Problem: Masha is fond of cacti. When she was a little girl, she decided to plant a tree. Now Masha wants to make a nice cactus out of her tree.

Recall that tree is a connected undirected graph that has no cycles. Cactus is a connected undirected graph such that each vertex belongs to at most one cycle.

Masha has some additional edges that she can add to a tree. For each edge she knows which vertices it would connect and the beauty of this edge. Masha can add some of these edges to the graph if the resulting graph is a cactus. Beauty of the resulting cactus is sum of beauties of all added edges. 

Help Masha find out what maximum beauty of the resulting cactus she can achieve.

Input

The first line of the input data contains two integers n and m — the number of vertices in a tree, and the number of additional edges available (3 ≤ n ≤ 2·105; 0 ≤ m ≤ 2·105).

Let us describe Masha's tree. It has a root at vertex 1. The second line contains n - 1 integers: p2, p3, ..., pn, here pi — is the parent of a vertex i — the first vertex on a path from the vertex i to the root of the tree (1 ≤ pi < i).

The following m lines contain three integers ui, vi and ci — pairs of vertices to be connected by the additional edges that Masha can add to the tree and beauty of edge (1 ≤ ui, vi ≤ n; ui ≠ vi; 1 ≤ ci ≤ 104).

It is guaranteed that no additional edge coincides with the edge of the tree.

Output

Output one integer — the maximum beauty of a cactus Masha can achieve.

Example

Input

7 3
1 1 2 2 3 3
4 5 1
6 7 1
2 3 1


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename... As>
struct tpl : public std::tuple<As...> {
  using std::tuple<As...>::tuple;
  tpl() {}
  tpl(std::tuple<As...> const& b) { std::tuple<As...>::operator=(b); }
  template <typename T = tuple<As...>>
  typename tuple_element<0, T>::type const& x() const {
    return get<0>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<0, T>::type& x() {
    return get<0>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<1, T>::type const& y() const {
    return get<1>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<1, T>::type& y() {
    return get<1>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<2, T>::type const& z() const {
    return get<2>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<2, T>::type& z() {
    return get<2>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<3, T>::type const& w() const {
    return get<3>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<3, T>::type& w() {
    return get<3>(*this);
  }
};
using pii = tpl<int, int>;
using piii = tpl<int, int, int>;
using piiii = tpl<int, int, int, int>;
using vi = vector<int>;
using vii = vector<pii>;
using viii = vector<piii>;
using vvi = vector<vi>;
using vvii = vector<vii>;
using vviii = vector<viii>;
template <class T>
using min_queue = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using max_queue = priority_queue<T>;
template <size_t... I>
struct my_index_sequence {
  using type = my_index_sequence;
  static constexpr array<size_t, sizeof...(I)> value = {{I...}};
};
namespace my_index_sequence_detail {
template <typename I, typename J>
struct concat;
template <size_t... I, size_t... J>
struct concat<my_index_sequence<I...>, my_index_sequence<J...>>
    : my_index_sequence<I..., (sizeof...(I) + J)...> {};
template <size_t N>
struct make_index_sequence
    : concat<typename make_index_sequence<N / 2>::type,
             typename make_index_sequence<N - N / 2>::type>::type {};
template <>
struct make_index_sequence<0> : my_index_sequence<> {};
template <>
struct make_index_sequence<1> : my_index_sequence<0> {};
}  // namespace my_index_sequence_detail
template <class... A>
using my_index_sequence_for =
    typename my_index_sequence_detail::make_index_sequence<sizeof...(A)>::type;
template <class T, size_t... I>
void print_tuple(ostream& s, T const& a, my_index_sequence<I...>) {
  using swallow = int[];
  (void)swallow{0, (void(s << (I == 0 ? "" : ", ") << get<I>(a)), 0)...};
}
template <class T>
ostream& print_collection(ostream& s, T const& a);
template <class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a);
template <class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a);
template <class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a);
template <class T, size_t I>
ostream& operator<<(ostream& s, array<T, I> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, vector<T> const& a) {
  return print_collection(s, a);
}
template <class T, class U>
ostream& operator<<(ostream& s, multimap<T, U> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, multiset<T> const& a) {
  return print_collection(s, a);
}
template <class T, class U>
ostream& operator<<(ostream& s, map<T, U> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, set<T> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& print_collection(ostream& s, T const& a) {
  s << '[';
  for (auto it = begin(a); it != end(a); ++it) {
    s << *it;
    if (it != prev(end(a))) s << " ";
  }
  return s << ']';
}
template <class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a) {
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}
template <class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a) {
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}
template <class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a) {
  return s << "(" << get<0>(a) << ", " << get<1>(a) << ")";
}
namespace std {
namespace {
template <class T>
inline void hash_combine(size_t& seed, T const& v) {
  seed ^= hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
template <class Tuple, size_t Index = tuple_size<Tuple>::value - 1>
struct HashValueImpl {
  static void apply(size_t& seed, Tuple const& tuple) {
    HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
    hash_combine(seed, get<Index>(tuple));
  }
};
template <class Tuple>
struct HashValueImpl<Tuple, 0> {
  static void apply(size_t& seed, Tuple const& tuple) {
    hash_combine(seed, get<0>(tuple));
  }
};
}  // namespace
template <typename... TT>
struct hash<tuple<TT...>> {
  size_t operator()(tuple<TT...> const& tt) const {
    size_t seed = 0;
    HashValueImpl<tuple<TT...>>::apply(seed, tt);
    return seed;
  }
};
template <typename... TT>
struct hash<tpl<TT...>> {
  size_t operator()(tpl<TT...> const& tt) const {
    size_t seed = 0;
    HashValueImpl<tuple<TT...>>::apply(seed, tt);
    return seed;
  }
};
}  // namespace std
namespace link_cut {
struct node {
  node() {}
  node(int value0_, int value1_)
      : value0(value0_), mvalue0(value0_), value1(value1_), mvalue1(value1_) {}
  int value0, mvalue0;
  int value1, mvalue1;
  node *p = 0, *cs[2] = {0, 0};
  bool isroot() const { return !p || (this != p->cs[0] && this != p->cs[1]); }
  int dir() const { return this == p->cs[1]; }
  bool flip = 0;
};
void push(node* n) {
  if (n->flip) {
    swap(n->cs[0], n->cs[1]);
    for (int i = 0; i < (int)(2); ++i)
      if (n->cs[i]) n->cs[i]->flip ^= 1;
    n->flip = 0;
  }
}
void update(node* n) {
  if (n) {
    n->mvalue0 = n->value0;
    for (int i = 0; i < (int)(2); ++i)
      if (n->cs[i]) n->mvalue0 += n->cs[i]->mvalue0;
    n->mvalue1 = n->value1;
    for (int i = 0; i < (int)(2); ++i)
      if (n->cs[i]) n->mvalue1 += n->cs[i]->mvalue1;
  }
}
void rotate(node* n) {
  int d = n->dir();
  node *p = n->p, *b = n->cs[1 - d];
  if (!p->isroot()) p->p->cs[p->dir()] = n;
  n->p = p->p;
  n->cs[1 - d] = p;
  p->p = n;
  p->cs[d] = b;
  if (b) b->p = p;
  update(n);
  update(p);
  update(n->p);
}
void splay(node* n) {
  push(n);
  while (!n->isroot()) {
    if (n->p->p) push(n->p->p);
    push(n->p);
    push(n);
    if (n->p->isroot()) {
      rotate(n);
    } else if (n->dir() == n->p->dir()) {
      rotate(n->p);
      rotate(n);
    } else {
      rotate(n);
      rotate(n);
    }
  }
}
node* leftmost(node* n) {
  while (n->cs[0]) n = n->cs[0];
  return n;
}
void splice(node* x) {
  push(x->p);
  x->p->cs[1] = x;
  update(x->p);
}
void expose(node* x) {
  {
    node* y = x;
    while (y) {
      splay(y);
      y = y->p;
    }
  }
  {
    node* y = x;
    while (y->p) {
      splice(y);
      y = y->p;
    }
  }
  splay(x);
}
void evert(node* n) {
  expose(n);
  if (n->cs[0]) {
    n->cs[0]->flip ^= 1;
    n->cs[0] = 0;
    update(n);
  }
}
void link(node* x, node* y) {
  evert(y);
  y->p = x;
}
void cut(node* x, node* y) {
  evert(x);
  expose(y);
  y->cs[0] = 0;
  x->p = 0;
  update(y);
}
int path0(node* x, node* y) {
  if (x == y) {
    return x->value0;
  }
  evert(x);
  expose(y);
  return y->cs[0]->mvalue0 + y->value0;
}
int path1(node* x, node* y) {
  if (x == y) {
    return x->value1;
  }
  evert(x);
  expose(y);
  return y->cs[0]->mvalue1 + y->value1;
}
}  // namespace link_cut
int read_positive() {
  char c;
  int x = 0;
  do {
    c = getchar();
  } while (c < '0' || c > '9');
  while (c >= '0' && c <= '9') {
    x = 10 * x + (c - '0');
    c = getchar();
  }
  return x;
}
const int N = 300000;
const int LN = 20;
int parent[LN][N];
int depth[N];
link_cut::node LA[N];
int main() {
  int n, m;
  n = read_positive();
  m = read_positive();
  vvi G(n);
  for (int i = 0; i < (int)(n - 1); ++i) {
    int u;
    u = read_positive() - 1;
    int v = 1 + i;
    G[u].push_back(v);
    G[v].push_back(u);
  }
  vector<tpl<int, int, int>> Q(m);
  for (int i = 0; i < (int)(m); ++i) {
    int u, v, c;
    u = read_positive() - 1;
    v = read_positive() - 1;
    c = read_positive();
    Q[i] = make_tuple(u, v, c);
  }
  function<void(int, int, int)> dfs = [&](int i, int p, int d) {
    parent[0][i] = p;
    depth[i] = d;
    for (int j : G[i])
      if (j != p) {
        dfs(j, i, d + 1);
      }
  };
  dfs(0, -1, 0);
  for (int j = 0; j < (int)(LN - 1); ++j) {
    for (int i = 0; i < (int)(n); ++i) {
      if (parent[j][i] != -1) {
        parent[j + 1][i] = parent[j][parent[j][i]];
      }
    }
  }
  function<int(int, int)> lca = [&](int i, int j) {
    if (depth[i] < depth[j]) swap(i, j);
    for (int k = (LN - 1); k >= (int)(0); --k)
      if (depth[i] - (1 << k) >= depth[j]) {
        i = parent[k][i];
      }
    if (i == j) return i;
    for (int k = (LN - 1); k >= (int)(0); --k)
      if (depth[i] >= (1 << k)) {
        if (parent[k][i] != parent[k][j]) {
          i = parent[k][i];
          j = parent[k][j];
        }
      }
    return parent[0][i];
  };
  function<int(int, int)> next0 = [&](int i, int lca) {
    for (int k = (LN - 1); k >= (int)(0); --k)
      if (depth[i] - (1 << k) > depth[lca]) {
        i = parent[k][i];
      }
    return i;
  };
  vector<vector<tpl<int, int, int>>> QS(n);
  for (int i = 0; i < (int)(m); ++i) {
    int u, v, c;
    tie(u, v, c) = Q[i];
    QS[lca(u, v)].push_back(Q[i]);
  }
  vector<int> V(n);
  vector<int> SV(n);
  function<void(int, int)> dfs2 = [&](int i, int p) {
    V[i] = 0;
    SV[i] = 0;
    for (int j : G[i])
      if (j != p) {
        dfs2(j, i);
        SV[i] += V[j];
      }
    V[i] = SV[i];
    for (auto const& q : QS[i]) {
      int u, v, c;
      tie(u, v, c) = q;
      int curv = c;
      curv += SV[i];
      if (u != i) {
        int u_ = next0(u, i);
        curv += link_cut::path0(&LA[u_], &LA[u]);
        curv -= link_cut::path1(&LA[u_], &LA[u]);
      }
      if (v != i) {
        int v_ = next0(v, i);
        curv += link_cut::path0(&LA[v_], &LA[v]);
        curv -= link_cut::path1(&LA[v_], &LA[v]);
      }
      V[i] = max(V[i], curv);
    }
    LA[i] = link_cut::node(SV[i], V[i]);
    for (int j : G[i])
      if (j != p) {
        link_cut::link(&LA[i], &LA[j]);
      }
  };
  dfs2(0, -1);
  cout << V[0] << endl;
  exit(0);
  return 0;
}