 << 18) + 135];
map<vector<int>, long long> mpa;
vector<int> V;
inline void FWT_or(long long* A, const int fla, int lenth) {
  for (int i = 1; i < lenth; i <<= 1)
    for (int(j) = 0; (j) < (int)(lenth); (j)++)
      if (j & i) A[j] += A[j ^ i];
}
long long t[20][(1 << 18) + 135], f[(1 << 18) + 135];
inline void dfs(int pre, int preSum) {
  if (preSum == n) {
    cc++;
    long long w = 0;
    int dep = (int)V.size();
    for (int i = 0; i < (1 << n); i++)
      if ((n - cnt[i]) & 1)
        w -= t[dep][i];
      else
        w += t[dep][i];
    mpa[V] = w;
    return;
  }
  for (int i = pre; i <= n - preSum; i++) {
    V.push_back(i);
    if (V.size() == 1) {
      for (int(z) = 0; (z) < (int)(1 << n); (z)++) t[1][z] = g[i][z];
    } else {
      int N = V.size();
      for (int(z) = 0; (z) < (int)(1 << n); (z)++)
        t[N][z] = t[N - 1][z] * g[i][z];
    }
    dfs(i, preSum + i);
    V.pop_back();
  }
}
void fmain(int tid) {
  scanf("%d", &n);
  for (int(i) = 0; (i) < (int)(n); (i)++) scanf("%s", S[i]);
  for (int(i) = 0; (i) < (int)(1 << n); (i)++) cnt[i] = __builtin_popcount(i);
  for (int s = 1; s < (1 << n); s++) {
    for (int(j) = 0; (j) < (int)(n); (j)++)
      if (s & (1 << j)) {
        int t = s ^ (1 << j);
        if (t == 0)
          dp[s][j] = 1;
        else {
          for (int(z) = 0; (z) < (int)(n); (z)++)
            if (dp[t][z] && S[z][j] == '1') {
              dp[s][j] += dp[t][z];
            }
        }
      }
  }
  for (int s = 1; s < (1 << n); s++) {
    for (int(j) = 0; (j) < (int)(n); (j)++) g[cnt[s]][s] += dp[s][j];
  }
  for (int(i) = 1; (i) <= (int)(n); (i)++) FWT_or(g[i], 1, 1 << n);
  dfs(1, 0);
  for (int(i) = 0; (i) < (int)(1 << (n - 1)); (i)++) {
    vector<int> vv;
    int pre = 1;
    for (int(j) = 0; (j) < (int)(n - 1); (j)++) {
      if ((i >> j) & 1) {
        pre++;
      } else {
        vv.push_back(pre);
        pre = 1;
      }
    }
    vv.push_back(pre);
    sort(vv.begin(), vv.end());
    assert(mpa.find(vv) != mpa.end());
    f[i] = mpa[vv];
  }
  for (int j = 0; j < n; j++) {
    for (int i = 1; i < (1 << n); i++) {
      if (i & (1 << j)) {
        f[i - (1 << j)] -= f[i];
      }
    }
  }
  for (int(i) = 0; (i) < (int)(1 << (n - 1)); (i)++) printf("%lld ", f[i]);
}
int main() {
  int t = 1;
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  return 0;
}
