#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"

const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"

namespace viewer {
void view(const long long &e) {
	if(e == INF)
		std::cerr << "INF";
	else if(e == -INF)
		std::cerr << "-INF";
	else
		std::cerr << e;
}

void view(const int &e) {
	if(e == inf)
		std::cerr << "inf";
	else if(e == -inf)
		std::cerr << "-inf";
	else
		std::cerr << e;
}

template <typename T>
void view(const T &e) {
	std::cerr << e;
}

template <typename T, typename U>
void view(const std::pair<T, U> &p) {
	std::cerr << "(";
	view(p.first);
	std::cerr << ", ";
	view(p.second);
	std::cerr << ")";
}

template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ")";
}

template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ", ";
	view(std::get<3>(p));
	std::cerr << ")";
}

template <typename T>
void view(const std::set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<T> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
	std::cerr << "{\n";
	for(const auto &v : vv) {
		std::cerr << "\t";
		view(v);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
	std::cerr << "{\n";
	for(const auto &c : v) {
		std::cerr << "\t(";
		view(c.first);
		std::cerr << ", ";
		view(c.second);
		std::cerr << ")\n";
	}
	std::cerr << "}";
}

template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <typename T, typename U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}
}  // namespace viewer

// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	viewer::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(0)
#define dump(x)                                      \
	do {                                             \
		std::cerr << __LINE__ << " " << #x << " : "; \
		viewer::view(x);                             \
		std::cerr << '\n';                           \
	} while(0)

#else
#define debug(...) (void(0))
#define dump(x)    (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"

#define pb        push_back
#define eb        emplace_back
#define fi        first
#define se        second
#define SZ(x)     ((int)(x).size())
#define all(x)    (x).begin(), (x).end()
#define rall(x)   (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"

struct fast_io {
	fast_io() {
		std::ios::sync_with_stdio(false);
		std::cin.tie(nullptr);
		std::cout << std::fixed << std::setprecision(15);
	}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < (int)s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"

template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	a = (a % mod + mod) % mod;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
	while(abs(ok - ng) > 1) {
		T mid = (ok + ng) >> 1;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
	for(int i = 0; i < loop; i++) {
		T mid = (ok + ng) / 2;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"


template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
	std::ostream::sentry s(dest);
	if(s) {
		__uint128_t tmp = value < 0 ? -value : value;
		char buffer[128];
		char *d = std::end(buffer);
		do {
			--d;
			*d = "0123456789"[tmp % 10];
			tmp /= 10;
		} while(tmp != 0);
		if(value < 0) {
			--d;
			*d = '-';
		}
		int len = std::end(buffer) - d;
		if(dest.rdbuf()->sputn(d, len) != len) {
			dest.setstate(std::ios_base::badbit);
		}
	}
	return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void println(const T a) { std::cout << a << '\n'; }
template <class T>
void println(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void println(Head H, Tail... T) {
	std::cout << H << '\n';
	println(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"

#define foa(v, a)                   for(auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...)                    repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x)                     for(int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x)                  for(int i = 0; i < (x); ++i)
#define rep2(i, l, r)               for(int i = (l); i < (r); ++i)
#define rep3(i, l, r, c)            for(int i = (l); i < (r); i += (c))

#define repsname(a, b, c, ...) c
#define reps(...)              repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x)               for(int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x)            for(int i = 1; i <= (x); ++i)

#define rrepname(a, b, c, ...) c
#define rrep(...)              rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x)               for(int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x)            for(int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp"

struct string_converter {
	char start = 0;
	char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' :
		                                                    isdigit(c)     ? '0' :
		                                                                     0); }
	int convert(const char &c) {
		if(!start) start = type(c);
		return c - start;
	}
	int convert(const char &c, const std::string &chars) { return chars.find(c); }
	template <typename T>
	auto convert(const T &v) {
		std::vector<decltype(convert(v[0]))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e));
		return ret;
	}
	template <typename T>
	auto convert(const T &v, const std::string &chars) {
		std::vector<decltype(convert(v[0], chars))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e, chars));
		return ret;
	}
	int operator()(const char &v, char s = 0) {
		start = s;
		return convert(v);
	}
	int operator()(const char &v, const std::string &chars) { return convert(v, chars); }
	template <typename T>
	auto operator()(const T &v, char s = 0) {
		start = s;
		return convert(v);
	}
	template <typename T>
	auto operator()(const T &v, const std::string &chars) { return convert(v, chars); }
} toint;
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"

template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...)              SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a)               std::sort((a).begin(), (a).end())
#define SORT1(a, c)            std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
   public:
	cum_vector() = default;
	template <class U>
	cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
		for(int i = 0; i < (int)vec.size(); i++)
			cum[i + 1] = cum[i] + vec[i];
	}
	T prod(int l, int r) {
		return cum[r] - cum[l];
	}

   private:
	std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
	const int n = s.size();
	std::vector<std::pair<char, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and s[l] == s[r]; r++) {}
		ret.emplace_back(s[l], r - l);
		l = r;
	}
	return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
	const int n = v.size();
	std::vector<std::pair<T, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and v[l] == v[r]; r++) {}
		ret.emplace_back(v[l], r - l);
		l = r;
	}
	return ret;
}
std::vector<int> iota(int n) {
	std::vector<int> p(n);
	std::iota(p.begin(), p.end(), 0);
	return p;
}
#line 12 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 2 "a.cpp"

// reference: http://www.cs.kent.edu/~dragan/GraphAn/p23-galil.pdf
class GeneralWeightedMatching {
	struct E {
		int u, v;
		ll w;
	};
	int n, m, in;
	vector<vector<E>> G;
	vector<int> mate, slack, root, par, isS, used;
	vector<vector<int>> flower, belong;
	vector<ll> dual;
	queue<int> que;

	ll dist(const E &e) { return dual[e.u] + dual[e.v] - e.w; }
	void update(int u, int v) {
		if(!slack[v] or dist(G[u][v]) < dist(G[slack[v]][v])) slack[v] = u;
	}
	void recalc(int v) {
		slack[v] = 0;
		rep(i, 1, n + 1) if(G[i][v].w and root[i] != v and isS[root[i]] == 1) update(i, v);
	}
	void push(int v) {
		if(v <= n)
			que.push(v);
		else
			for(auto &nxt : flower[v]) push(nxt);
	}
	void set(int v, int rt) {
		root[v] = rt;
		if(v > n)
			for(auto &nxt : flower[v]) set(nxt, rt);
	}
	int findeven(int b, int v) {
		int pos = find(all(flower[b]), v) - flower[b].begin();
		if(pos & 1) {
			reverse(flower[b].begin() + 1, flower[b].end());
			pos = flower[b].size() - pos;
		}
		return pos;
	}
	void match(int u, int v) {
		mate[u] = G[u][v].v;
		if(u > n) {
			int x = belong[u][G[u][v].u];
			int pos = findeven(u, x);
			rep(i, 0, pos) match(flower[u][i], flower[u][i ^ 1]);
			match(x, v);
			rotate(flower[u].begin(), flower[u].begin() + pos, flower[u].end());
		}
	}
	void link(int u, int v) {
		for(;;) {
			int nv = root[mate[u]];
			match(u, v);
			if(!nv) break;
			v = nv, u = root[par[nv]];
			match(v, u);
		}
	}
	void make(int u, int v, int lca) {
		int id = n + 1;
		while(id <= m and root[id]) id++;
		if(id > m) m++;
		flower[id].clear();
		rep(i, 1, m + 1) G[id][i].w = G[i][id].w = 0;
		rep(i, 1, n + 1) belong[id][i] = 0;
		isS[id] = 1, dual[id] = 0, mate[id] = mate[lca];
		while(u != lca) {
			flower[id].push_back(u);
			u = root[mate[u]];
			push(u);
			flower[id].push_back(u);
			u = root[par[u]];
		}
		flower[id].push_back(lca);
		reverse(all(flower[id]));
		while(v != lca) {
			flower[id].push_back(v);
			v = root[mate[v]];
			push(v);
			flower[id].push_back(v);
			v = root[par[v]];
		}
		set(id, id);
		for(auto &c : flower[id]) {
			rep(i, 1, m + 1) if(!G[id][i].w or dist(G[c][i]) < dist(G[id][i])) {
				G[id][i] = G[c][i], G[i][id] = G[i][c];
			}
			rep(i, 1, n + 1) if(belong[c][i]) belong[id][i] = c;
		}
		recalc(id);
	}
	void expand(int b) {
		for(auto &c : flower[b]) set(c, c);
		int x = belong[b][G[b][par[b]].u];
		isS[x] = 2, par[x] = par[b];
		int pos = findeven(b, x);
		for(int i = 0; i < pos; i += 2) {
			int T = flower[b][i], S = flower[b][i + 1];
			isS[S] = 1, isS[T] = 2;
			par[T] = G[S][T].u;
			slack[S] = slack[T] = 0;
			push(S);
		}
		rep(i, pos + 1, flower[b].size()) {
			isS[flower[b][i]] = 0;
			recalc(flower[b][i]);
		}
		flower[b].clear();
		root[b] = 0;
	}
	bool path(const E &e) {
		int u = root[e.u], v = root[e.v];
		if(!isS[v]) {
			par[v] = e.u;
			isS[v] = 2;
			int nu = root[mate[v]];
			slack[v] = slack[nu] = 0;
			isS[nu] = 1;
			push(nu);
		} else if(isS[v] == 1) {
			int lca = 0, bu = u, bv = v;
			in++;
			while(bu) {
				used[bu] = in;
				bu = root[mate[bu]];
				if(bu) bu = root[par[bu]];
			}
			while(bv) {
				if(used[bv] == in) {
					lca = bv;
					break;
				}
				bv = root[mate[bv]];
				if(bv) bv = root[par[bv]];
			}
			if(lca)
				make(u, v, lca);
			else {
				link(u, v), link(v, u);
				return true;
			}
		}
		return false;
	}
	bool augment() {
		isS = slack = par = vector<int>(n * 2);
		que = queue<int>();
		rep(i, 1, m + 1) if(root[i] == i and !mate[i]) {
			isS[i] = 1;
			push(i);
		}
		if(que.empty()) return false;
		for(;;) {
			while(!que.empty()) {
				int v = que.front();
				que.pop();
				rep(i, 1, n + 1) if(G[v][i].w and root[i] != root[v]) {
					if(!dist(G[v][i])) {
						if(path(G[v][i])) return true;
					} else if(isS[root[i]] != 2)
						update(v, root[i]);
				}
			}
			ll delta = INF;
			rep(i, n + 1, m + 1) if(root[i] == i and isS[i] == 2) chmin(delta, dual[i] / 2);
			rep(i, 1, m + 1) if(root[i] == i and slack[i] and isS[i] != 2) {
				if(!isS[i])
					chmin(delta, dist(G[slack[i]][i]));
				else
					chmin(delta, dist(G[slack[i]][i]) / 2);
			}
			rep(i, 1, n + 1) {
				if(isS[root[i]] == 1) {
					dual[i] -= delta;
					if(dual[i] <= 0) return false;
				} else if(isS[root[i]] == 2)
					dual[i] += delta;
			}
			rep(i, n + 1, m + 1) if(root[i] == i and isS[i]) {
				if(isS[i] == 1)
					dual[i] += delta * 2;
				else
					dual[i] -= delta * 2;
			}
			rep(i, 1, m + 1) if(root[i] == i and slack[i] and root[slack[i]] != i) {
				if(dist(G[slack[i]][i]) == 0 and path(G[slack[i]][i])) return true;
			}
			rep(i, n + 1, m + 1) if(root[i] == i and isS[i] == 2 and dual[i] == 0) expand(i);
		}
	}

   public:
	GeneralWeightedMatching(int _n) : n(_n), m(n), in(0), G(n * 2, vector<E>(n * 2)), mate(n * 2), root(n * 2), used(n * 2), flower(n * 2), belong(n * 2, vector<int>(n * 2)), dual(n * 2) {
		rep(i, 0, n + 1) {
			root[i] = i;
			belong[i][i] = i;
			if(i) dual[i] = INF;
			rep(j, 0, n + 1) G[i][j] = E{i, j, 0};
		}
	}
	void add_edge(int u, int v, ll w) {
		u++, v++;
		chmax(G[u][v].w, w * 2);
		chmax(G[v][u].w, w * 2);
	}
	vector<int> run() {
		while(augment())
			;
		vector<int> res(n, -1);
		rep(i, 1, n + 1) if(mate[i]) res[i - 1] = mate[i] - 1;
		return res;
	}
};


void main_();
int main() {
	int t = 1;
	while(t--) main_();
}

void main_() {
	INT(q);
	VEC(pii, lr, q);
	VEC(ll, a, 2 * q);
	cum_vector<ll> cum(a);
	ll res = 0;
	for(auto [l, r] : lr) {
		res += cum.prod(l - 1, r);
	}
	GeneralWeightedMatching mt(q);
	vector es(q, vector(q, 0ll));
	rep(i, q) {
		auto [l, r] = lr[i];
		rep(j, i + 1, q) {
			auto [l2, r2] = lr[j];
			int lef = max(l, l2);
			int rig = min(r, r2);
			if(lef < rig and ((lef == l and rig == r2) or (lef == l2 and rig == r))) {
				es[i][j] = cum.prod(lef - 1, rig);
				mt.add_edge(i, j, es[i][j]);
			}
		}
	}
	auto vec = mt.run();
	rep(i, q) {
		if(vec[i] > i) {
			res -= es[i][vec[i]];
		}
	}
	print(res);
}