#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#include <bits/extc++.h>
using namespace std;
/*
#include <atcoder/all>
using namespace atcoder;
*/
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using bll = boost::multiprecision::cpp_int;
using bdouble = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>>;
using namespace boost::multiprecision;
*/
#if defined(LOCAL_TEST) || defined(LOCAL_DEV)
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE 1
	#include <boost/stacktrace.hpp>
#endif
#ifdef LOCAL_TEST
	namespace std {
		template <typename T> class dvector : public std::vector<T> {
		public:
			using std::vector<T>::vector;
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			std::vector<bool>::reference operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_ operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			T_& operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_& operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
		};
		template <typename T, typename Compare = std::less<T>, typename Allocator = std::allocator<T>> class dmultiset : public std::multiset<T,Compare,Allocator> {
		public:
			using std::multiset<T,Compare,Allocator>::multiset;
			const typename std::multiset<T,Compare,Allocator>::iterator erase(const typename std::multiset<T,Compare,Allocator>::iterator it) {
				return std::multiset<T,Compare,Allocator>::erase(it);
			}
			std::size_t erase([[maybe_unused]] const T& x) {
				std::cerr << boost::stacktrace::stacktrace() << '\n'; assert(false);
			}
			std::size_t erase_all_elements(const T& x) {
				return std::multiset<T,Compare,Allocator>::erase(x);
			}
		};
	}
	#define vector dvector
	#define multiset dmultiset
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); }
	void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#else
	#define erase_all_elements erase
#endif
#ifdef LOCAL_DEV
	template <typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	template <typename T, std::size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (std::size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::deque<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<std::vector<T>>& vv) {
		s << "\\\n"; for (std::size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template <typename T, std::size_t N, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&v)[N]) {
		for (std::size_t i = 0; i < N; ++i){ s << v[i]; if (i < N - 1) s << "\t"; } return s; }
	template <typename T, std::size_t N, std::size_t M, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&vv)[N][M]) {
		s << "\\\n"; for (std::size_t i = 0; i < N; ++i){ s << vv[i] << "\n"; } return s; }
	#if __has_include(<ext/pb_ds/assoc_container.hpp>)
		template <typename Key, typename Compare> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::tree<Key, __gnu_pbds::null_type, Compare, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>& se) {
			s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
		template <typename Key, typename T, typename Hash> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::gp_hash_table<Key, T, Hash>& m) {
			s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	#endif
	void debug_impl() { std::cerr << '\n'; }
	template <typename Head, typename... Tail> void debug_impl(const Head& head, const Tail&... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << ":" << __LINE__ << " (" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return local; }
#else
	#define debug(...) do {} while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return prod; }
#endif
//#define int long long
using ll = long long;
//INT_MAX = (1<<31)-1 = 2147483647, INT64_MAX = (1LL<<63)-1 = 9223372036854775807
constexpr ll INF = std::numeric_limits<ll>::max() == INT_MAX ? (ll)1e9 + 7 : (ll)1e18;
//constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5
constexpr ll MOD = 998244353; //primitive root = 3
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1, 0, -1, 0};
constexpr ll dy[4] = {0, 1, 0, -1};
constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define repoverload3(_1, _2, _3, name, ...) name
#define rep3(i, a, b) for(ll i=(a), i##_length=(b); i<i##_length; ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep3(i, 0, n)
#define rep(...) repoverload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repeq3(i, a, b) rep3(i, (a)+1, (b)+1)
#define repeq2(i, n) rep3(i, 1, (n)+1)
#define repeq1(n) rep3(i, 1, (n)+1)
#define repeq(...) repoverload3(__VA_ARGS__, repeq3, repeq2, repeq1)(__VA_ARGS__)
#define rrep3(i, a, b) for(ll i=(b)-1; i>=(a); --i)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep1(n) rrep3(i, 0, n)
#define rrep(...) repoverload3(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define rrepeq3(i, a, b) rrep3(i, (a)+1, (b)+1)
#define rrepeq2(i, n) rrep3(i, 1, (n)+1)
#define rrepeq1(n) rrep3(i, 1, (n)+1)
#define rrepeq(...) repoverload3(__VA_ARGS__, rrepeq3, rrepeq2, rrepeq1)(__VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
void p() { std::cout << '\n'; }
template <typename Head, typename... Tail> void p(const Head& head, const Tail&... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template <typename T> inline void pv(const std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template <typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template <typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template <typename T> inline void uniq(std::vector<T>& v) { std::sort(v.begin(), v.end()); v.erase(std::unique(v.begin(), v.end()), v.end()); }
template <typename T> inline ll sz(const T& v) { return std::size(v); }
template <typename T, std::size_t N> std::vector<T> make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N==1), const T&>::type x) { return std::vector<T>(sizes.front(),x); }
template <typename T, std::size_t N> auto make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N>1), const T&>::type x) { ll size=sizes.back(); sizes.pop_back(); return std::vector<decltype(make_vector_impl<T,N-1>(sizes,x))>(size,make_vector_impl<T,N-1>(sizes,x)); }
template <typename T, std::size_t N> auto make_vector(const ll (&sizes)[N], const T& x=T()) { std::vector<ll> s(N); for(std::size_t i=0; i<N; ++i)s[i]=sizes[N-1-i]; return make_vector_impl<T,N>(s,x); }
#if __has_include(<ext/pb_ds/assoc_container.hpp>)
	template <typename Key, typename Mapped, typename Hash = std::hash<Key>, typename std::enable_if_t<std::is_integral_v<Key>, std::nullptr_t> = nullptr> struct fmap : public __gnu_pbds::gp_hash_table<Key, Mapped, Hash> {
		using __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::gp_hash_table;
		template <typename T> fmap(std::initializer_list<std::initializer_list<T>> il) : __gnu_pbds::gp_hash_table<Key, Mapped, Hash>() {
			for (auto&& x : il) __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::insert(std::pair<Key, Mapped>(*x.begin(), *(x.begin() + 1)));
		}
		template <typename T> ll count(const T& x) const {
			return __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::find(x) != __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::end();
		}
	};
#else
	template <typename Key, typename Mapped> using fmap = std::map<Key, Mapped>;
#endif
template <typename T> struct each_hepler {
	struct iterator {
		ll _pos;
		typename T::iterator _it;
		iterator(typename T::iterator it): _pos(0), _it(it) {}
		std::pair<ll, typename std::iterator_traits<typename T::iterator>::reference> operator*() const { return {_pos, *_it}; }
		iterator& operator++() { ++_pos; ++_it; return *this; }
		iterator operator++(int) { iterator tmp(*this); ++*this; return tmp; }
		bool operator==(iterator const& it) const { return _it == it._it; }
		bool operator!=(iterator const& it) const { return !(*this == it); }
	};
	T& _container;
	each_hepler(T& t): _container(t) {}
	iterator begin() const { return iterator(_container.begin()); }
	iterator end() const { return iterator(_container.end()); }
};
template <typename T> each_hepler<T> each(T& t) { return each_hepler<T>(t); } // for (auto&& [i, val] : each(v))
template <typename... T> class zip_helper {
public:
	class iterator : std::iterator<std::forward_iterator_tag, std::tuple<decltype(*std::declval<T>().begin())...>> {
	private:
		std::tuple<decltype(std::declval<T>().begin())...> iters_;
		template <std::size_t... I> auto deref(std::index_sequence<I...>) const { return typename iterator::value_type{*std::get<I>(iters_)...}; }
		template <std::size_t... I> void increment(std::index_sequence<I...>) { [[maybe_unused]] auto l = {(++std::get<I>(iters_), 0)...}; }
	public:
		explicit iterator(decltype(iters_) iters) : iters_{std::move(iters)} {}
		iterator& operator++() { increment(std::index_sequence_for<T...>{}); return *this; }
		iterator operator++(int) { auto saved{*this}; increment(std::index_sequence_for<T...>{}); return saved; }
		bool operator!=(const iterator& other) const { return iters_ != other.iters_; }
		auto operator*() const { return deref(std::index_sequence_for<T...>{}); }
	};
	zip_helper(T&... seqs) : begin_{std::make_tuple(seqs.begin()...)}, end_{std::make_tuple(seqs.end()...)} {}
	iterator begin() const { return begin_; }
	iterator end() const { return end_; }
private:
	iterator begin_, end_;
};
template <typename... T> auto zip(T&&... seqs) { return zip_helper<T...>{seqs...}; } // for (auto&& [a, b, c] : zip(A, B, C))

/*-----8<-----template-----8<-----*/


//[lib]johnsons_algorithm.cpp
using EdgeCostType = ll;
using usize = std::size_t;
template <class T> class edge_type {
public:
	usize from, to;
	T cost, rawcost;
	edge_type() {}
	edge_type(usize from, usize to, T cost) : from(from), to(to), cost(cost) {}
	edge_type(usize from, usize to, T cost, T rawcost) : from(from), to(to), cost(cost), rawcost(rawcost) {}
	bool operator<(const edge_type& r) const { return r.cost < cost; }
};
using Edge = edge_type<EdgeCostType>;
ostream& operator<<(ostream& s, const Edge& e) {
    s << "{ " << e.from << " -> " << e.to << ", " << e.cost << " }";
    return s;
}
inline void addedge(vector<vector<Edge>>& g, usize from, usize to, EdgeCostType cost) {
	g[from].emplace_back(from, to, cost);
	g[to].emplace_back(to, from, cost);
}
//最短路木の親頂点を元にstart->goalの経路を作成
vector<ll> buildPath(const vector<ll> &prev, ll goal) {
	vector<ll> path;
	for (ll u = goal; u >= 0; u = prev[u])
		path.push_back(u);
	reverse(path.begin(), path.end());
	return path;
}
template <class T> class fibonacci_heap {
	class node_type;
	using node_ptr = node_type *;
	class node_type {
	public:
		node_ptr parent;
		node_ptr child;
		node_ptr left;
		node_ptr right;
		usize rank;
		bool mark;
		T key;
		usize prev;
		T rawcost;
		node_type()
				: parent(nullptr), child(nullptr), left(nullptr), right(nullptr),
					rank(0), mark(false), key(std::numeric_limits<T>::max()), prev(-1) {}
	};

	vector<node_type> nodes;
	node_ptr root;
	vector<node_ptr> table;

public:
	fibonacci_heap(const usize n)
			: nodes(n), root(nullptr),
				table(std::ceil(std::log(n + 1) * 2.08), nullptr) {}

	bool empty() const { return root == nullptr; }

	edge_type<T> pop() {
		edge_type<T> ret = {root->prev, static_cast<usize>(root - nodes.data()), root->key, root->rawcost};

		usize max = 0;
		const auto push = [&](node_ptr v) -> void {
			while (true) {
				node_ptr u = table[v->rank];
				if (u == nullptr) {
					table[v->rank] = v;
					break;
				}
				table[v->rank] = nullptr;
				if (u->key < v->key) {
					std::swap(u, v);
				}
				const node_ptr c = v->child;
				if (c == nullptr) {
					u->left = u;
					u->right = u;
					v->child = u;
				} else {
					u->left = c->left;
					u->right = c;
					c->left->right = u;
					c->left = u;
				}
				u->parent = v;
				v->rank += 1;
			}
			max = std::max(max, v->rank + 1);
		};

		{
			node_ptr v = root->right;
			while (v != root) {
				const node_ptr next = v->right;
				push(v);
				v = next;
			}
		}
		if (root->child != nullptr) {
			node_ptr v = root->child;
			do {
				const node_ptr next = v->right;
				v->mark = false;
				push(v);
				v = next;
			} while (v != root->child);
		}
		root = nullptr;

		for (usize i = 0; i != max; i += 1) {
			const node_ptr v = table[i];
			if (v == nullptr) {
				continue;
			}
			table[i] = nullptr;
			v->parent = nullptr;
			if (root == nullptr) {
				root = v;
				v->left = v;
				v->right = v;
			} else {
				v->left = root->left;
				v->right = root;
				root->left->right = v;
				root->left = v;
				if (root->key > v->key) {
					root = v;
				}
			}
		}

		return ret;
	}

	void update_key(const usize v_, const T key, const usize prev, const T rawcost) {
		node_ptr v = &nodes[v_];

		if (v->key <= key) {
			return;
		}
		v->key = key;
		v->prev = prev;
		v->rawcost = rawcost;

		if (v->left == nullptr) {
			if (root == nullptr) {
				v->left = v;
				v->right = v;
				root = v;
			} else {
				v->left = root->left;
				v->right = root;
				root->left->right = v;
				root->left = v;
				if (key < root->key) {
					root = v;
				}
			}
			return;
		}

		if (v->parent == nullptr) {
			if (key < root->key) {
				root = v;
			}
			return;
		} else {
			if (v->parent->key <= key) {
				return;
			}
		}

		while (true) {
			const node_ptr p = v->parent;
			v->left->right = v->right;
			v->right->left = v->left;
			v->parent = nullptr;
			p->rank -= 1;
			if (p->child == v) {
				if (p->rank == 0) {
					p->child = nullptr;
				} else {
					p->child = v->right;
				}
			}

			v->left = root->left;
			v->right = root;
			root->left->right = v;
			root->left = v;
			v->mark = false;

			v = p;
			if (v->parent == nullptr) {
				break;
			}
			if (!v->mark) {
				v->mark = true;
				break;
			}
		}
		if (root->key > key) {
			root = &nodes[v_];
		}
	}
};
/*
計算量：O(E+VlogV)
引数
　g:探索するグラフ
　start:探索するスタートノード番号
戻り値
　dist:スタートノードから各頂点までの距離
　prev:最短路木の親頂点
*/
void dijkstra(const vector<vector<Edge>> &g, ll start, vector<EdgeCostType> &dist, vector<ll> &prev) {
	dist.assign(g.size(), INF); dist[start] = 0;
	prev.assign(g.size(), -1);
	fibonacci_heap<EdgeCostType> heap(g.size());
	heap.update_key(start, 0, -1, 0);
	while (!heap.empty()) {
		const auto top = heap.pop();
		dist[top.to] = top.rawcost;
		if (top.from != (usize)-1) prev[top.to] = top.from;
		for (const auto &edge : g[top.to]) {
			heap.update_key(edge.to, top.cost + edge.cost, edge.from, top.rawcost + edge.rawcost);
		}
	}
}

bool bellman_ford(const vector<vector<Edge>> &g, ll start, vector<EdgeCostType> &dist, vector<ll> &prev) {
	ll gsize = g.size();
	dist.assign(gsize, INF+INF); dist[start] = 0;
	prev.assign(gsize, -1);
	
	bool negative_cycle = false;
	for(ll k=0; k<gsize*2; k++){
		for(ll i=0; i<gsize; i++){
			for(const Edge &e : g[i]) {
				if (dist[e.from] == INF+INF) continue;
				if (dist[e.to] > dist[e.from] + e.cost) {
					dist[e.to] = dist[e.from] + e.cost;
					prev[e.to] = e.from;
					if (k >= gsize-1) {
						dist[e.to] = -INF;
						negative_cycle = true;
					}
				}
			}
		}
	}
	return negative_cycle;
}
//dijkstraはこれ専用に改造されている
//https://dic.kimiyuki.net/johnson-algorithm
//全点対間最短経路問題を解くアルゴリズム
//負閉路を検出するとtrueを返す その場合dist,prevは使えない
//計算量：O(∣V∣^2log∣V∣+∣V∣∣E∣)
bool johnsons_algorithm(const vector<vector<Edge>> &g, vector<vector<EdgeCostType>> &dist, vector<vector<ll>> &prev){
	ll gsize = g.size();
	dist.resize(gsize);
	prev.resize(gsize);
	bool hasminusedge = false;
	vector<vector<Edge>> convertedg(g);
	for (auto&& v : convertedg) for (auto&& edge : v) {
		edge.rawcost = edge.cost;
		if (edge.cost < 0) {
			hasminusedge = true;
		}
	}

	if (hasminusedge) {
		convertedg.emplace_back();
		convertedg.back().reserve(gsize);
		for (ll v = 0; v < gsize; v++) {
			convertedg.back().emplace_back(gsize, v, 0);
		}
		vector<EdgeCostType> bellmandist;
		vector<ll> bellmanprev;
		bool negative_cycle = bellman_ford(convertedg, gsize, bellmandist, bellmanprev);
		if (negative_cycle) return true;
		convertedg.pop_back();
		for (auto&& v : convertedg) for (auto&& edge : v) {
			edge.cost += bellmandist[edge.from] - bellmandist[edge.to];
		}
	}
	for (ll v = 0; v < gsize; v++) {
		dijkstra(convertedg, v, dist[v], prev[v]);
	}
	return false;
}

[[nodiscard]] inline ll up(ll bit, ll i) { return bit | (1LL<<i); }
[[nodiscard]] inline ll down(ll bit, ll i) { return bit & ~(1LL<<i); }
[[nodiscard]] inline ll flip(ll bit, ll i) { return bit ^ (1LL<<i); }
inline bool isup(ll bit, ll i) { return bit & (1LL<<i); }
inline bool isdown(ll bit, ll i) { return !(bit & (1LL<<i)); }
inline ll bsr(ll bit){ assert(bit); return 63 - __builtin_clzll(bit); } //最上位ビットの位置
inline ll bsf(ll bit){ assert(bit); return __builtin_ctzll(bit); } //最下位ビットの位置
//numeric_limits<ll>::digits -> llのビット数の定数
//__builtin_popcountll(bit); -> bitの立っている個数を返す
//__builtin_clzll(bit); -> bitの頭の0の数を返す 0のときは未定義に注意
//__builtin_ctzll(bit); -> bitのお尻の0の数を返す 0のときは未定義に注意
/*
//bitの部分集合を全列挙
for (ll subbit = bit; subbit >= 0; subbit--) {
	subbit &= bit;
	//if(subbit==bit)continue; //全体集合bit自身をスキップ
	//if(subbit==0)continue; //空集合をスキップ
	debug(subbit, bit & ~subbit); // 部分集合、およびその残り
}
*/


//[lib]warshall_floyd.cpp
//計算量：O(N^3)
void warshall_floyd(vector<vector<ll>> &d) {
	ll N=d.size();
	for (ll k=0; k<N; k++) {
		for (ll i=0; i<N; i++) {
			for (ll j=0; j<N; j++){
				if(d[i][k] != INF && d[k][j] != INF && d[i][k] + d[k][j] < d[i][j]){
					d[i][j] = d[i][k] + d[k][j];
				}
			}
		}
	}
}

/*-----8<-----library-----8<-----*/

void solve() {
	ll N, M, K;
	cin>>N>>M>>K;
	vector<ll> a(N);
	rep(i, N) cin >> a[i];

	/*
	vector<vector<Edge>> g(N);

	rep(i,M){
		ll a, b, c;
		cin >> a >> b >> c;
		a--, b--;
		g[a].emplace_back(a, b, c);
		g[b].emplace_back(b, a, c);
	}

	vector<vector<EdgeCostType>> dist;
	vector<vector<ll>> prev;
	bool negative_cycle = johnsons_algorithm(g, dist, prev);
	*/

	vector<vector<ll>> dist(N, vector<ll>(N, INF));
	for (ll i = 0; i < (ll)dist.size(); i++) dist[i][i] = 0;

	for(ll i=0; i<M; i++) {
		ll from,to,cost;
		cin >> from >> to >> cost;
		from--;to--;
		dist[from][to] = cost;
		dist[to][from] = cost;//無向グラフの場合は両方に辺を張る
	}

	warshall_floyd(dist);

	vector<ll> dp(1 << N, INF);
	dp[0] = 0;
	rep(bit, 1LL << N) {
		rep(i,N){
			if (isup(bit, i)) continue;
			ll nextbit = up(bit, i);
			if(bit==0){
				chmin(dp[nextbit], a[i]);
				continue;
			}
			ll t = INF;
			rep(j,N){
				if (isdown(bit, j)) continue;
				ll s = dist[i][j];
				chmin(t, s);
			}
			chmin(dp[nextbit], a[i]+t+dp[bit]);
		}
	}

	ll ans = INF;
	rep(bit,1LL<<N){
		if(__builtin_popcountll(bit)==K){
			chmin(ans, dp[bit]);
		}
	}
	p(ans);
}

signed main() {
#ifndef LOCAL_DEV
	std::cin.tie(nullptr);
	std::ios::sync_with_stdio(false);
#endif
	//ll Q; cin >> Q; while(Q--)solve();
	solve();
	return 0;
}