// #define MULTI_TESTCASE
// #define AOJ_TESTCASE

// #define FAST_CIO
// #define INTERACTIVE

#define INF 4'000'000'000'000'000'037LL

// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp

#include <bits/stdc++.h>
namespace {
using namespace std;

using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;

#define vc vector
template <class T>
using vvc = vc<vc<T>>;

using vpll = vc<pll>;

using i128 = __int128_t;
using u128 = __uint128_t;

#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp

#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)

#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp

template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;

template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;

template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp

namespace default_infty_detail
{
  template <class T, class = void>
  struct has_infty : false_type {};

  template <class T>
  struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};

  template <class T>
  const T &custom_value()
  {
    static const T value = T::infty();
    return value;
  }

  template <class T>
  inline constexpr bool unsupported = false;
}

template <class T>
constexpr decltype(auto) default_infty()
{
  if constexpr (default_infty_detail::has_infty<T>::value)
    return default_infty_detail::custom_value<T>();
  else if constexpr (is_same_v<T, i128> || is_same_v<T, u128>)
    return T(INF) * T(INF);
  else if constexpr (is_integral_ext<T> && !is_same_v<T, bool>)
  {
    if constexpr (sizeof(T) >= sizeof(ll))
      return T(INF);
    else if constexpr (numeric_limits<T>::digits >= 31)
      return (T(1) << 30) - 1;
    else
      return T(numeric_limits<T>::max() / 2);
  }
  else if constexpr (numeric_limits<T>::has_infinity)
    return numeric_limits<T>::infinity();
  else
    static_assert(default_infty_detail::unsupported<T>, "No default infinity for this type; specify infty explicitly or define T::infty().");
}

template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }

// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp

#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back

#define LMD(x,fx) ([&](const auto &x) { return fx; })

// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp

template <class T, auto x, enable_if_t<!is_invocable_v<decltype(x)>, int> = 0>
constexpr T resolved_value()
{
  return T(x);
}

template <class T, auto x, enable_if_t<is_invocable_v<decltype(x)>, long> = 0>
const T &resolved_value()
{
  static const T value = T(x());
  return value;
}

template <class T, auto x = nullptr>
constexpr decltype(auto) resolved_infty()
{
  if constexpr (is_same_v<decltype(x), nullptr_t>)
    return default_infty<T>();
  else
    return resolved_value<T, x>();
}

template <class V>
auto MAX(const V &v) { return *max_element(ALL(v)); }

template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;

template <class T>
struct MonoidAdd
{
  using S = T;
  static constexpr S op(S a, S b) { return a + b; }
  static constexpr S e()
  {
    if constexpr (has_e0_v<S>)
      return S::e0();
    else
      return {};
  }
};

namespace internal
{
}

template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
  const int n = v.size();
  vc<typename M::S> res(n + 1);
  res[0] = M::e();
  repi(i, n) res[i + 1] = M::op(res[i], v[i]);
  res.erase(res.begin(), res.begin() + left_index);
  return res;
}

template <class T>
vc<T> cumlsum(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidAdd<T>>(v, left_index); }

constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp

template <class T>
struct is_random_access_iterator
{
  static constexpr bool value = is_same_v<
    typename iterator_traits<T>::iterator_category,
    random_access_iterator_tag
  >;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;

namespace internal
{
};

// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp

template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }

inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }

// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp

#define CPP_DUMP_DEFINE_DATA(...) 
#define dump(...) 
#define oj(...) __VA_ARGS__

namespace fastio {
template <class T>
struct unsigned_integer
{
  using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
  using type = u128;
};
template <>
struct unsigned_integer<u128>
{
  using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;

static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];

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, SIZ - pir + pil, stdin);
  pil = 0;
  if (pir < SIZ) ibuf[pir++] = '\n';
}

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

template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
  using U = unsigned_integer_t<T>;
  bool minus = false;
  U val = 0;
  if constexpr (check_buffer)
    if (pil + 100 > pir) load();
  uint32_t p = pil;
  while (ibuf[p] < '-') ++p;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (ibuf[p] == '-') minus = true, ++p;
  }
  while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
  pil = p;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (minus)
    {
      const U min_abs = U(numeric_limits<T>::max()) + 1;
      x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
    }
    else x = T(val);
  }
  else
    x = T(val);
}

void rd1(ll &x) { rd1_integer(x); }

template <class T, class U>
void rd1(pair<T, U> &p) {
  return rd1(p.first), rd1(p.second);
}

template <class T>
void rd1(vc<T> &x) {
  for (auto &d: x) rd1(d);
}

template <class... T>
void read(T &...x) {
  if constexpr (sizeof...(T) <= SIZ / 100 &&
                ((!is_same_v<T, char> &&
                  (is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
    if (pil + 100 * sizeof...(T) > pir) load();
    (rd1_integer<false>(x), ...);
  }
  else
    (rd1(x), ...);
}

void wt1(const char c) {
  if (por == SIZ) flush();
  obuf[por++] = c;
}

template <typename T>
void wt1_integer(T x) {
  if (por > SIZ - 100) flush();
  using U = unsigned_integer_t<T>;
  U ux;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (x < 0)
      obuf[por++] = '-', ux = U(0) - U(x);
    else
      ux = U(x);
  }
  else
    ux = x;
  int outi;
  for (outi = 96; ux >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[ux % 10000], 4);
    ux /= 10000;
  }
  if (ux >= 1000) {
    memcpy(obuf + por, pre.num[ux], 4);
    por += 4;
  } else if (ux >= 100) {
    memcpy(obuf + por, pre.num[ux] + 1, 3);
    por += 3;
  } else if (ux >= 10) {
    int q = (ux * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (ux - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = ux | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }

template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);

template <class... T>
void write(T &&...x) {
  (wt1(std::forward<T>(x)), ...);
}

template <class... T>
void print(T &&...x) {
  if constexpr (sizeof...(T))
  {
    int i = 0;
    ((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
  }
  wt1('\n');
}

} 

struct Dummy {
  Dummy() { atexit(fastio::flush); }
} dummy;

namespace internal
{

template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }

template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
  (v.resize(n), ...);
  READnodump(v...);
}

}; 

#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)

#define LL(...) IN(ll, __VA_ARGS__)

#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)

#define PRINT fastio::print

template <class T, class U, class P>
pair<T, U> &operator+=(pair<T, U> &a, const P &b)
{
  a.first += b.first;
  a.second += b.second;
  return a;
}

namespace internal
{

}; 

template <class T, class Add>
void offset(vc<T> &v, const Add &add) { for (auto &vi : v) vi += add; }
template <class T, class Add>
void offset(vvc<T> &v, const Add &add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }

namespace internal
{

};

// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp

mt19937_64 mt;

namespace internal
{
}; 

// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp

namespace larger_int_detail
{
}

template <class T>
struct larger_int
{
private:
  static constexpr bool check();
  static_assert(check());

public:
  using type = T;
};

#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };

LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)

LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)

#undef LARGER_INT

template <class T>
struct Rational;

template <class T>
struct larger_int<Rational<T>>
{
  using type = Rational<typename larger_int<T>::type>;
};

template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp

namespace internal
{

template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
  if (m == 1)
    return 0;
  using U = make_unsigned_t<T>;
  using L = larger_int_t<U>;

  U r = 1, y = safemod(x, m);
  while (n)
  {
    if (n & 1)
      r = L(r) * y % m;
    y = L(y) * y % m;
    n >>= 1;
  }
  return r;
}

template <auto n>
constexpr bool isprime = isprime_constexpr(n);

};

namespace internal
{

template <auto M>
struct policy_static
{
  using mod_type = decltype(M);
  using value_type = make_unsigned_t<mod_type>;
  using calc_type = larger_int_t<value_type>;

  static constexpr bool is_prime = isprime_constexpr(M);

  static constexpr value_type init(value_type v) { return v; }
  static constexpr mod_type val(value_type v);
};

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp

namespace internal
{

struct barrett32
{
  uint m;
  ull im;
  explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
};

template <int id>
struct policy_barrett32
{
  using value_type = uint;
  using calc_type = ull;
  using mod_type = int;
  
  static constexpr bool is_prime = false;
  static inline barrett32 reducer{998244353};
  static value_type init(value_type v) { return v; }
  static mod_type val(value_type v);
};

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp

namespace internal
{

inline constexpr ull inv64(ull a)
{
  ull x = a;
  while (a * x != 1) x *= 2 - a * x;
  return x;
}

struct montgomery64odd
{
  ull m, im, sq;
  explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
  ull reduce(u128 x) const
  {
    auto t = (x + u128(m) * (-im * ull(x))) >> 64;
    if (t >= m) t -= m;
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};

struct montgomery64
{
  ull m, mx, imx, d, q;
  uint b;
  explicit montgomery64(ull m) : m(m)
  {
    b = countr_zero(m), mx = m >> b; 
    imx = inv64(mx);
    d = powmod_constexpr((mx + 1) / 2, b, mx); 
    u128 sq = -u128(mx) % mx; 
    q = (1 + (((sq - 1) * d) << b)) % m;
  }
  ull reduce(u128 x) const
  {
    if (b == 0)
    {
      auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
      if (t >= m) t -= m;
      return (ull)t;
    }
    ull p = x & MASK(b); 
    x = (x >> b) + p * d;
    ull y = p << (64 - b);
    auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
    if (t >= m) { t -= m; if (t >= m) t -= m; }
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};

template <int id>
struct policy_montgomery64_odd
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64odd reducer{(1LL << 61) - 1};
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v);
};

template <int id>
struct policy_montgomery64
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64 reducer{(1LL << 61) - 1};
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v);
};

};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp

namespace internal
{

  template <class Policy>
  struct modint_impl
  {
    using V = typename Policy::value_type;
    using M = typename Policy::mod_type;
    using mint = modint_impl;

  private:
    V _v;

  public:

    modint_impl();

    template <class T, typename = enable_if_t<is_integral_ext<T>>>
    modint_impl(T v);

    M val() const;

    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
  
    friend void rd1(mint &x)
    {
      long long a;
      fastio::rd1(a);
      x = a;
    }
    friend void wt1(const mint &x)
    {
      fastio::wt1(x.val());
    }

  };

};

template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;

using modint998244353 = static_modint32<998244353>;

template <class T>
struct is_modint : std::false_type
{
};
template <class Policy>
struct is_modint<internal::modint_impl<Policy>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;

template <class T>
struct is_static_modint : false_type {};
template <int m>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;

template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;

// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp

template <class T>
struct Binomial
{
private:
  inline static decltype(T::mod()) mod;
  
public:
  inline static vc<T> fac_, finv_, inv_;

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp

// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp

namespace cpp_dump
{
  template <class T>
  struct rat_value
  {
    T p, q;

    friend ostream &operator<<(ostream &os, const rat_value &x)
    {
      os << x.p;
      if (x.q != 1)
        os << '/' << x.q;
      return os;
    }
  };

  template <class T>
  inline constexpr bool rat_is_map = false;
  template <class... Args>
  inline constexpr bool rat_is_map<std::map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;

}

using mint = modint998244353;
// using mint = modint1000000007;
// using mint = static_modint<1000000000>;
// using mint = modint;

void init()
{
  oj(mt.seed(random_device()()));
}

// https://github.com/miscalculation53/library/tree/wip/graph/connected_components.hpp

// https://github.com/miscalculation53/library/tree/wip/graph/graph.hpp

// https://github.com/miscalculation53/library/tree/wip/ds/csr.hpp

template <class T, bool is_erasable = false>
struct CSR
{
protected:
  int n, m;
  
  vc<int> start;
  vc<T> elist;
  vc<int> len;
  inline int get_last(int i) const
  {
    if constexpr (is_erasable)
      return start[i] + len[i];
    else
      return start[i + 1];
  }

  template <class Iter>
  struct RowBase
  {
    using iterator = Iter;
    using reference = typename iterator_traits<iterator>::reference;

  private:
    iterator begi, endi;

  public:
    RowBase(const iterator &begi, const iterator &endi) : begi(begi), endi(endi) {}
    inline iterator begin() const { return begi; }
    inline iterator end() const { return endi; }
    template <class I = ll>
    inline I size() const { return endi - begi; }
    inline bool empty() const { return size() == 0; }

    inline reference operator[](int i) const { return *(begi + i); }

    inline reference back() const
    {
      assert(!empty());
      return *prev(endi);
    }

  };
  using Row = RowBase<typename vc<T>::iterator>;
  using ConstRow = RowBase<typename vc<T>::const_iterator>;

public:
  CSR() {}
  
  CSR(const vc<int> &row_sizes)
      : n(row_sizes.size())
  {
    fec(s : row_sizes) assert(s >= 0);
    start = cumlsum(row_sizes);
    m = start.back();
    elist.resize(m);
    if constexpr (is_erasable)
      len = row_sizes;
  }
  
  template <class I>
  CSR(int n, const vc<pair<I, T>> &ies) : n(n), m(ies.size()), start(n, 0), elist(m)
  {
    if constexpr (is_erasable)
      len.resize(n);
    fec([ i, e ] : ies)
    {
      assert(0 <= i && i < n);
      start[i]++;
    }
    start = cumlsum(start);
    if constexpr (is_erasable)
      repi(i, n) len[i] = start[i + 1] - start[i];
    auto cnt = start;
    repi(j, m)
    {
      cauto & [ i, e ] = ies[j];
      int &k = cnt[i];
      elist[k] = e;
      k++;
    }
  }
  
  CSR(const vvc<T> &vv) : n(vv.size()), start(n + 1, 0)
  {
    m = 0;
    fec(row : vv) m += row.size();
    elist.resize(m);
    if constexpr (is_erasable)
      len.resize(n);
    for (int i = 0, j = 0; i < n; i++)
    {
      start[i] = j;
      if constexpr (is_erasable)
        len[i] = vv[i].size();
      fec(e : vv[i])
      {
        elist[j] = e;
        j++;
      }
    }
    start.back() = m;
  }

  Row operator[](int i) { return Row(elist.begin() + start[i], elist.begin() + get_last(i)); }
  ConstRow operator[](int i) const
  { return ConstRow(elist.begin() + start[i], elist.begin() + get_last(i)); }
  ConstRow at(int i) const
  {
    if (!(0 <= i && i < n))
      return ConstRow(elist.begin(), elist.begin());
    return ConstRow(elist.begin() + start[i], elist.begin() + get_last(i));
  }

  int offset(int i) const
  {
    assert(0 <= i && i <= n);
    return start[i];
  }

  template <class I = ll>
  I size() const { return n; }

  const vc<T> &get_elist() const { return elist; }
};

template <class Cost = void>
struct Edge
{
  int from, to;
  Cost cost;
  int index;
  CPP_DUMP_DEFINE_DATA(from, to, cost, index);
  
};

template <>
struct Edge<void>
{
  int from, to, index;
  static constexpr ll cost = 1;
  CPP_DUMP_DEFINE_DATA(from, to, cost, index);
  Edge() : from(-1), to(-1), index(-1) {}
  Edge(int s, int t, int i = -1) : from(s), to(t), index(i) {}
  operator int() const { return to; }
  bool operator<(const Edge &) const { return false; }
};

template <bool is_directed, class Cost = void, bool is_erasable = false>
struct Graph
{
  using E = Edge<Cost>;

protected:
  template <class C, bool unweighted = is_void_v<C>>
  struct InternalEdge
  {
    int to, index;
    C cost;
  };
  template <class C>
  struct InternalEdge<C, true>
  {
    int to, index;
    static constexpr ll cost = 1;
  };
  using GE = conditional_t<is_erasable, E, InternalEdge<Cost>>;
  using Weight = decay_t<decltype(E::cost)>;

  int n = 0, m = 0, era = 0;
  CSR<GE, is_erasable> g;
  vc<int> eid_to_elist_id;

  static E make_edge(int from, int to, const Weight &cost, int index)
  {
    if constexpr (is_void_v<Cost>)
      return E(from, to, index);
    else
      return E(from, to, cost, index);
  }

  struct OutEdgeRow;
  struct OutEdgeIter
  {
    using iterator_category = input_iterator_tag;
    using value_type = E;
    using difference_type = ptrdiff_t;
    using pointer = const E *;
    using reference = const E &;

  private:
    friend struct OutEdgeRow;
    int from = -1;
    typename vc<GE>::const_iterator it;
    mutable E e;
    OutEdgeIter(int from, typename vc<GE>::const_iterator it) : from(from), it(it) {}

  public:
    OutEdgeIter() = default;
    reference operator*() const
    {
      if constexpr (is_erasable)
        return *it;
      else
      {
        e = make_edge(from, it->to, it->cost, it->index);
        return e;
      }
    }
    OutEdgeIter &operator++()
    {
      ++it;
      return *this;
    }
    bool operator==(const OutEdgeIter &rhs) const { return it == rhs.it; }
    bool operator!=(const OutEdgeIter &rhs) const { return !(*this == rhs); }
  };

  struct OutEdgeRow
  {
  private:
    const Graph *g;
    int from, l, r;

    OutEdgeIter iter(int pos) const
    {
      return {from, g->g.get_elist().begin() + pos};
    }

  public:
    OutEdgeRow(const Graph *g, int from)
        : g(g), from(from), l(g->g.offset(from)), r(l + g->g[from].size()) {}
    OutEdgeIter begin() const { return iter(l); }
    OutEdgeIter end() const { return iter(r); }
    template <class I = ll>
    I size() const { return r - l; }
    bool empty() const { return l == r; }
    E back() const
    {
      assert(!empty());
      return (*this)[size() - 1];
    }
  };

  template <class F>
  void build(F input_edge)
  {
    vc<int> row_sizes(n);
    repi(i, m)
    {
      auto [u, v, w] = input_edge(i);
      assert(0 <= u && u < n && 0 <= v && v < n);
      row_sizes[u]++;
      if constexpr (!is_directed)
        if (u != v) row_sizes[v]++;
    }
    g = CSR<GE, is_erasable>(row_sizes);
    if constexpr (is_erasable)
      eid_to_elist_id.assign((is_directed ? 1 : 2) * m, -1);

    vc<int> cnt(n);
    repi(i, m)
    {
      auto [u, v, w] = input_edge(i);
      int j = cnt[u]++;
      int k = g.offset(u) + j;
      if constexpr (is_erasable)
        g[u][j] = make_edge(u, v, w, i);
      else if constexpr (is_void_v<Cost>)
        g[u][j] = GE{int(v), i};
      else
        g[u][j] = GE{int(v), i, w};
      if constexpr (is_erasable)
      {
        int id = is_directed ? i : 2 * i + (u <= v);
        eid_to_elist_id[id] = k;
      }
      if constexpr (!is_directed)
      {
        if (u != v)
        {
          j = cnt[v]++;
          k = g.offset(v) + j;
          if constexpr (is_erasable)
            g[v][j] = make_edge(v, u, w, i);
          else if constexpr (is_void_v<Cost>)
            g[v][j] = GE{int(u), i};
          else
            g[v][j] = GE{int(u), i, w};
          if constexpr (is_erasable)
            eid_to_elist_id[2 * i + (v <= u)] = k;
        }
      }
    }
  }

public:
  Graph() {}
  template <class I>
  Graph(int n, const vc<pair<I, I>> &es) : n(n), m(es.size()), era(0)
  {
    build(LMD(i, (tuple{es[i].first, es[i].second, Weight(1)})));
  }
  template <class I, class C = Cost, enable_if_t<!is_void_v<C>, int> = 0>
  Graph(int n, const vc<pair<I, I>> &es, const Weight &dflt_cost) : n(n), m(es.size()), era(0)
  {
    build(LMD(i, (tuple{es[i].first, es[i].second, dflt_cost})));
  }
  template <class I, class C, enable_if_t<is_same_v<C, Cost> && !is_void_v<C>, int> = 0>
  Graph(int n, const vc<tuple<I, I, C>> &es) : n(n), m(es.size()), era(0)
  {
    build(LMD(i, es[i]));
  }
  Graph(int n, const vc<E> &es) : n(n), m(es.size()), era(0)
  {
    build(LMD(i, (tuple{es[i].from, es[i].to, es[i].cost})));
  }

  template <class I = ll>
  I size() const { return n; }
  
  auto out_edges(int v) const
  {
    return OutEdgeRow(this, v);
  }
  
  template <class I = ll>
  vc<I> indegs() const
  {
    vc<I> res(n);
    if constexpr (is_directed)
    {
      repi(v, n) fec(e : g[v]) res[e.to]++;
    }
    else
      repi(v, n) res[v] = g[v].size();
    return res;
  }
  
  template <class I = ll>
  vc<I> outdegs() const
  {
    vc<I> res(n);
    repi(v, n) res[v] = g[v].size();
    return res;
  }

private:
};

template <bool is_directed, bool is_erasable = false, class I>
Graph(int, const vc<pair<I, I>> &) -> Graph<is_directed, void, is_erasable>;
template <bool is_directed, bool is_erasable = false, class I, class Cost>
Graph(int, const vc<tuple<I, I, Cost>> &) -> Graph<is_directed, Cost, is_erasable>;
template <bool is_directed, bool is_erasable = false, class I, class Cost>
Graph(int, const vc<pair<I, I>> &, const Cost &) -> Graph<is_directed, Cost, is_erasable>;
template <bool is_directed, bool is_erasable = false, class Cost>
Graph(int, const vc<Edge<Cost>> &) -> Graph<is_directed, Cost, is_erasable>;

template <class Cost = void, bool is_erasable = false>
using GraphDirected = Graph<true, Cost, is_erasable>;
template <class Cost = void, bool is_erasable = false>
using GraphUndirected = Graph<false, Cost, is_erasable>;

// https://github.com/miscalculation53/library/tree/wip/ds/my_queue.hpp

template <class T>
struct MyQueue
{
private:
  vc<T> d;
  int pos = 0;

public:
  template <class I = ll>
  I size() const { return SZ<I>(d) - pos; }
  bool empty() const { return pos == SZ<int>(d); }
  void push(const T &t) { d.eb(t); }
  T &front() { return d[pos]; }
  void clear()
  {
    d.clear();
    pos = 0;
  }
  void pop() { pos++; }

};

template <class I = ll, class Cost>
vc<I> connected_component_ids(const GraphUndirected<Cost> &g)
{
  const int n = g.size();
  vc<I> res(n, -1);
  int id = 0;
  MyQueue<int> que;
  repi(sv, n)
  {
    if (res[sv] != -1)
      continue;
    res[sv] = id;
    que.clear();
    que.push(sv);
    while (!que.empty())
    {
      int v = que.front();
      que.pop();
      fe(nv : g.out_edges(v))
      {
        if (res[nv] != -1)
          continue;
        res[nv] = id;
        que.push(nv);
      }
    }
    id++;
  }
  return res;
}
// https://github.com/miscalculation53/library/tree/wip/ds/group_index.hpp

template <class I = ll>
struct GroupIndex
{
private:
  int n, m;
  CSR<I> csr;

public:
  GroupIndex() {}
  template <class T>
  GroupIndex(const vc<T> &a) : n(a.size()), m(a.empty() ? 0 : MAX(a) + 1)
  {
    vc<pair<int, I>> ies(n);
    repi(i, n)
    {
      assert(0 <= a[i]);
      ies[i] = {a[i], i};
    }
    csr = CSR(m, ies);
  }

  auto idxs(int val) const { return csr.at(val); }

  I value_bound() const { return m; }

};

// 0 -> 2
// 0 -> 3
// 1 -> 1
// 3 -> 3
// -2, 0, 1, 1

ll solve(ll N, vpll UV)
{
  GraphUndirected Gund(N, UV);
  GraphDirected Gd(N, UV);

  auto in = Gd.indegs(), out = Gd.outdegs();

  auto ccid = connected_component_ids(Gund);
  GroupIndex ccgrp(ccid);
  ll ccnum = MAX(ccid) + 1;

  ll isol = 0;
  rep(i, N) if (in[i] == 0 && out[i] == 0) isol++;

  dump(ccnum, isol);

  ll ans = 0;
  rep(k, ccgrp.value_bound())
  {
    auto is = ccgrp.idxs(k);
    ll tmp = 0;
    fe(i : is) tmp += max(0LL, in[i] - out[i]);
    dump(is, tmp);
    ans += tmp;
  }
  ans += ccnum - isol;
  return ans;
}

void main2()
{
  LL(N, M);
  VEC(pll, M, UV);
  offset(UV, pll{-1, -1});

  PRINT(solve(N, UV));
}

void test()
{
  //*
  //*/
}

// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp

template <auto init, auto main2, auto test>
struct Main
{
  Main()
  {
    cauto CERR = [](string val, string color)
    {
      string s = "\033[" + color + "m" + val + "\033[m";
      
    };
  
    CERR("\n[FAST_IO]\n\n", "32");
    
    cout << fixed << setprecision(20);
  
    init();
    
    CERR("\n[SINGLE_TESTCASE]\n\n", "36");
    main2();
  }
};
Main<init, main2, test> main_dummy;
}
int main() {}