#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  template <typename U>
  friend const Modular<U>& abs(const Modular<U>& v) {
    return v;
  }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = 998244353;
using Mint = Modular<integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int)fact.size() < n + 1) {
    fact.push_back(fact.back() * (int)fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}
struct node {
  int x, y;
  node(int x = 0, int y = 0) : x(x), y(y) {}
  friend inline bool operator<(const node& a, const node& b) {
    if (a.x == b.x) return a.y < b.y;
    if (max(a.x, b.x) <= 20) {
      int v1 = (1 << a.x) + a.y;
      int v2 = (1 << b.x) + b.y;
      if (v1 != v2) return v1 < v2;
      return a.x < b.x;
    }
    return a.x < b.x;
  }
  friend inline bool operator>(const node& a, const node& b) {
    return !(a < b);
  }
  void operator=(const node& a) {
    x = a.x;
    y = a.y;
  }
  inline bool operator!=(const node& a) { return (x != a.x || y != a.y); }
  node operator+(const node& a) const { return node(x + a.x, y + a.y); }
};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<vector<pair<int, node>>> edge(n + 1);
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    edge[u].emplace_back(v, node(0, 1));
    edge[v].emplace_back(u, node(1, 1));
  }
  int nlog = 21;
  vector<vector<node>> d(n + 1, vector<node>(nlog, node((int)1e9)));
  d[1][0] = node(0, 0);
  using T = tuple<node, int, int>;
  priority_queue<T, vector<T>, greater<T>> s;
  s.emplace(make_tuple(d[1][0], 1, 0));
  while ((int)s.size()) {
    auto x = s.top();
    s.pop();
    if (d[get<1>(x)][get<2>(x)] != get<0>(x)) continue;
    int v = get<1>(x);
    int type = get<2>(x);
    node val = get<0>(x);
    for (auto& y : edge[v]) {
      int u = y.first;
      node add = y.second;
      add.x = ((type & 1) != y.second.x);
      int nxt = type + add.x;
      if (nxt >= nlog) nxt -= 2;
      if (val + add < d[u][nxt]) {
        d[u][nxt] = val + add;
        s.emplace(make_tuple(d[u][nxt], u, nxt));
      }
    }
  }
  node res = *min_element(d[n].begin(), d[n].end());
  cout << power(Mint(2), res.x) + res.y - 1;
}

### Prompt

In Cpp, your task is to solve the following problem:

You are given a directed graph of n vertices and m edges. Vertices are numbered from 1 to n. There is a token in vertex 1.

The following actions are allowed: 

  * Token movement. To move the token from vertex u to vertex v if there is an edge u → v in the graph. This action takes 1 second. 
  * Graph transposition. To transpose all the edges in the graph: replace each edge u → v by an edge v → u. This action takes increasingly more time: k-th transposition takes 2^{k-1} seconds, i.e. the first transposition takes 1 second, the second one takes 2 seconds, the third one takes 4 seconds, and so on. 



The goal is to move the token from vertex 1 to vertex n in the shortest possible time. Print this time modulo 998 244 353.

Input

The first line of input contains two integers n, m (1 ≤ n, m ≤ 200 000).

The next m lines contain two integers each: u, v (1 ≤ u, v ≤ n; u ≠ v), which represent the edges of the graph. It is guaranteed that all ordered pairs (u, v) are distinct.

It is guaranteed that it is possible to move the token from vertex 1 to vertex n using the actions above.

Output

Print one integer: the minimum required time modulo 998 244 353.

Examples

Input


4 4
1 2
2 3
3 4
4 1


Output


2


Input


4 3
2 1
2 3
4 3


Output


10

Note

The first example can be solved by transposing the graph and moving the token to vertex 4, taking 2 seconds.

The best way to solve the second example is the following: transpose the graph, move the token to vertex 2, transpose the graph again, move the token to vertex 3, transpose the graph once more and move the token to vertex 4.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  template <typename U>
  friend const Modular<U>& abs(const Modular<U>& v) {
    return v;
  }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = 998244353;
using Mint = Modular<integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int)fact.size() < n + 1) {
    fact.push_back(fact.back() * (int)fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}
struct node {
  int x, y;
  node(int x = 0, int y = 0) : x(x), y(y) {}
  friend inline bool operator<(const node& a, const node& b) {
    if (a.x == b.x) return a.y < b.y;
    if (max(a.x, b.x) <= 20) {
      int v1 = (1 << a.x) + a.y;
      int v2 = (1 << b.x) + b.y;
      if (v1 != v2) return v1 < v2;
      return a.x < b.x;
    }
    return a.x < b.x;
  }
  friend inline bool operator>(const node& a, const node& b) {
    return !(a < b);
  }
  void operator=(const node& a) {
    x = a.x;
    y = a.y;
  }
  inline bool operator!=(const node& a) { return (x != a.x || y != a.y); }
  node operator+(const node& a) const { return node(x + a.x, y + a.y); }
};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<vector<pair<int, node>>> edge(n + 1);
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    edge[u].emplace_back(v, node(0, 1));
    edge[v].emplace_back(u, node(1, 1));
  }
  int nlog = 21;
  vector<vector<node>> d(n + 1, vector<node>(nlog, node((int)1e9)));
  d[1][0] = node(0, 0);
  using T = tuple<node, int, int>;
  priority_queue<T, vector<T>, greater<T>> s;
  s.emplace(make_tuple(d[1][0], 1, 0));
  while ((int)s.size()) {
    auto x = s.top();
    s.pop();
    if (d[get<1>(x)][get<2>(x)] != get<0>(x)) continue;
    int v = get<1>(x);
    int type = get<2>(x);
    node val = get<0>(x);
    for (auto& y : edge[v]) {
      int u = y.first;
      node add = y.second;
      add.x = ((type & 1) != y.second.x);
      int nxt = type + add.x;
      if (nxt >= nlog) nxt -= 2;
      if (val + add < d[u][nxt]) {
        d[u][nxt] = val + add;
        s.emplace(make_tuple(d[u][nxt], u, nxt));
      }
    }
  }
  node res = *min_element(d[n].begin(), d[n].end());
  cout << power(Mint(2), res.x) + res.y - 1;
}

```