#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T>
using vec = std::vector<T>;
template <class T>
using vec2d = std::vector<std::vector<T>>;
template <class T>
vec2d<T> makeVec2d(const int n1, const int n2, const T initValue) {
  return vec2d<T>(n1, vec<T>(n2, initValue));
}
bool __hack = std::ios::sync_with_stdio(false);
auto __hack1 = cin.tie(nullptr);
struct Input {
  Input(istream &in) : in(&in) {}
  template <class T>
  T next() const {
    T x;
    *in >> x;
    return x;
  }
  int ni() const { return next<int>(); }
  istream *in;
};
Input in(cin);
class Output {
 private:
  ostream *out;
  template <typename T>
  void printSingle(const T &value) {
    *out << value;
  }

 public:
  Output(ostream &out) : out(&out) {}
  inline void print() {}
  template <typename T, typename... Ts>
  inline void print(const T &f, const Ts &...args) {
    printSingle(f);
    if (sizeof...(args) != 0) {
      *out << ' ';
      print(args...);
    }
  }
  template <typename... Ts>
  inline void println(const Ts &...args) {
    print(args...);
    *out << '\n';
  }
  template <typename... Ts>
  inline void operator()(const Ts &...args) {
    println(args...);
  }
};
Output out(cout);
namespace template_util {
constexpr int bytecount(uint64_t x) { return x ? 1 + bytecount(x >> 8) : 0; }
template <int N>
struct bytetype {};
template <uint64_t N>
struct minimal_uint : bytetype<bytecount(N)> {};
}  // namespace template_util
template <typename T>
static constexpr T wrap_pos(T a, T m) {
  return a < 0 ? a + m : a;
}
template <typename T>
static constexpr T mod(T a, T m) {
  return wrap_pos(a % m, m);
}
template <typename T>
static constexpr T inverse2(T a, T m) {
  return a <= 1 ? a : mod((1 - inverse2(m % a, a) * m) / a, m);
}
template <typename T>
static constexpr T inverse(T a, T m) {
  return inverse2(mod(a, m), m);
}
template <typename T, typename C, T Modulus>
class MR {
 private:
  struct tag_plus {};
  struct tag_minus {};
  struct tag_good {};
  static_assert(std::numeric_limits<C>::max() / Modulus / Modulus > 0,
                "compute type is too small");
  static_assert(Modulus < std::numeric_limits<T>::max() / 2,
                "storage type is too small");
  static constexpr T reduce(T value, tag_plus) {
    return value >= Modulus ? value - Modulus : value;
  }
  static constexpr T reduce(T value, tag_minus) {
    return value < 0 ? value + Modulus : value;
  }
  static constexpr T reduce(T value, tag_good) { return value; }

 public:
  T value;
  constexpr MR() : value(0) {}
  constexpr MR(C value) : value(reduce(value % Modulus, tag_minus())) {}
  template <typename tag_t>
  constexpr MR(T value, tag_t tag) : value(reduce(value, tag)) {}
  MR &operator=(C value) {
    this->value = reduce(value % Modulus, tag_minus());
    return *this;
  }
  constexpr MR operator*(MR b) const {
    return MR(C(value) * C(b.value) % Modulus, tag_good());
  }
  MR &operator+=(MR b) {
    value = reduce(value + b.value, tag_plus());
    return *this;
  }
  constexpr T get() const { return value; }
  constexpr MR inverse() const {
    return MR(::inverse(C(value), C(Modulus)), tag_good());
  }
  constexpr MR operator/(MR b) const { return *this * b.inverse(); }
};
template <typename T, typename C, T Modulus>
static inline std::ostream &operator<<(std::ostream &o, MR<T, C, Modulus> mr) {
  return o << mr.get();
}
template <class T>
vector<T> getFactorials(int n) {
  vector<T> res(n);
  res[0] = T(1);
  for (int i = 1; i < n; ++i) {
    res[i] = res[i - 1] * i;
  }
  return res;
}
template <class T>
inline T setBit(T mask, int bit) {
  assert(0 <= bit && bit < numeric_limits<T>::digits);
  return mask | ((T)(1) << bit);
}
template <class T>
inline bool getBit(T mask, int bit) {
  assert(0 <= bit && bit < numeric_limits<T>::digits);
  return mask & ((T)(1) << bit);
}
template <class T>
inline int bitCnt(T mask);
template <>
inline int bitCnt(int32_t mask) {
  return __builtin_popcount(mask);
}
struct Component {
  vec<int> vs;
  vec2d<MR<int, int64_t, 998244353>> dp;
  Component() {}
};
void solve(istream &inStream, ostream &outStream) {
  in = Input(inStream);
  out = Output(outStream);
  auto n = in.ni();
  auto m = in.ni();
  vec2d<pair<int, int>> events(n + 2);
  for (int i = 0; i < (n); ++i) {
    auto x = in.ni();
    auto y = in.ni() + 1;
    events[x].push_back({1, i});
    events[y].push_back({0, i});
  }
  vec2d<int> g(n);
  set<pair<int, int>> edges;
  for (int i = 0; i < (m); ++i) {
    auto x = in.ni() - 1;
    auto y = in.ni() - 1;
    edges.insert({x, y});
    edges.insert({y, x});
    g[x].push_back(y);
    g[y].push_back(x);
  }
  vec<int> u(n, 0);
  vec<int> vs;
  vec<Component> components;
  function<void(int)> dfs = [&](int v) {
    u[v] = true;
    vs.push_back(v);
    for (auto to : g[v]) {
      if (!u[to]) {
        dfs(to);
      }
    }
  };
  for (int i = 0; i < (n); ++i) {
    if (u[i]) continue;
    if (g[i].empty()) {
      continue;
    }
    vs.clear();
    dfs(i);
    Component cc;
    cc.vs = vs;
    int cn = (int)vs.size();
    cc.dp = makeVec2d<MR<int, int64_t, 998244353>>(1 << cn, cn + 1, 0);
    for (int mask = 0; mask < (1 << cn); ++mask) {
      bool good = true;
      for (int b1 = 0; b1 < (cn); ++b1) {
        if (getBit(mask, b1)) {
          for (int b2 = 0; b2 < (b1); ++b2) {
            if (getBit(mask, b2)) {
              if (edges.find({cc.vs[b1], cc.vs[b2]}) != edges.end()) {
                good = false;
                break;
              }
            }
          }
          if (!good) break;
        }
      }
      if (good) {
        cc.dp[mask][bitCnt(mask)] = 1;
      }
    };
    ;
    for (int j = 0; j < (cn); ++j) {
      for (int b = 0; b < (cn); ++b) {
        for (int mask = 0; mask < (1 << cn); ++mask) {
          if (!getBit(mask, b)) {
            cc.dp[setBit(mask, b)][j] += cc.dp[mask][j];
          }
        }
      }
    }
    components.push_back(cc);
  }
  auto fs = getFactorials<MR<int, int64_t, 998244353>>(n + 1);
  auto rfs = fs;
  for (int i = 0; i < (rfs.size()); ++i) {
    rfs[i] = MR<int, int64_t, 998244353>(1) / rfs[i];
  }
  auto C = [&](int n, int k) -> MR<int, int64_t, 998244353> {
    return fs[n] * rfs[k] * rfs[n - k];
  };
  unordered_set<int> presentIds;
  presentIds.reserve(1 << 16);
  presentIds.max_load_factor(0.25);
  MR<int, int64_t, 998244353> res = 0;
  for (int i = (1); i < (n + 1); ++i) {
    for (const auto &e : events[i]) {
      if (e.first == 0) {
        presentIds.erase(e.second);
      } else {
        presentIds.insert(e.second);
      }
    }
    vec<MR<int, int64_t, 998244353>> dp(2 * m + 1, 0);
    dp[0] = 1;
    int inC = 0;
    for (const auto &c : components) {
      int mask = 0;
      for (int i = 0; i < c.vs.size(); ++i) {
        if (presentIds.find(c.vs[i]) != presentIds.end()) {
          mask = setBit(mask, i);
        }
      }
      inC += bitCnt(mask);
      for (int j = (int)dp.size() - 1; j >= 0; --j) {
        for (int add = (1); add < (c.vs.size() + 1); ++add) {
          if (j + add < dp.size()) {
            dp[j + add] += dp[j] * c.dp[mask][add];
          }
        }
      }
    }
    for (int j = 0; j < (dp.size()); ++j) {
      if (presentIds.size() - inC >= i - j && i - j >= 0) {
        res += dp[j] * C(presentIds.size() - inC, i - j);
      }
    }
  }
  out(res);
}
int main() {
  solve(cin, cout);
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

Polycarp plays a (yet another!) strategic computer game. In this game, he leads an army of mercenaries.

Polycarp wants to gather his army for a quest. There are n mercenaries for hire, and the army should consist of some subset of them.

The i-th mercenary can be chosen if the resulting number of chosen mercenaries is not less than l_i (otherwise he deems the quest to be doomed) and not greater than r_i (he doesn't want to share the trophies with too many other mercenaries). Furthermore, m pairs of mercenaries hate each other and cannot be chosen for the same quest. 

How many non-empty subsets does Polycarp need to consider? In other words, calculate the number of non-empty subsets of mercenaries such that the size of this subset belongs to [l_i, r_i] for each chosen mercenary, and there are no two mercenaries in the subset that hate each other.

The answer may be large, so calculate it modulo 998244353.

Input

The first line contains two integers n and m (1 ≤ n ≤ 3 ⋅ 10^5, 0 ≤ m ≤ min(20, (n(n-1))/(2))) — the number of mercenaries and the number of pairs of mercenaries that hate each other.

Then n lines follow, the i-th of them contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).

Then m lines follow, the i-th of them contains two integers a_i and b_i (1 ≤ a_i < b_i ≤ n) denoting that the mercenaries a_i and b_i hate each other. There are no two equal pairs in this list.

Output

Print one integer — the number of non-empty subsets meeting the constraints, taken modulo 998244353.

Examples

Input


3 0
1 1
2 3
1 3


Output


3


Input


3 1
1 1
2 3
1 3
2 3


Output


2

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
template <class T>
using vec = std::vector<T>;
template <class T>
using vec2d = std::vector<std::vector<T>>;
template <class T>
vec2d<T> makeVec2d(const int n1, const int n2, const T initValue) {
  return vec2d<T>(n1, vec<T>(n2, initValue));
}
bool __hack = std::ios::sync_with_stdio(false);
auto __hack1 = cin.tie(nullptr);
struct Input {
  Input(istream &in) : in(&in) {}
  template <class T>
  T next() const {
    T x;
    *in >> x;
    return x;
  }
  int ni() const { return next<int>(); }
  istream *in;
};
Input in(cin);
class Output {
 private:
  ostream *out;
  template <typename T>
  void printSingle(const T &value) {
    *out << value;
  }

 public:
  Output(ostream &out) : out(&out) {}
  inline void print() {}
  template <typename T, typename... Ts>
  inline void print(const T &f, const Ts &...args) {
    printSingle(f);
    if (sizeof...(args) != 0) {
      *out << ' ';
      print(args...);
    }
  }
  template <typename... Ts>
  inline void println(const Ts &...args) {
    print(args...);
    *out << '\n';
  }
  template <typename... Ts>
  inline void operator()(const Ts &...args) {
    println(args...);
  }
};
Output out(cout);
namespace template_util {
constexpr int bytecount(uint64_t x) { return x ? 1 + bytecount(x >> 8) : 0; }
template <int N>
struct bytetype {};
template <uint64_t N>
struct minimal_uint : bytetype<bytecount(N)> {};
}  // namespace template_util
template <typename T>
static constexpr T wrap_pos(T a, T m) {
  return a < 0 ? a + m : a;
}
template <typename T>
static constexpr T mod(T a, T m) {
  return wrap_pos(a % m, m);
}
template <typename T>
static constexpr T inverse2(T a, T m) {
  return a <= 1 ? a : mod((1 - inverse2(m % a, a) * m) / a, m);
}
template <typename T>
static constexpr T inverse(T a, T m) {
  return inverse2(mod(a, m), m);
}
template <typename T, typename C, T Modulus>
class MR {
 private:
  struct tag_plus {};
  struct tag_minus {};
  struct tag_good {};
  static_assert(std::numeric_limits<C>::max() / Modulus / Modulus > 0,
                "compute type is too small");
  static_assert(Modulus < std::numeric_limits<T>::max() / 2,
                "storage type is too small");
  static constexpr T reduce(T value, tag_plus) {
    return value >= Modulus ? value - Modulus : value;
  }
  static constexpr T reduce(T value, tag_minus) {
    return value < 0 ? value + Modulus : value;
  }
  static constexpr T reduce(T value, tag_good) { return value; }

 public:
  T value;
  constexpr MR() : value(0) {}
  constexpr MR(C value) : value(reduce(value % Modulus, tag_minus())) {}
  template <typename tag_t>
  constexpr MR(T value, tag_t tag) : value(reduce(value, tag)) {}
  MR &operator=(C value) {
    this->value = reduce(value % Modulus, tag_minus());
    return *this;
  }
  constexpr MR operator*(MR b) const {
    return MR(C(value) * C(b.value) % Modulus, tag_good());
  }
  MR &operator+=(MR b) {
    value = reduce(value + b.value, tag_plus());
    return *this;
  }
  constexpr T get() const { return value; }
  constexpr MR inverse() const {
    return MR(::inverse(C(value), C(Modulus)), tag_good());
  }
  constexpr MR operator/(MR b) const { return *this * b.inverse(); }
};
template <typename T, typename C, T Modulus>
static inline std::ostream &operator<<(std::ostream &o, MR<T, C, Modulus> mr) {
  return o << mr.get();
}
template <class T>
vector<T> getFactorials(int n) {
  vector<T> res(n);
  res[0] = T(1);
  for (int i = 1; i < n; ++i) {
    res[i] = res[i - 1] * i;
  }
  return res;
}
template <class T>
inline T setBit(T mask, int bit) {
  assert(0 <= bit && bit < numeric_limits<T>::digits);
  return mask | ((T)(1) << bit);
}
template <class T>
inline bool getBit(T mask, int bit) {
  assert(0 <= bit && bit < numeric_limits<T>::digits);
  return mask & ((T)(1) << bit);
}
template <class T>
inline int bitCnt(T mask);
template <>
inline int bitCnt(int32_t mask) {
  return __builtin_popcount(mask);
}
struct Component {
  vec<int> vs;
  vec2d<MR<int, int64_t, 998244353>> dp;
  Component() {}
};
void solve(istream &inStream, ostream &outStream) {
  in = Input(inStream);
  out = Output(outStream);
  auto n = in.ni();
  auto m = in.ni();
  vec2d<pair<int, int>> events(n + 2);
  for (int i = 0; i < (n); ++i) {
    auto x = in.ni();
    auto y = in.ni() + 1;
    events[x].push_back({1, i});
    events[y].push_back({0, i});
  }
  vec2d<int> g(n);
  set<pair<int, int>> edges;
  for (int i = 0; i < (m); ++i) {
    auto x = in.ni() - 1;
    auto y = in.ni() - 1;
    edges.insert({x, y});
    edges.insert({y, x});
    g[x].push_back(y);
    g[y].push_back(x);
  }
  vec<int> u(n, 0);
  vec<int> vs;
  vec<Component> components;
  function<void(int)> dfs = [&](int v) {
    u[v] = true;
    vs.push_back(v);
    for (auto to : g[v]) {
      if (!u[to]) {
        dfs(to);
      }
    }
  };
  for (int i = 0; i < (n); ++i) {
    if (u[i]) continue;
    if (g[i].empty()) {
      continue;
    }
    vs.clear();
    dfs(i);
    Component cc;
    cc.vs = vs;
    int cn = (int)vs.size();
    cc.dp = makeVec2d<MR<int, int64_t, 998244353>>(1 << cn, cn + 1, 0);
    for (int mask = 0; mask < (1 << cn); ++mask) {
      bool good = true;
      for (int b1 = 0; b1 < (cn); ++b1) {
        if (getBit(mask, b1)) {
          for (int b2 = 0; b2 < (b1); ++b2) {
            if (getBit(mask, b2)) {
              if (edges.find({cc.vs[b1], cc.vs[b2]}) != edges.end()) {
                good = false;
                break;
              }
            }
          }
          if (!good) break;
        }
      }
      if (good) {
        cc.dp[mask][bitCnt(mask)] = 1;
      }
    };
    ;
    for (int j = 0; j < (cn); ++j) {
      for (int b = 0; b < (cn); ++b) {
        for (int mask = 0; mask < (1 << cn); ++mask) {
          if (!getBit(mask, b)) {
            cc.dp[setBit(mask, b)][j] += cc.dp[mask][j];
          }
        }
      }
    }
    components.push_back(cc);
  }
  auto fs = getFactorials<MR<int, int64_t, 998244353>>(n + 1);
  auto rfs = fs;
  for (int i = 0; i < (rfs.size()); ++i) {
    rfs[i] = MR<int, int64_t, 998244353>(1) / rfs[i];
  }
  auto C = [&](int n, int k) -> MR<int, int64_t, 998244353> {
    return fs[n] * rfs[k] * rfs[n - k];
  };
  unordered_set<int> presentIds;
  presentIds.reserve(1 << 16);
  presentIds.max_load_factor(0.25);
  MR<int, int64_t, 998244353> res = 0;
  for (int i = (1); i < (n + 1); ++i) {
    for (const auto &e : events[i]) {
      if (e.first == 0) {
        presentIds.erase(e.second);
      } else {
        presentIds.insert(e.second);
      }
    }
    vec<MR<int, int64_t, 998244353>> dp(2 * m + 1, 0);
    dp[0] = 1;
    int inC = 0;
    for (const auto &c : components) {
      int mask = 0;
      for (int i = 0; i < c.vs.size(); ++i) {
        if (presentIds.find(c.vs[i]) != presentIds.end()) {
          mask = setBit(mask, i);
        }
      }
      inC += bitCnt(mask);
      for (int j = (int)dp.size() - 1; j >= 0; --j) {
        for (int add = (1); add < (c.vs.size() + 1); ++add) {
          if (j + add < dp.size()) {
            dp[j + add] += dp[j] * c.dp[mask][add];
          }
        }
      }
    }
    for (int j = 0; j < (dp.size()); ++j) {
      if (presentIds.size() - inC >= i - j && i - j >= 0) {
        res += dp[j] * C(presentIds.size() - inC, i - j);
      }
    }
  }
  out(res);
}
int main() {
  solve(cin, cout);
  return 0;
}

```