#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 1 "/home/maspy/compro/library/other/mex.hpp"
int mex(const vc<int>& A) {
  int n = len(A);
  vc<bool> aru(n + 1);
  for (auto& x: A)
    if (x < n) aru[x] = 1;
  int mex = 0;
  while (aru[mex]) ++mex;
  return mex;
}
#line 5 "main.cpp"
// #include "nt/nim_product.hpp"
#line 1 "/home/maspy/compro/library/linalg/matrix_rank.hpp"
template <typename T>
int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) {
  if (n == 0) return 0;
  if (n == -1) { n = len(a), m = len(a[0]); }
  assert(n == len(a) && m == len(a[0]));
  int rk = 0;
  FOR(j, m) {
    if (rk == n) break;
    if (a[rk][j] == 0) {
      FOR(i, rk + 1, n) if (a[i][j] != T(0)) {
        swap(a[rk], a[i]);
        break;
      }
    }
    if (a[rk][j] == 0) continue;
    T c = T(1) / a[rk][j];
    FOR(k, j, m) a[rk][k] *= c;
    FOR(i, rk + 1, n) {
      T c = a[i][j];
      FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
    }
    ++rk;
  }
  return rk;
}
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  assert(0 <= n && n < mod);
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  static vvc<mint> C;
  static int H = 0, W = 0;
  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<mint, 1>(n, k);
}

// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
  return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "/home/maspy/compro/library/mod/modint.hpp"

template <int mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(u128 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 120586241) return {20, 74066978};
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1004535809) return {21, 836905998};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
  fastio::rd(x.val);
  x.val %= mod;
  // assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
  fastio::wt(x.val);
}
#endif

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 1 "/home/maspy/compro/library/linalg/transpose.hpp"
template <typename VC>
vc<VC> transpose(const vc<VC>& A, int H = -1, int W = -1) {
  if (H == -1) { H = len(A), W = len(A[0]); }
  vc<VC> B(W, VC(H, A[0][0]));
  FOR(x, H) FOR(y, W) B[y][x] = A[x][y];
  return B;
}
#line 1 "/home/maspy/compro/library/linalg/basis.hpp"

// basis[i]: i 番目に追加成功したもの. 別のラベルがあるなら外で管理する.
// rbasis: 上三角化された基底. [i][i]==1.
// way[i][j]: rbasis[i] = sum way[i][j] basis[j]
template <typename mint>
struct Basis {
  int n, rank;
  vvc<mint> basis;
  vvc<mint> rbasis;
  vvc<mint> way;
  Basis(int max_dim) : n(max_dim), rank(0), basis{} {
    rbasis.assign(max_dim, vc<mint>(max_dim));
    way.assign(max_dim, vc<mint>(max_dim));
  }

  // return : (sum==X にできるか, その方法)
  pair<bool, vc<mint>> solve(vc<mint> X) {
    vc<mint> CF(n);
    FOR(i, n) {
      if (rbasis[i][i] == mint(1)) {
        CF[i] = X[i];
        FOR(j, i, n) X[j] -= CF[i] * rbasis[i][j];
      }
    }
    for (auto& x: X) {
      if (x != mint(0)) { return {false, {}}; }
    }
    vc<mint> ANS(rank);
    FOR(i, n) { FOR(j, rank) ANS[j] += CF[i] * way[i][j]; }
    return {true, ANS};
  }

  // return : (sum==x にできるか, その方法). false の場合には追加する
  pair<bool, vc<mint>> solve_or_add(vc<mint> X) {
    vc<mint> Y = X;
    vc<mint> CF(n);
    FOR(i, n) {
      if (rbasis[i][i] == mint(1)) {
        CF[i] = X[i];
        FOR(j, i, n) X[j] -= CF[i] * rbasis[i][j];
      }
    }
    int p = [&]() -> int {
      FOR(i, n) if (X[i] != mint(0)) return i;
      return -1;
    }();
    if (p == -1) {
      vc<mint> ANS(rank);
      FOR(i, n) { FOR(j, rank) ANS[j] += CF[i] * way[i][j]; }
      return {true, ANS};
    }
    mint c = X[p].inverse();
    FOR(j, p, n) X[j] *= c;
    FOR(i, n) CF[i] *= c;
    basis.eb(Y), rbasis[p] = X;
    way[p][rank] = c;
    FOR(i, n) { FOR(j, rank) way[p][j] -= CF[i] * way[i][j]; }
    ++rank;
    return {false, {}};
  }

  // rank==r の時点まで戻す. Frobenius Form 用.
  void rollback(int r) {
    while (rank > r) {
      --rank;
      POP(basis);
      FOR(i, n) if (way[i][rank] != mint(0)) {
        fill(all(rbasis[i]), mint(0));
        fill(all(way[i]), mint(0));
      }
    }
  }
};
#line 10 "main.cpp"

// https://judge.yosupo.jp/submission/153427
#define ctz32(a) ((a) ? __builtin_ctz((a)) : (32))
typedef uint16_t u16;

static const u32 nf[16]
    = {0x0001u, 0x071cu, 0x6bd1u, 0x1224u, 0x6ba8u, 0x1333u, 0x1553u, 0x0007u, 0x071eu, 0x0925u, 0xc586u, 0x5dbdu, 0xc463u, 0x5efdu, 0x2aa1u, 0x155au};
static const u32 fn[16]
    = {0x0001u, 0x0102u, 0x0183u, 0x8041u, 0x015cu, 0x5f24u, 0xde2cu, 0x957eu, 0x01f4u, 0xf7d8u, 0x76b0u, 0x5d52u, 0xa977u, 0x20d1u, 0xc1a4u, 0x271fu};
static inline u32 to_field(u32 x) {
  u32 y = 0;
  for (; x; x &= x - 1) y ^= nf[ctz32(x)];
  return y;
}
static inline u32 to_nimber(u32 x) {
  u32 y = 0;
  for (; x; x &= x - 1) y ^= fn[ctz32(x)];
  return y;
}
static inline u32 to_double(u32 x) { return x << 1 ^ (x < 32768 ? 0 : 93099U); }
u16 ln[65536];
u16 expo[196605];
u16 *Hexpo = expo + 62133;
u16 *H2expo = expo + 58731;
__attribute__((constructor)) void _construct_nimber_product_() {
  *expo = 1;
  for (int i = 1; i < 65535; ++i) expo[i] = to_double(expo[i - 1]);
  for (int i = 1; i < 65535; ++i) {
    expo[i] = to_nimber(expo[i]);
    ln[expo[i]] = i;
  }
  memcpy(expo + 65535, expo, 131070);
  memcpy(expo + 131070, expo, 131070);
}
u16 product_16(u16 A, u16 B) { return A && B ? expo[ln[A] + ln[B]] : 0; }
u16 H_16(u16 A) { return A ? Hexpo[ln[A]] : 0; }
u16 H2_16(u16 A) { return A ? H2expo[ln[A]] : 0; }
u16 Hproduct_16(u16 A, u16 B) { return A && B ? Hexpo[ln[A] + ln[B]] : 0; }
u32 product_32(u32 A, u32 B) {
  u16 a = A & 65535;
  u16 b = B & 65535;
  u16 c = A >> 16;
  u16 d = B >> 16;
  u16 e = product_16(a, b);
  return (u32)(product_16((u16)(a ^ c), (u16)(b ^ d)) ^ e) << 16 | (Hproduct_16(c, d) ^ e);
}
u32 H_32(u32 A) {
  u16 a = A & 65535;
  u16 b = A >> 16;
  return H_16((u16)(a ^ b)) << 16 | H2_16(b);
}
u64 product(u64 A, u64 B) {
  u32 a = A & UINT_MAX;
  u32 b = B & UINT_MAX;
  u32 c = A >> 32;
  u32 d = B >> 32;
  u32 e = product_32(a, b);
  return (u64)(product_32(a ^ c, b ^ d) ^ e) << 32 | (H_32(product_32(c, d)) ^ e);
}

u64 nim_product(u64 a, u64 b) { return product(a, b); }
/*
結局、表がひとつしかない場合のグランディーが知りたいということに
*/

void test() {
  // int H = 4, W = 4;
  // vc<int> MP(1 << 20);
  // auto dfs = [&](auto& dfs, vvc<int> A) -> int {
  //   int k = 0;
  //   FOR(i, H) FOR(j, W) k |= 1 << (W * i + j);
  //   vc<int> TO;
  //   FOR(i, 1, H) FOR(j, 1, W) {
  //     if (A[i][j] == 0) continue;
  //     FOR(p, i) FOR(q, j) {
  //       vvc<int> B = A;
  //       B[p][q] ^= 1;
  //       B[p][j] ^= 1;
  //       B[i][q] ^= 1;
  //       B[i][j] ^= 1;
  //       TO.eb(dfs(dfs, B));
  //     }
  //   }
  //   return MP[k] = mex(TO);
  // };
  // vv(int, ANS, H, W);
  // FOR(x, H) FOR(y, W) {
  //   vv(int, A, H, W);
  //   A[x][y] = 1;
  //   int ans = dfs(dfs, A);
  //   print(H, W, x, y, ans);
  //   flush();
  //   ANS[x][y] = ans;
  // }
  // FOR(x, H) print(ANS[x]);

  int H = 16, W = 16;
  vv(int, dp, H, W);
  FOR(x, 1, H) FOR(y, 1, W) {
    vc<int> TO;
    FOR(a, x) FOR(b, y) { TO.eb(dp[a][y] ^ dp[x][b] ^ dp[a][b]); }
    dp[x][y] = mex(TO);
  }
  FOR(x, H) print(dp[x]);
}

/*
nim product じゃないか！
入力に合わせると
G(x,y) = prod(x-1,y-1)

結局なにこれ？
sum H[i][j]W[j] == 0
つまり nim product field での連立方程式の解ということに
matrix rank
*/

struct F {
  u64 val;

  constexpr F(u64 x = 0) : val(x) {}
  F &operator+=(const F &p) {
    val ^= p.val;
    return *this;
  }
  F &operator-=(const F &p) {
    val ^= p.val;
    return *this;
  }
  F &operator*=(const F &p) {
    val = nim_product(val, p.val);
    return *this;
  }
  F &operator/=(const F &p) {
    *this *= p.inverse();
    return *this;
  }
  F operator-() const { return *this; }
  F operator+(const F &p) const { return F(*this) += p; }
  F operator-(const F &p) const { return F(*this) -= p; }
  F operator*(const F &p) const { return F(*this) *= p; }
  F operator/(const F &p) const { return F(*this) /= p; }
  bool operator==(const F &p) const { return val == p.val; }
  bool operator!=(const F &p) const { return val != p.val; }
  F inverse() const { return pow(u64(-2)); }
  F pow(u64 n) const {
    assert(n >= 0);
    u64 ret = 1, mul = val;
    while (n > 0) {
      if (n & 1) ret = nim_product(ret, mul);
      mul = nim_product(mul, mul);
      n >>= 1;
    }
    return F(ret);
  }
};

using V = array<F, 18>;
using MAT = array<array<F, 18>, 18>;

void add(MAT &B, V X) {
  FOR(i, 18) {
    if (B[i][i] == F(0)) {
      if (X[i] == F(0)) continue;
      F c = X[i].inverse();
      X[i] = 1;
      FOR(j, i + 1, 18) X[j] *= c;
      B[i] = X;
    }
    F c = X[i];
    X[i] = 0;
    FOR(j, i + 1, 18) X[j] -= B[i][j] * c;
  }
}

int basis_rank(MAT &B) {
  int ans = 0;
  FOR(i, 18) if (B[i][i] == F(1))++ ans;
  return ans;
}

void solve() {
  LL(W, H);
  vv(F, A, H, W, F(0));
  FOR(x, H) FOR(y, W) {
    U64(w);
    A[x][y] = F(w - 1);
  }
  // ll r = matrix_rank<F>(mat);

  // N 変数
  // 自由度

  /*
  連立方程式の解なのだが、どの成分も 0 ではないという条件がつく！！！
  雑な方法：すべての subset で求めて包除する

  適当な列集合だけとりだしたときのランクということに？
  */

  int N = W;
  A = transpose(A);

  vc<V> rows(N);
  FOR(i, N) { FOR(j, H) rows[i][j] = A[i][j]; }

  using mint = modint998;

  mint ans = 0;
  auto dfs = [&](auto &dfs, int s, int k, MAT basis) -> void {
    if (k == N) {
      ll r = basis_rank(basis);
      ll n = popcnt(s) - r;
      mint x = mint(2).pow(64 * n);
      if ((N - popcnt(s)) % 2 == 0) {
        ans += x;
      } else {
        ans -= x;
      }
      return;
    }
    dfs(dfs, s, k + 1, basis);
    add(basis, rows[k]);
    dfs(dfs, s | 1 << k, k + 1, basis);
  };

  MAT basis{};
  dfs(dfs, 0, 0, basis);
  print(ans);
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}