/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

#include <bits/stdc++.h>

// #include <atcoder/all>
#include <atcoder/mincostflow>

using namespace std;
// using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
        cerr << fixed << setprecision(25);
    }
} setup_io;
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
// #define endl '\n'

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0)
        x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T>
using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;

} // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint &lhs, const mint &rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint &lhs, const mint &rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint &lhs, const mint &rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint &lhs, const mint &rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint &lhs, const mint &rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint &lhs, const mint &rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint &lhs, const mint &rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint &lhs, const mint &rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint &lhs, const mint &rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint &lhs, const mint &rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint &lhs, const mint &rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint &lhs, const mint &rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal

} // namespace atcoder

using namespace atcoder;

using mint = modint998244353;

constexpr int N = 2011;
vector<vector<pll>> G(N);

vl dijkstra(int s, int n, vector<vector<pair<ll, ll>>> G) {
    priority_queue<pll, vector<pll>, greater<pll>> pq;
    int i;
    vl d(n, INF);
    d[s] = 0;
    pq.push(make_pair(0, s));

    while (!pq.empty()) {
        pll f = pq.top();
        pq.pop();
        int u = f.second;
        if (d[u] < f.first) {
            continue;
        }
        for (i = 0; i < G[u].size(); i++) {
            int v = G[u][i].second;
            if (d[v] > d[u] + G[u][i].first) {
                d[v] = d[u] + G[u][i].first;
                pq.push(make_pair(d[v], v));
            }
        }
    }
    return d;
}

// Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
// Verified:
// - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702
// - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT
template <class Cap = long long, class Cost = long long, Cost INF_COST = std::numeric_limits<Cost>::max() / 2>
struct MinCostFlow {
    // https://hitonanode.github.io/cplib-cpp/combinatorial_opt/mincostflow_nonegativeloop.hpp
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
        template <class Ostream>
        friend Ostream &operator<<(Ostream &os, const _edge &e) {
            return os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')';
        }
    };
    bool _is_dual_infeasible;
    int V;
    std::vector<std::vector<_edge>> g;
    std::vector<Cost> dist;
    std::vector<int> prevv, preve;
    std::vector<Cost> dual; // dual[V]: potential
    std::vector<std::pair<int, int>> pos;

    bool _initialize_dual_dag() {
        std::vector<int> deg_in(V);
        for (int i = 0; i < V; i++) {
            for (const auto &e : g[i])
                deg_in[e.to] += (e.cap > 0);
        }
        std::vector<int> st;
        st.reserve(V);
        for (int i = 0; i < V; i++) {
            if (!deg_in[i]) st.push_back(i);
        }
        for (int n = 0; n < V; n++) {
            if (int(st.size()) == n) return false; // Not DAG
            int now = st[n];
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                deg_in[e.to]--;
                if (deg_in[e.to] == 0) st.push_back(e.to);
                if (dual[e.to] >= dual[now] + e.cost) dual[e.to] = dual[now] + e.cost;
            }
        }
        return true;
    }

    bool _initialize_dual_spfa() { // Find feasible dual's when negative cost edges exist
        dual.assign(V, 0);
        std::queue<int> q;
        std::vector<int> in_queue(V);
        std::vector<int> nvis(V);
        for (int i = 0; i < V; i++)
            q.push(i), in_queue[i] = true;
        while (q.size()) {
            int now = q.front();
            q.pop(), in_queue[now] = false;
            if (nvis[now] > V) return false; // Negative cycle exists
            nvis[now]++;
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                if (dual[e.to] > dual[now] + e.cost) {
                    dual[e.to] = dual[now] + e.cost;
                    if (!in_queue[e.to]) in_queue[e.to] = true, q.push(e.to);
                }
            }
        }
        return true;
    }

    bool initialize_dual() {
        return !_is_dual_infeasible or _initialize_dual_dag() or _initialize_dual_spfa();
    }

    void _dijkstra(int s) { // O(ElogV)
        prevv.assign(V, -1);
        preve.assign(V, -1);
        dist.assign(V, INF_COST);
        dist[s] = 0;
        using P = std::pair<Cost, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> q;
        q.emplace(0, s);
        while (!q.empty()) {
            P p = q.top();
            q.pop();
            int v = p.second;
            if (dist[v] < p.first) continue;
            for (int i = 0; i < (int)g[v].size(); i++) {
                _edge &e = g[v][i];
                Cost c = dist[v] + e.cost + dual[v] - dual[e.to];
                if (e.cap > 0 and dist[e.to] > c) {
                    dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i;
                    q.emplace(dist[e.to], e.to);
                }
            }
        }
    }

    MinCostFlow(int V = 0) : _is_dual_infeasible(false), V(V), g(V), dual(V, 0) {
        static_assert(INF_COST > 0, "INF_COST must be positive");
    }

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from and from < V);
        assert(0 <= to and to < V);
        assert(cap >= 0);
        if (cost < 0) _is_dual_infeasible = true;
        pos.emplace_back(from, g[from].size());
        g[from].push_back({to, (int)g[to].size() + (from == to), cap, cost});
        g[to].push_back({from, (int)g[from].size() - 1, (Cap)0, -cost});
        return int(pos.size()) - 1;
    }

    // Flush flow f from s to t. Graph must not have negative cycle.
    std::pair<Cap, Cost> flow(int s, int t, const Cap &flow_limit) {
        if (!initialize_dual()) throw; // Fail to find feasible dual
        Cost cost = 0;
        Cap flow_rem = flow_limit;
        while (flow_rem > 0) {
            _dijkstra(s);
            if (dist[t] == INF_COST) break;
            for (int v = 0; v < V; v++)
                dual[v] = std::min(dual[v] + dist[v], INF_COST);
            Cap d = flow_rem;
            for (int v = t; v != s; v = prevv[v])
                d = std::min(d, g[prevv[v]][preve[v]].cap);
            flow_rem -= d;
            cost += d * (dual[t] - dual[s]);
            for (int v = t; v != s; v = prevv[v]) {
                _edge &e = g[prevv[v]][preve[v]];
                e.cap -= d;
                g[v][e.rev].cap += d;
            }
        }
        return std::make_pair(flow_limit - flow_rem, cost);
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
        template <class Ostream>
        friend Ostream &operator<<(Ostream &os, const edge &e) {
            return os << '(' << e.from << "->" << e.to << ',' << e.flow << '/' << e.cap << ",$" << e.cost << ')';
        }
    };

    edge get_edge(int edge_id) const {
        int m = int(pos.size());
        assert(0 <= edge_id and edge_id < m);
        auto _e = g[pos[edge_id].first][pos[edge_id].second];
        auto _re = g[_e.to][_e.rev];
        return {pos[edge_id].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost};
    }
    std::vector<edge> edges() const {
        std::vector<edge> ret(pos.size());
        for (int i = 0; i < int(pos.size()); i++)
            ret[i] = get_edge(i);
        return ret;
    }

    template <class Ostream>
    friend Ostream &operator<<(Ostream &os, const MinCostFlow &mcf) {
        os << "[MinCostFlow]V=" << mcf.V << ":";
        for (int i = 0; i < mcf.V; i++) {
            for (auto &e : mcf.g[i])
                os << "\n"
                   << i << "->" << e.to << ":cap" << e.cap << ",$" << e.cost;
        }
        return os;
    }
};

signed main() {
    int k, n, m;
    cin >> k >> n >> m;
    vi num(n);
    rep(i, k) {
        int x;
        cin >> x;
        x--;
        num[x]++;
    }
    vi b(n);
    rep(i, n) {
        cin >> b[i];
    }

    // MinCostFlow<ll, ll> mcf(n + n + 2);
    atcoder::mcf_graph<ll, ll> mcf(n + 2);
    rep(i, m) {
        ll u, v, d;
        cin >> u >> v >> d;
        u--;
        v--;
        G[u].emplace_back(d, v);
        G[v].emplace_back(d, u);
        mcf.add_edge(u, v, INF, d);
        mcf.add_edge(v, u, INF, d);
    }

    // vll d(n);
    // rep(i, n) {
    //     d[i] = dijkstra(i, n, G);
    // }

    int S = n, T = n + 1;
    rep(i, n) {
        mcf.add_edge(S, i, num[i], 0);
        mcf.add_edge(i, T, b[i], 0);
    }

    // rep(i, n) {
    //     rep(j, n) {
    //         mcf.add_edge(i, n + j, INF, d[i][j]);
    //     }
    // }

    auto [cap, cost] = mcf.flow(S, T, k);
    assert(cap == k);

    cout << cost << endl;
}