#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using VLL = std::vector<LL>;
using VVLL = std::vector<VLL>;
using VVVLL = std::vector<VVLL>;
using LD = long double;
using VLD = std::vector<LD>;
using VVLD = std::vector<VLD>;
using VVVLD = std::vector<VVLD>;
using BL = bool;
using VBL = std::vector<BL>;
using VVBL = std::vector<VBL>;
using VVVBL = std::vector<VVBL>;
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
void bye(T a) {
  cout << a << '\n';
  exit(0);
}
template <class T>
void PRINTSP(vector<T> v, size_t w = 3) {
  for (auto(a) : v) {
    cerr << setw(w) << a << " ";
  }
  cerr << endl;
}
struct mll {
  static LL MOD;
  LL val;
  mll(LL v = 0) : val(v % MOD) {
    if (val < 0) val += MOD;
  }
  mll operator-() const { return -val; }
  mll operator+(const mll &b) const { return val + b.val; }
  mll operator-(const mll &b) const { return val - b.val; }
  mll operator*(const mll &b) const { return val * b.val; }
  mll operator/(const mll &b) const { return mll(*this) /= b; }
  mll operator+(LL b) const { return *this + mll(b); }
  mll operator-(LL b) const { return *this - mll(b); }
  mll operator*(LL b) const { return *this * mll(b); }
  friend mll operator+(LL a, const mll &b) { return b + a; }
  friend mll operator-(LL a, const mll &b) { return -b + a; }
  friend mll operator*(LL a, const mll &b) { return b * a; }
  mll &operator+=(const mll &b) {
    val = (val + b.val) % MOD;
    return *this;
  }
  mll &operator-=(const mll &b) {
    val = (val + MOD - b.val) % MOD;
    return *this;
  }
  mll &operator*=(const mll &b) {
    val = (val * b.val) % MOD;
    return *this;
  }
  mll &operator/=(const mll &b) {
    LL c = b.val, d = MOD, u = 1, v = 0;
    while (d) {
      LL t = c / d;
      c -= t * d;
      swap(c, d);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0) val += MOD;
    return *this;
  }
  mll &operator+=(LL b) { return *this += mll(b); }
  mll &operator-=(LL b) { return *this -= mll(b); }
  mll &operator*=(LL b) { return *this *= mll(b); }
  mll &operator/=(LL b) { return *this /= mll(b); }
  bool operator==(const mll &b) { return val == b.val; }
  bool operator!=(const mll &b) { return val != b.val; }
  bool operator==(LL b) { return *this == mll(b); }
  bool operator!=(LL b) { return *this != mll(b); }
  friend bool operator==(LL a, const mll &b) { return mll(a) == b.val; }
  friend bool operator!=(LL a, const mll &b) { return mll(a) != b.val; }
  friend ostream &operator<<(ostream &os, const mll &a) { return os << a.val; }
  friend istream &operator>>(istream &is, mll &a) { return is >> a.val; }
  static mll Combination(LL a, LL b) {
    chmin(b, a - b);
    if (b < 0) return mll(0);
    mll c = 1;
    for (LL(i) = 0; (i) < (LL)(b); (i)++) c *= a - i;
    for (LL(i) = 0; (i) < (LL)(b); (i)++) c /= i + 1;
    return c;
  }
  static mll Kumiawase(LL a, LL b) {
    chmin(b, a - b);
    if (b < 0) return mll(0);
    return Junretu(a, b) / Kaijou(b);
  }
  static mll Kaijou(LL a) {
    if (a < 0) return mll(0);
    mll c = 1;
    for (LL i = 1; i <= a; i++) {
      c *= i;
    }
    return c;
  }
  static mll Junretu(LL a, LL b) {
    if (a < b) {
      return mll(0);
    }
    mll c = 1;
    for (LL i = a; i > a - b; i--) {
      c *= i;
    }
    return c;
  }
  static mll _Junretu(LL a, LL b) {
    if (a < b) {
      return mll(0);
    }
    return Kaijou(a) / (Kaijou(a - b));
  }
  LL get() { return val; }
};
LL mll::MOD = (LL)(1e9 + 7);
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
LL modpow(LL a, LL n, LL mod) {
  long long res = 1;
  while (n > 0) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}
template <typename TTT>
vector<LL> arg_sort(vector<TTT> A, bool ascend = true) {
  vector<LL> index(A.size());
  iota(index.begin(), index.end(), 0);
  if (ascend) {
    std::sort(index.begin(), index.end(),
              [&A](TTT i1, TTT i2) { return A[i1] < A[i2]; });
  } else {
    std::sort(index.begin(), index.end(),
              [&A](TTT i1, TTT i2) { return A[i1] > A[i2]; });
  }
  return index;
}
template <typename _Iterator, typename _Compare>
LL num_of_ika(_Iterator _first, _Iterator _last, _Compare key) {
  return (LL)(upper_bound(_first, _last, key) - _first);
}
template <typename _Iterator, typename _Compare>
LL num_of_ookii(_Iterator _first, _Iterator _last, _Compare key) {
  return (LL)(_last - upper_bound(_first, _last, key));
}
template <typename _Iterator, typename _Compare>
LL num_of_chisai(_Iterator _first, _Iterator _last, _Compare key) {
  return (LL)(lower_bound(_first, _last, key) - _first);
}
template <typename _Iterator, typename _Compare>
LL num_of_ijou(_Iterator _first, _Iterator _last, _Compare key) {
  return (LL)(_last - lower_bound(_first, _last, key));
}
template <typename _Iterator, typename _Compare>
LL num_of_onaji(_Iterator _first, _Iterator _last, _Compare key) {
  return (LL)(upper_bound(_first, _last, key) -
              lower_bound(_first, _last, key));
}
inline VLL cinvll(LL N, LL minus = 0) {
  VLL A(N);
  for (LL(i) = 0; (i) < (LL)(N); (i)++) {
    cin >> A[i];
    A[i] -= minus;
  }
  return move(A);
}
inline VVLL zerosll(LL H, LL W, LL val = 0) {
  VVLL A(H, VLL(W, val));
  return move(A);
}
inline VVVLL zerosll3(LL H, LL W, LL C, LL val = 0) {
  VVVLL A(H, VVLL(W, VLL(C, val)));
  return move(A);
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec) is >> x;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
ostream &operator<<(ostream &os, const vector<string> &vec) {
  LL N = to_string((LL)vec.size()).length();
  string head;
  for (LL(i) = 0; (i) < (LL)(N + 2); (i)++) {
    head += "-";
  }
  for (LL(i) = 0; (i) < (LL)(40); (i)++) {
    head += to_string(i % 10);
  }
  os << setw(N) << head << endl;
  for (LL i = 0; i < (LL)vec.size(); i++) {
    os << setw(N) << i << ": " << vec[i] << endl;
  }
  return os;
}
ostream &operator<<(ostream &os, const vector<LL> &vec) {
  LL N = to_string((LL)vec.size()).length();
  for (LL i = 0; i < (LL)vec.size(); i++) {
    os << setw(N) << i << ": " << vec[i] << endl;
  }
  return os;
}
ostream &operator<<(ostream &os, const vector<LD> &vec) {
  LL N = to_string((LL)vec.size()).length();
  for (LL i = 0; i < (LL)vec.size(); i++) {
    os << setw(N) << i << ": " << vec[i] << endl;
  }
  return os;
}
ostream &operator<<(ostream &os, const vector<vector<LL>> &mat) {
  LL keta = 1;
  for (LL(i) = 0; (i) < (LL)(mat.size()); (i)++) {
    for (LL(j) = 0; (j) < (LL)(mat[i].size()); (j)++) {
      LL x = mat[i][j];
      chmax(keta, (LL)to_string(x).length());
    }
  }
  LL N = to_string((LL)mat.size()).length();
  for (LL(i) = 0; (i) < (LL)(mat.size()); (i)++) {
    os << setw(N) << i << ": ";
    for (LL(j) = 0; (j) < (LL)(mat[i].size()); (j)++) {
      LL x = mat[i][j];
      os << setw(keta + 1) << x;
    }
    os << endl;
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (LL i = 0; i < (LL)vec.size(); i++) {
    os << setw(5) << vec[i];
  }
  os << endl;
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  os << "{";
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << *itr;
    itr++;
    if (itr != map_var.end()) os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, set<T> &set_var) {
  os << "{";
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    itr++;
    if (itr != set_var.end()) os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
void dump_func() { cerr << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  cerr << ("\033[36m");
  cerr << head;
  if (sizeof...(Tail) > 0) {
    cerr << ", ";
  }
  dump_func(std::move(tail)...);
  cerr << "\033[m";
}
struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
  }
} fast;
struct UnionFindTree {
 private:
  vector<LL> UFT;

 public:
  UnionFindTree(LL N) {
    UFT.resize(N);
    for (LL i = 0; i < N; i++) {
      UFT[i] = -1;
    }
  }
  LL root(LL i) {
    if (UFT[i] < 0) {
      return i;
    } else {
      LL j = root(UFT[i]);
      UFT[i] = j;
      return j;
    }
  }
  bool same(LL i, LL j) { return (root(i) == root(j)); }
  bool unite(LL i, LL j) {
    if (same(i, j)) {
      return false;
    }
    LL root_i = root(i);
    LL root_j = root(j);
    if (root_i != root_j) {
      if (size(root_i) < size(root_j)) {
        swap(root_i, root_j);
      }
      UFT[root_i] += UFT[root_j];
      UFT[root_j] = root_i;
    }
    return true;
  }
  LL size(LL i) { return -UFT[root(i)]; }
  LL get_root_num() {
    set<LL> roots;
    for (LL i = 0; i < (LL)UFT.size(); ++i) {
      roots.insert(root(i));
    }
    return (LL)roots.size();
  }
  map<LL, vector<LL>> get_root_child() {
    map<LL, vector<LL>> a;
    for (LL i = 0; i < (LL)UFT.size(); ++i) {
      LL j = root(i);
      a[j].push_back(i);
    }
    return move(a);
  }
  unordered_map<LL, vector<LL>> get_root_child2() {
    unordered_map<LL, vector<LL>> a;
    for (LL i = 0; i < (LL)UFT.size(); ++i) {
      LL j = root(i);
      a[j].push_back(i);
    }
    return move(a);
  }
  void print() {
    map<LL, vector<LL>> M = get_root_child();
    for (auto m : M) {
      ;
    }
    cerr << endl;
  }
};
bool isPrime(LL N) {
  if (N < 2) {
    return false;
  } else if (N == 2) {
    return true;
  } else if (N % 2 == 0) {
    return false;
  }
  LD sqrtNum = sqrt(N);
  for (LL i = 3; i <= sqrtNum; i += 2) {
    if (N % i == 0) {
      return false;
    }
  }
  return true;
}
map<LL, LL> prime_factor(LL n) {
  map<LL, LL> ret;
  for (LL i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1) ret[n] = 1;
  return ret;
}
LL GCD(LL m, LL n) {
  if (m < n) {
    swap(m, n);
  }
  while (n != 0) {
    LL n_new = m % n;
    m = n;
    n = n_new;
  }
  return m;
}
LL LCM(LL x, LL y) { return x / GCD(x, y) * y; }
struct Furui {
  LL n;
  VLL f;
  VLL prime;
  Furui(LL n = 1) : n(n), f(n + 1) {
    f[0] = -1;
    f[1] = -1;
    for (LL i = 2; i <= n; i++) {
      if (f[i]) {
        continue;
      }
      prime.push_back(i);
      for (LL j = i; j <= n; j += i) {
        if (f[j] == 0) {
          f[j] = i;
        }
      }
    }
  }
  bool isPrime(LL x) {
    if (x <= 1) {
      return false;
    }
    return (f[x] == x);
  }
  VLL factorList(LL x) {
    VLL res;
    if (x >= 2 and x <= n) {
      while (x != 1) {
        res.push_back(f[x]);
        x /= f[x];
      }
    }
    return res;
  }
  vector<pair<LL, LL>> factor(LL x) {
    VLL factors = factorList(x);
    vector<pair<LL, LL>> P;
    if (factors.size() == 0) {
      return P;
    }
    P.emplace_back(factors[0], 0);
    for (auto p : factors) {
      if (P.back().first == p) {
        P.back().second++;
      } else {
        P.emplace_back(p, 1);
      }
    }
    return P;
  }
};
template <typename T>
struct edge {
  int src, to;
  T cost;
  edge(int to, T cost) : src(-1), to(to), cost(cost) {}
  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T>
using Matrix = vector<vector<T>>;
template <typename T>
void warshall_floyd(Matrix<T> &g, T INF) {
  for (int k = 0; k < g.size(); k++) {
    for (int i = 0; i < g.size(); i++) {
      for (int j = 0; j < g.size(); j++) {
        if (g[i][k] == INF || g[k][j] == INF) continue;
        g[i][j] = min(g[i][j], g[i][k] + g[k][j]);
      }
    }
  }
}
template <typename T>
T kruskal(Edges<T> &edges, LL V) {
  sort(begin(edges), end(edges),
       [](const edge<T> &a, const edge<T> &b) { return (a.cost < b.cost); });
  UnionFindTree tree(V);
  T ret = 0;
  for (auto &e : edges) {
    if (tree.unite(e.src, e.to)) ret += e.cost;
  }
  return (ret);
}
bool isOK(LL mid) { return true; }
LL binary_search() {
  LL ng = 0;
  LL ok = 100000;
  while (abs(ok - ng) > 1) {
    LL mid = (ok + ng) / 2;
    if (isOK(mid))
      ok = mid;
    else
      ng = mid;
  }
  return ok;
}
LL powll(LL a, LL b) {
  LL c = 1LL;
  for (LL(i) = 0; (i) < (LL)(b); (i)++) {
    c *= a;
  }
  return c;
}
LL knapsack(vector<LL> v, vector<LL> w, LL W) {
  LL N = (LL)v.size();
  vector<LL> dp(W + 1, 0);
  for (LL i = 0; i < N; ++i) {
    for (LL j = w[i]; j <= W; ++j) {
      dp[j] = max(dp[j], dp[j - w[i]] + v[i]);
    }
  }
  return dp[W];
}
template <typename T>
vector<T> dijkstra(WeightedGraph<T> &g, int s) {
  const auto INF = numeric_limits<T>::max();
  vector<T> dist(g.size(), INF);
  using Pi = pair<T, int>;
  priority_queue<Pi, vector<Pi>, greater<Pi>> que;
  dist[s] = 0;
  que.emplace(dist[s], s);
  while (!que.empty()) {
    T cost;
    int idx;
    tie(cost, idx) = que.top();
    que.pop();
    if (dist[idx] < cost) continue;
    for (auto &e : g[idx]) {
      auto next_cost = cost + e.cost;
      if (dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      que.emplace(dist[e.to], e.to);
    }
  }
  return dist;
}
template <typename T>
struct BinaryIndexedTree {
  vector<T> data;
  BinaryIndexedTree(int sz = 10) { data.assign(++sz, 0); }
  T sum(int k) {
    T ret = 0;
    for (++k; k > 0; k -= k & -k) ret += data[k];
    return (ret);
  }
  void add(int k, T x) {
    for (++k; k < data.size(); k += k & -k) data[k] += x;
  }
  void resize(int sz) { data.assign(++sz, 0); }
};
LL Combination(LL a, LL b) {
  chmin(b, a - b);
  if (b < 0) return 0;
  LL c = 1;
  for (LL(i) = 0; (i) < (LL)(b); (i)++) c *= a - i;
  for (LL(i) = 0; (i) < (LL)(b); (i)++) c /= i + 1;
  return c;
}
struct IntegralImage {
  VVLL I;
  LL H;
  LL W;
  IntegralImage(VVLL M) {
    I = M;
    H = M.size();
    W = M[0].size();
    bool isOK = true;
    for (LL(i) = 0; (i) < (LL)(H); (i)++) {
      if ((LL)I[i].size() != W) {
        isOK = false;
      }
    }
    if (not isOK) {
      cerr << "shape error :";
      for (LL(i) = 0; (i) < (LL)(H); (i)++) {
        cerr << I[i].size() << " ";
      }
      cerr << endl;
      throw 0;
    }
    for (LL(i) = 0; (i) < (LL)(H); (i)++) {
      for (LL(j) = 0; (j) < (LL)(W - 1); (j)++) {
        I[i][j + 1] += I[i][j];
      }
    }
    for (LL(j) = 0; (j) < (LL)(W); (j)++) {
      for (LL(i) = 0; (i) < (LL)(H - 1); (i)++) {
        I[i + 1][j] += I[i][j];
      }
    }
  }
  LL get_sum(LL y, LL h, LL x, LL w) {
    if (y < 0 or x < 0 or h < 0 or w < 0 or y + h >= H or x + w >= W) {
      fprintf(stderr, "H=%lld, W=%lld, y=%lld, h=%lld, x=%lld, w=%lld\n", H, W,
              y, h, x, w);
      throw 1;
    }
    LL a1 = I[y + h][x + w];
    LL a2 = 0;
    if (y > 0) {
      a2 = I[y - 1][x + w];
    }
    LL a3 = 0;
    if (x > 0) {
      a3 = I[y + h][x - 1];
    }
    LL a4 = 0;
    if (y > 0 && x > 0) {
      a4 = I[y - 1][x - 1];
    }
    return (a1 + a4 - a2 - a3);
  }
  LL get_sum2(LL y0, LL y1, LL x0, LL x1) {
    if (y0 > y1) {
      swap(y0, y1);
    }
    if (x0 > x1) {
      swap(x0, x1);
    }
    return get_sum(y0, y1 - y0, x0, x1 - x0);
  }
  void print() {
    for (LL(i) = 0; (i) < (LL)((LL)I.size()); (i)++) {
      PRINTSP(I[i]);
    }
  }
};
bool isKaibun(string S) {
  bool ok = true;
  LL N = (LL)S.length();
  for (LL(i) = 0; (i) < (LL)(N); (i)++) {
    if (S[i] != S[N - i - 1]) {
      ok = false;
      break;
    }
  }
  return ok;
}
tuple<VLL, VLL, VLL> my_dycstra(VVVLL &R, LL start, LL MOD = 0) {
  LL N = R.size();
  LL INFINF = 1e15;
  priority_queue<VLL, VVLL, greater<VLL>> Q;
  VLL Cost(N, INFINF);
  VLL Path(N, -1);
  VLL Num(N, 0);
  Cost[start] = 0;
  Num[start] = 1;
  Q.push({0, start});
  while (!Q.empty()) {
    VLL q = Q.top();
    Q.pop();
    LL cost = q[0];
    LL from = q[1];
    if (Cost[from] < cost) {
      continue;
    }
    for (auto r : R[from]) {
      LL to = r[0];
      LL cost_to = r[1];
      if (chmin(Cost[to], (cost + cost_to))) {
        Q.push({cost + cost_to, to});
        Path[to] = from;
        Num[to] = Num[from];
      } else if (Cost[to] == (cost + cost_to)) {
        Num[to] += Num[from];
        if (MOD != 0) {
          Num[to] %= MOD;
        }
      }
    }
  }
  return move(make_tuple(Cost, Path, Num));
}
VLL haba_yuusen_kyori(VVLL &V, LL n) {
  LL N = V.size();
  VLL D(N, -1);
  queue<pair<LL, LL>> Q;
  Q.push({n, 0});
  while (!Q.empty()) {
    auto q = Q.front();
    Q.pop();
    LL no = q.first;
    LL d = q.second;
    D[no] = d;
    for (auto v : V[no]) {
      if (D[v] != -1) {
        continue;
      }
      D[v] = d + 1;
      Q.push({v, d + 1});
    }
  }
  return move(D);
}
struct SegmentTree {
  VLL D;
  LL N;
  LL DEFAULT;
  string mode;
  void init(LL N, string mode = "min") {
    this->mode = mode;
    if (mode == "min") {
      DEFAULT = LONG_LONG_MAX;
    } else if (mode == "max") {
      DEFAULT = LONG_LONG_MIN;
    } else if (mode == "sum") {
      DEFAULT = 0LL;
    } else {
      this->mode = "min";
      DEFAULT = LONG_LONG_MAX;
    }
    LL K = 1;
    while (K < N) {
      K *= 2;
    }
    this->N = K;
    this->D.resize(2 * this->N, DEFAULT);
    ;
  }
  SegmentTree(LL N, string mode = "min") { init(N, mode); }
  SegmentTree(VLL &A, string mode = "min") {
    LL N = A.size();
    this->init(N, mode);
    ;
    for (LL(i) = 0; (i) < (LL)(N); (i)++) {
      ;
      set(i, A[i]);
    };
    build();
  }
  void set(LL i, LL x) { D[i + N] = x; }
  void build() {
    for (LL i = N - 1; i > 0; i--) {
      if (mode == "min") {
        D[i] = min({D[2 * i], D[2 * i + 1]});
      } else if (mode == "max") {
        D[i] = max({D[2 * i], D[2 * i + 1]});
      } else if (mode == "sum") {
        D[i] = D[2 * i] + D[2 * i + 1];
      }
    }
  }
  void update(LL i, LL x) {
    D[i + N] = x;
    LL j = i + N;
    while (j > 1) {
      LL k = j / 2;
      if (mode == "min") {
        chmin(D[k], D[j]);
      } else if (mode == "max") {
        chmax(D[k], D[j]);
      } else if (mode == "sum") {
        D[k] += D[j];
      }
      j = k;
    }
  }
  void print() {
    ;
    for (LL(i) = 1; (i) < (LL)(2 * N); (i)++) {
      cerr << D[i] << " ";
      if (__builtin_popcountll(i + 1) == 1) {
        cerr << endl;
      }
    }
  }
  LL query(LL a, LL b, LL k = 1, LL l = 0, LL r = -1) {
    if (r == -1) {
      r = N;
    }
    if (b <= l || r <= a) {
      return DEFAULT;
    }
    if (a <= l && r <= b) {
      return D[k];
    }
    LL vl = query(a, b, 2 * k, l, (l + r) / 2);
    LL vr = query(a, b, 2 * k + 1, (l + r) / 2, r);
    if (mode == "min") {
      return min({vl, vr});
    } else if (mode == "max") {
      return max({vl, vr});
    } else if (mode == "sum") {
      return vl + vr;
    }
  }
};
void oira_tua(LL me, LL oya, VVLL &T, VLL &IO) {
  IO.push_back(me);
  ;
  for (LL i = 0; i < (LL)T[me].size(); i++) {
    LL ko = T[me][i];
    if (ko == oya) {
      continue;
    }
    oira_tua(ko, me, T, IO);
    IO.push_back(me);
  }
}
VVLL cinvll2(LL H, LL W, LL bias = 0) {
  VVLL A = zerosll(H, W);
  for (LL(i) = 0; (i) < (LL)(H); (i)++) {
    for (LL(j) = 0; (j) < (LL)(W); (j)++) {
      cin >> A[i][j];
      A[i][j] += bias;
    }
  }
  return move(A);
}
void print(vector<priority_queue<LL>> P) {
  for (LL(i) = 0; (i) < (LL)(P.size()); (i)++) {
    auto p = P[i];
    cerr << i << " : ";
    while (!p.empty()) {
      LL f = p.top();
      p.pop();
      cerr << f << " ";
    }
    cerr << endl;
  }
}
void print(vector<multiset<LL, greater<LL>>> P) {
  for (LL(i) = 0; (i) < (LL)(P.size()); (i)++) {
    auto p = P[i];
    cerr << i << " : ";
    for (auto f : p) {
      cerr << f << " ";
    }
    cerr << endl;
  }
}
void print(vector<map<LL, LL, greater<LL>>> P) {
  for (LL(i) = 0; (i) < (LL)(P.size()); (i)++) {
    auto p = P[i];
    cerr << i << " : ";
    for (auto f : p) {
      cerr << f << " ";
    }
    cerr << endl;
  }
}
tuple<LD, LD, LD> point2line(LD y1, LD x1, LD y2, LD x2) {
  LD A = y1 - y2;
  LD B = x2 - x1;
  LD C = -A * x1 - B * y1;
  return make_tuple(A, B, C);
}
LD dist_point_line(LD y1, LD x1, LD A, LD B, LD C) {
  return abs(A * x1 + B * y1 + C) / sqrtl(A * A + B * B);
}
string rec(LL n, LL k, VLL &C) {
  if (k == 0) {
    if (n == 0) {
      return "A";
    }
    if (n == 1) {
      return "B";
    }
    return "C";
  }
  if (n == 0) {
    return "A";
  }
  n -= 1;
  if (n >= 0 and n < C[k - 1]) {
    return rec(n, k - 1, C);
  }
  n -= C[k - 1];
  if (n == 0) {
    return "B";
  }
  n -= 1;
  if (n >= 0 and n < C[k - 1]) {
    return rec(n, k - 1, C);
  }
  n -= C[k - 1];
  if (n == 0) {
    return "C";
  };
  return "-";
}
VLL permute(VLL src, VLL idx) {
  VLL dst(src.size());
  for (LL(i) = 0; (i) < (LL)(src.size()); (i)++) {
    dst[i] = src[idx[i]];
  }
  return move(dst);
}
bool isOK(LL b, VLL &Futosa, VLL &Price, LL K, LL N, LL Yosan) {
  auto it = lower_bound(Futosa.begin(), Futosa.end(), b);
  LL index = distance(Futosa.begin(), it);
  ;
  ;
  if (N - index < K) {
    ;
    return false;
  }
  VLL Z;
  for (LL(i) = index; (i) < (LL)(N); (i)++) {
    Z.push_back(Price[i]);
  }
  sort(Z.begin(), Z.end());
  LL cnt = 0;
  for (LL(i) = 0; (i) < (LL)(K); (i)++) {
    cnt += Z[i];
  }
  if (cnt <= Yosan) {
    ;
    return true;
  };
  return false;
}
void dfs(LL me, LL oya, VVVLL &T, VLL &C) {
  for (auto t : T[me]) {
    LL ko = t[0];
    LL w = t[1];
    if (ko == oya) {
      continue;
    }
    if (w % 2 == 0) {
      C[ko] = C[me];
      ;
    } else {
      C[ko] = 1 - C[me];
      ;
    }
    dfs(ko, me, T, C);
  }
}
tuple<VLD, VLL, VLL> my_dycstra_v1(vector<vector<pair<LL, LD>>> &R, LL start,
                                   LL MOD = 0) {
  LL N = R.size();
  LL INFINF = 1e15;
  using PQ = pair<LD, LL>;
  priority_queue<PQ, vector<PQ>, greater<PQ>> Q;
  VLD Cost(N, INFINF);
  VLL Path(N, -1);
  VLL Num(N, 0);
  Cost[start] = 0;
  Num[start] = 1;
  Q.push({0, start});
  LL cnt = 0;
  while (!Q.empty()) {
    PQ q = Q.top();
    Q.pop();
    LD cost = q.first;
    LL from = q.second;
    if (Cost[from] < cost) {
      continue;
    }
    for (auto r : R[from]) {
      cnt++;
      LL to = r.first;
      LD cost_to = r.second;
      if (chmin(Cost[to], (cost + cost_to))) {
        Q.push({cost + cost_to, to});
        Path[to] = from;
        Num[to] = Num[from];
      } else if (Cost[to] == (cost + cost_to)) {
        Num[to] += Num[from];
        if (MOD != 0) {
          Num[to] %= MOD;
        }
      }
    }
  };
  return move(make_tuple(Cost, Path, Num));
}
void func() {
  LL N, M;
  cin >> N >> M;
  VVLL A = cinvll2(M, 3);
  VVVLL Z(N);
  for (auto R : A) {
    LL a = R[0];
    LL b = R[1];
    LL w = R[2];
    a--;
    b--;
    Z[a].push_back({b, w});
    Z[b].push_back({a, w});
  }
  map<VLL, LL> U;
  for (LL(i) = 0; (i) < (LL)(N); (i)++) {
    VLL C, P, E;
    tie(C, P, E) = my_dycstra(Z, i);
    for (LL(j) = 0; (j) < (LL)(N); (j)++) {
      LL s = P[j];
      if (s == -1) {
        continue;
      }
      while (P[s] != -1) {
        LL a = s;
        LL b = P[s];
        if (a > b) {
          swap(a, b);
        }
        U[{a, b}] = 1;
        s = P[s];
      }
    };
  };
  bye(M - U.size());
}
int main() {
  func();
  return 0;
}
