#include #include #include #include #include template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct CoordComp { std::vector v; bool sorted; CoordComp() : sorted(false) {} int size() { return v.size(); } void add(T x) { v.push_back(x); } void build() { std::sort(v.begin(), v.end()); v.erase(std::unique(v.begin(), v.end()), v.end()); sorted = true; } int get_idx(T x) { assert(sorted); return lower_bound(v.begin(), v.end(), x) - v.begin(); } T &operator[](int i) { return v[i]; } }; #define For(i, a, b) for (int i = (int)(a); (i) < (int)(b); ++(i)) #define rFor(i, a, b) for (int i = (int)(a)-1; (i) >= (int)(b); --(i)) #define rep(i, n) For(i, 0, n) #define rrep(i, n) rFor(i, n, 0) #define fi first #define se second using namespace std; using lint = long long; using pii = pair; using pll = pair; using namespace atcoder; using mint = modint1000000007; vector fact; vector revfact; void setfact(int n) { fact.resize(n + 1); revfact.resize(n + 1); fact[0] = 1; rep(i, n) fact[i + 1] = fact[i] * mint(i + 1); revfact[n] = fact[n].inv(); for (int i = n - 1; i >= 0; i--) revfact[i] = revfact[i + 1] * mint(i + 1); } mint getC(int n, int r) { if (n < r || r < 0) return 0; return fact[n] * revfact[r] * revfact[n - r]; } mint getP(int n, int r) { if (n < r || r < 0) return 0; return fact[n] * revfact[n - r]; } int main() { int n; scanf("%d", &n); string s[n]; rep(i, n) cin >> s[i]; sort(s, s + n); setfact(n); int lcp[n][n]; rep(i, n) For(j, i + 1, n) { int tmp = 0; for (int k = 0; k < (int)s[i].size() && k < (int)s[j].size(); ++k) { if (s[i][k] != s[j][k]) break; ++tmp; } lcp[i][j] = lcp[j][i] = tmp; } mint dp[1 << n]; rep(S, 1 << n) { int tmp[n]; memset(tmp, 0, sizeof(tmp)); int last = -1; rep(i, n) if (!(S >> i & 1)) { if (last >= 0) chmax(tmp[i], lcp[last][i]); last = i; } last = n; rrep(i, n) if (!(S >> i & 1)) { if (last < n) chmax(tmp[i], lcp[last][i]); last = i; } int num = __builtin_popcount(S); rep(i, n) if (!(S >> i & 1)) dp[S | (1 << i)] += dp[S] + fact[num] * (tmp[i] + 1); } mint ans[n + 1]; rep(S, 1 << n) ans[__builtin_popcount(S)] += dp[S]; For(i, 1, n + 1) printf("%u\n", ans[i].val()); }