#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#endif
#include <bits/stdc++.h>
#include <ext/rope>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;
template <class T> using pbds_set = tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
using Trie = trie<string, null_type, trie_string_access_traits<>, pat_trie_tag, trie_prefix_search_node_update>;
// template <class T> using heapq = __gnu_pbds::priority_queue<T, greater<T>, pairing_heap_tag>;
template <class T> using heapq = std::priority_queue<T, vector<T>, greater<T>>;
using ll   =                long long;
using u32  =                unsigned int;
using u64  =                unsigned long long;
using i128 =                __int128;
using u128 =                __uint128_t;
using f128 =                __float128;
using ld   =                long double;
using ui   =                unsigned int;
using ull  =                unsigned long long;
using pii  =                pair<int, int>;
using pll  =                pair<ll, ll>;
using pdd  =                pair<ld, ld>;
using vi   =                vector<int>;
using vvi  =                vector<vector<int>>;
using vll  =                vector<ll>;
using vvll =                vector<vector<ll>>;
using vpii =                vector<pii>;
using vpll =                vector<pll>;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = std::priority_queue<T>;
template <class T>
using pqg = std::priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define lb                  lower_bound
#define ub                  upper_bound
#define pb                  push_back
#define pf                  push_front
#define eb                  emplace_back
#define fi                  first
#define se                  second
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define rep1(n)             for(ll _ = 0; _ < n; ++_)
#define rep2(i, n)          for(ll i = 0; i < n; ++i)
#define rep3(i, a, b)       for(ll i = a; i < b; ++i)
#define rep4(i, a, b, c)    for(int i = a; i < b; i += c)
#define rep(...)            overload4(__VA_ARGS__, rep4, rep3, rep2, rep1) (__VA_ARGS__)
#define rrep1(n)            for(ll i = n; i--; )
#define rrep2(i, n)         for(ll i = n; i--; )
#define rrep3(i, a, b)      for(ll i = a; i > b; i--)
#define rrep4(i, a, b, c)   for(ll i = a; i > b; i -= c)
#define rrep(...)           overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1) (__VA_ARGS__)
#define each1(i, a)         for(auto&& i : a)
#define each2(x, y, a)      for(auto&& [x, y] : a)
#define each3(x, y, z, a)   for(auto&& [x, y, z] : a)
#define each(...)           overload4(__VA_ARGS__, each3, each2, each1) (__VA_ARGS__)
#define FOR1(a)             for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a)          for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b)       for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c)    for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a)           for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a)        for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b)     for (ll i = (b)-1; i >= ll(a); --i)
#define FOR(...)            overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1) (__VA_ARGS__)
#define FOR_R(...)          overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R) (__VA_ARGS__)
#define FOR_subset(t, s)    for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define len(x)              (int)x.size()
#define elif                else if
#define all1(i)             begin(i), end(i)
#define all2(i, a)          begin(i), begin(i) + a
#define all3(i, a, b)       begin(i) + a, begin(i) + b
#define all(...)            overload3(__VA_ARGS__, all3, all2, all1) (__VA_ARGS__)
#define rall1(i)            rbegin(i), rend(i)
#define rall2(i, a)         rbegin(i), rbegin(i) + a
#define rall3(i, a, b)      rbegin(i) + a, rbegin(i) + b
#define rall(...)           overload3(__VA_ARGS__, rall3, rall2, rall1) (__VA_ARGS__)
#define mst(x, a)           memset(x, a, sizeof(x))
#define bitcnt(x)           (__builtin_popcountll(x))
#define endl                "\n"
#define MIN(v)              *min_element(all(v))
#define MAX(v)              *max_element(all(v))
#define LB(c, x)            distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x)            distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x)           sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
#define SORT(a)             sort(all(a))
#define REV(a)              reverse(all(a))
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template <typename T, typename U>
T ceil(T x, U y) {
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
    T q = floor(x, y);
    return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
    T sum = 0;
    for (auto &&a: A) sum += a;
    return sum;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
    int N = A.size();
    vector<T> B(N + 1);
    for (int i = 0; i < N; i++) B[i + 1] = B[i] + A[i];
    if (off == 0) B.erase(B.begin());
    return B;
}
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  while (iter--) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}
template <class T, class S> inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S> inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}
mt19937 rng( chrono::steady_clock::now().time_since_epoch().count() );
#define Ran(a, b) rng() % ( (b) - (a) + 1 ) + (a)
struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }

    size_t operator()(pair<uint64_t,uint64_t> x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x.first + FIXED_RANDOM) ^ (splitmix64(x.second + FIXED_RANDOM) >> 1);
    }
};
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

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

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

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
const i128 ONE = 1;
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(fastio::wt(*v.begin())) {
    for (auto it = v.begin(); it != v.end();) {
        fastio::wt(*it);
        if (++it != v.end()) fastio::wt(sep);
    }
    fastio::wt(end);
}
ll gcd(ll x, ll y) {
    if(!x) return y;
    if(!y) return x;
    int t = __builtin_ctzll(x | y);
    x >>= __builtin_ctzll(x);
    do {
        y >>= __builtin_ctzll(y);
        if (x > y) swap(x, y);
        y -= x;
    } while (y);
    return x << t;
}
ll lcm(ll x, ll y) { return x * y / gcd(x, y); }
ll exgcd(ll a, ll b, ll &x, ll &y) {
    if(!b) return x = 1, y = 0, a;
    ll d = exgcd(b, a % b, x, y);
    ll t = x;
    x = y;
    y = t - a / b * x;
    return d;
}
ll max(ll x, ll y) { return x > y ? x : y; }
ll min(ll x, ll y) { return x < y ? x : y; }
ll Mod(ll x, int mod) { return (x % mod + mod) % mod; }
ll pow(ll x, ll y, ll mod){
    ll res = 1, cur = x;
    while (y) {
        if (y & 1) res = res * cur % mod;
        cur = ONE * cur * cur % mod;
        y >>= 1;
    }
    return res % mod;
}
ll probabilityMod(ll x, ll y, ll mod) {
    return x * pow(y, mod-2, mod) % mod;
}
vvi getGraph(int n, int m, bool directed = false) {
    vvi res(n);
    rep(_, 0, m) {
        INT(u, v);
        u--, v--;
        res[u].emplace_back(v);
        if(!directed) res[v].emplace_back(u);
    }
    return res;
}
vector<vpii> getWeightedGraph(int n, int m, bool directed = false) {
    vector<vpii> res(n);
    rep(_, 0, m) {
        INT(u, v, w);
        u--, v--;
        res[u].emplace_back(v, w);
        if(!directed) res[v].emplace_back(u, w);
    }
    return res;
}
template <class... Args> auto ndvector(size_t n, Args &&...args) {
    if constexpr (sizeof...(args) == 1) {
        return vector(n, args...);
    } else {
        return vector(n, ndvector(args...));
    }
}
const ll LINF = 0x1fffffffffffffff;
const ll MINF = 0x7fffffffffff;
const int INF = 0x3fffffff;
const int MOD = 1000000007;
const int MODD = 998244353;
const int N = 1e6 + 10;

// atcoder library のものを改変

namespace internal {

template <class E>
struct csr {
  std::vector<int> start;
  std::vector<E> elist;
  explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
      : start(n + 1), elist(edges.size()) {
    for (auto e: edges) { start[e.first + 1]++; }
    for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; }
    auto counter = start;
    for (auto e: edges) { elist[counter[e.first]++] = e.second; }
  }
};

template <class T>
struct simple_queue {
  std::vector<T> payload;
  int pos = 0;
  void reserve(int n) { payload.reserve(n); }
  int size() const { return int(payload.size()) - pos; }
  bool empty() const { return pos == int(payload.size()); }
  void push(const T& t) { payload.push_back(t); }
  T& front() { return payload[pos]; }
  void clear() {
    payload.clear();
    pos = 0;
  }
  void pop() { pos++; }
};

} // namespace internal

/*
・atcoder library をすこし改変したもの
・DAG = true であれば、負辺 OK （1 回目の最短路を dp で行う）
ただし、頂点番号は toposort されていることを仮定している。
*/
template <class Cap = int, class Cost = ll, bool DAG = false>
struct mcf_graph {
public:
  mcf_graph() {}
  explicit mcf_graph(int n) : _n(n) {}

  // frm, to, cap, cost
  int add(int frm, int to, Cap cap, Cost cost) {
    assert(0 <= frm && frm < _n);
    assert(0 <= to && to < _n);
    assert(0 <= cap);
    assert(DAG || 0 <= cost);
    if (DAG) assert(frm < to);
    int m = int(_edges.size());
    _edges.push_back({frm, to, cap, 0, cost});
    return m;
  }

  void debug() {
    print("flow graph");
    print("frm, to, cap, cost");
    for (auto&& [frm, to, cap, flow, cost]: _edges) {
      print(frm, to, cap, cost);
    }
  }

  struct edge {
    int frm, to;
    Cap cap, flow;
    Cost cost;
  };

  edge get_edge(int i) {
    int m = int(_edges.size());
    assert(0 <= i && i < m);
    return _edges[i];
  }
  std::vector<edge> edges() { return _edges; }

  // (流量, 費用)
  std::pair<Cap, Cost> flow(int s, int t) {
    return flow(s, t, std::numeric_limits<Cap>::max());
  }
  // (流量, 費用)
  std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
    return slope(s, t, flow_limit).back();
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
    return slope(s, t, std::numeric_limits<Cap>::max());
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    assert(s != t);

    int m = int(_edges.size());
    std::vector<int> edge_idx(m);

    auto g = [&]() {
      std::vector<int> degree(_n), redge_idx(m);
      std::vector<std::pair<int, _edge>> elist;
      elist.reserve(2 * m);
      for (int i = 0; i < m; i++) {
        auto e = _edges[i];
        edge_idx[i] = degree[e.frm]++;
        redge_idx[i] = degree[e.to]++;
        elist.push_back({e.frm, {e.to, -1, e.cap - e.flow, e.cost}});
        elist.push_back({e.to, {e.frm, -1, e.flow, -e.cost}});
      }
      auto _g = internal::csr<_edge>(_n, elist);
      for (int i = 0; i < m; i++) {
        auto e = _edges[i];
        edge_idx[i] += _g.start[e.frm];
        redge_idx[i] += _g.start[e.to];
        _g.elist[edge_idx[i]].rev = redge_idx[i];
        _g.elist[redge_idx[i]].rev = edge_idx[i];
      }
      return _g;
    }();

    auto result = slope(g, s, t, flow_limit);

    for (int i = 0; i < m; i++) {
      auto e = g.elist[edge_idx[i]];
      _edges[i].flow = _edges[i].cap - e.cap;
    }

    return result;
  }

private:
  int _n;
  std::vector<edge> _edges;

  // inside edge
  struct _edge {
    int to, rev;
    Cap cap;
    Cost cost;
  };

  std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge>& g, int s, int t,
                                          Cap flow_limit) {
    // variants (C = maxcost):
    // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
    // reduced cost (= e.cost + dual[e.frm] - dual[e.to]) >= 0 for all edge

    // dual_dist[i] = (dual[i], dist[i])
    if (DAG) assert(s == 0 && t == _n - 1);
    std::vector<std::pair<Cost, Cost>> dual_dist(_n);
    std::vector<int> prev_e(_n);
    std::vector<bool> vis(_n);
    struct Q {
      Cost key;
      int to;
      bool operator<(Q r) const { return key > r.key; }
    };
    std::vector<int> que_min;
    std::vector<Q> que;
    auto dual_ref = [&]() {
      for (int i = 0; i < _n; i++) {
        dual_dist[i].second = std::numeric_limits<Cost>::max();
      }
      std::fill(vis.begin(), vis.end(), false);
      que_min.clear();
      que.clear();

      // que[0..heap_r) was heapified
      size_t heap_r = 0;

      dual_dist[s].second = 0;
      que_min.push_back(s);
      while (!que_min.empty() || !que.empty()) {
        int v;
        if (!que_min.empty()) {
          v = que_min.back();
          que_min.pop_back();
        } else {
          while (heap_r < que.size()) {
            heap_r++;
            std::push_heap(que.begin(), que.begin() + heap_r);
          }
          v = que.front().to;
          std::pop_heap(que.begin(), que.end());
          que.pop_back();
          heap_r--;
        }
        if (vis[v]) continue;
        vis[v] = true;
        if (v == t) break;
        // dist[v] = shortest(s, v) + dual[s] - dual[v]
        // dist[v] >= 0 (all reduced cost are positive)
        // dist[v] <= (n-1)C
        Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
        for (int i = g.start[v]; i < g.start[v + 1]; i++) {
          auto e = g.elist[i];
          if (!e.cap) continue;
          // |-dual[e.to] + dual[v]| <= (n-1)C
          // cost <= C - -(n-1)C + 0 = nC
          Cost cost = e.cost - dual_dist[e.to].first + dual_v;
          if (dual_dist[e.to].second > dist_v + cost) {
            Cost dist_to = dist_v + cost;
            dual_dist[e.to].second = dist_to;
            prev_e[e.to] = e.rev;
            if (dist_to == dist_v) {
              que_min.push_back(e.to);
            } else {
              que.push_back(Q{dist_to, e.to});
            }
          }
        }
      }
      if (!vis[t]) { return false; }

      for (int v = 0; v < _n; v++) {
        if (!vis[v]) continue;
        // dual[v] = dual[v] - dist[t] + dist[v]
        //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
        //         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
        //         t) + dual[t] + shortest(s, v) = shortest(s, v) -
        //         shortest(s, t) >= 0 - (n-1)C
        dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
      }
      return true;
    };

    auto dual_ref_dag = [&]() {
      for (int i = 0; i < _n; i++) {
        dual_dist[i].second = std::numeric_limits<Cost>::max();
      }
      dual_dist[s].second = 0;
      std::fill(vis.begin(), vis.end(), false);
      vis[0] = true;

      for (int v = 0; v < _n; ++v) {
        if (!vis[v]) continue;
        Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
        for (int i = g.start[v]; i < g.start[v + 1]; i++) {
          auto e = g.elist[i];
          if (!e.cap) continue;
          Cost cost = e.cost - dual_dist[e.to].first + dual_v;
          if (dual_dist[e.to].second > dist_v + cost) {
            vis[e.to] = true;
            Cost dist_to = dist_v + cost;
            dual_dist[e.to].second = dist_to;
            prev_e[e.to] = e.rev;
          }
        }
      }
      if (!vis[t]) { return false; }

      for (int v = 0; v < _n; v++) {
        if (!vis[v]) continue;
        // dual[v] = dual[v] - dist[t] + dist[v]
        //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
        //         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
        //         t) + dual[t] + shortest(s, v) = shortest(s, v) -
        //         shortest(s, t) >= 0 - (n-1)C
        dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
      }
      return true;
    };

    Cap flow = 0;
    Cost cost = 0, prev_cost_per_flow = -1;
    std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
    while (flow < flow_limit) {
      if (DAG && flow == 0) {
        if (!dual_ref_dag()) break;
      } else {
        if (!dual_ref()) break;
      }
      Cap c = flow_limit - flow;
      for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
        c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
      }
      for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
        auto& e = g.elist[prev_e[v]];
        e.cap += c;
        g.elist[e.rev].cap -= c;
      }
      Cost d = -dual_dist[s].first;
      flow += c;
      cost += c * d;
      if (prev_cost_per_flow == d) { result.pop_back(); }
      result.push_back({flow, cost});
      prev_cost_per_flow = d;
    }
    return result;
  }
};

void solve() {
    INT(K, N, M);
    VEC(int, A, K);
    each(i, A) i--;
    VEC(int, B, N);
    mcf_graph<ll> G(N + 2);
    int S = N, T = S + 1;
    rep(i, K) G.add(S, A[i], 1, 0);
    rep(i, N) G.add(i, T, B[i], 0);
    rep(M) {
        LL(U, V, D);
        U--, V--;
        G.add(U, V, infty<int>, D);
        G.add(V, U, infty<int>, D);
    }
    auto [flow, cost] = G.flow(S, T);
    print(cost);

    
}

signed main() {
    int T = 1;
    // read(T);
    while (T--) {
        solve();
    }
    return 0;
}