Problem: There are N jewelry shops numbered 1 to N.

Shop i (1 \leq i \leq N) sells K_i kinds of jewels. The j-th of these jewels (1 \leq j \leq K_i) has a size and price of S_{i,j} and P_{i,j}, respectively, and the shop has C_{i,j} jewels of this kind in stock.

A jewelry box is said to be good if it satisfies all of the following conditions:

* For each of the jewelry shops, the box contains one jewel purchased there.
* All of the following M restrictions are met.
* Restriction i (1 \leq i \leq M): (The size of the jewel purchased at Shop V_i)\leq (The size of the jewel purchased at Shop U_i)+W_i



Answer Q questions. In the i-th question, given an integer A_i, find the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes. If it is impossible to make A_i good jewelry boxes, report that fact.

Constraints

* 1 \leq N \leq 30
* 1 \leq K_i \leq 30
* 1 \leq S_{i,j} \leq 10^9
* 1 \leq P_{i,j} \leq 30
* 1 \leq C_{i,j} \leq 10^{12}
* 0 \leq M \leq 50
* 1 \leq U_i,V_i \leq N
* U_i \neq V_i
* 0 \leq W_i \leq 10^9
* 1 \leq Q \leq 10^5
* 1 \leq A_i \leq 3 \times 10^{13}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
Description of Shop 1
Description of Shop 2
\vdots
Description of Shop N
M
U_1 V_1 W_1
U_2 V_2 W_2
\vdots
U_M V_M W_M
Q
A_1
A_2
\vdots
A_Q


The description of Shop i (1 \leq i \leq N) is in the following format:


K_i
S_{i,1} P_{i,1} C_{i,1}
S_{i,2} P_{i,2} C_{i,2}
\vdots
S_{i,K_i} P_{i,K_i} C_{i,K_i}


Output

Print Q lines. The i-th line should contain the minimum total price of jewels that need to be purchased to make A_i good jewelry boxes, or -1 if it is impossible to make them.

Examples

Input

3
2
1 10 1
3 1 1
3
1 10 1
2 1 1
3 10 1
2
1 1 1
3 10 1
2
1 2 0
2 3 0
3
1
2
3


Output

3
42
-1


Input

5
5
86849520 30 272477201869
968023357 28 539131386006
478355090 8 194500792721
298572419 6 894877901270
203794105 25 594579473837
5
730211794 22 225797976416
842538552 9 420531931830
871332982 26 81253086754
553846923 29 89734736118
731788040 13 241088716205
5
903534485 22 140045153776
187101906 8 145639722124
513502442 9 227445343895
499446330 6 719254728400
564106748 20 333423097859
5
332809289 8 640911722470
969492694 21 937931959818
207959501 11 217019915462
726936503 12 382527525674
887971218 17 552919286358
5
444983655 13 487875689585
855863581 6 625608576077
885012925 10 105520979776
980933856 1 711474069172
653022356 19 977887412815
10
1 2 231274893
2 3 829836076
3 4 745221482
4 5 935448462
5 1 819308546
3 5 815839350
5 3 513188748
3 1 968283437
2 3 202352515
4 3 292999238
10
510266667947
252899314976
510266667948
374155726828
628866122125
628866122123
1
628866122124
510266667949
30000000000000


Output

26533866733244
13150764378752
26533866733296
19456097795056
-1
33175436167096
52
33175436167152
26533866733352
-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair 
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) { 
	bool fst = 1; str res = "{";
	F0R(i,sz(v)) {
		if (!fst) res += ", ";
		fst = 0; res += ts(v[i]);
	}
	res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
	str res = ""; F0R(i,SZ) res += char('0'+b[i]);
	return res; }
template<class T> str ts(T v) {
	bool fst = 1; str res = "{";
	for (const auto& x: v) {
		if (!fst) res += ", ";
		fst = 0; res += ts(x);
	}
	res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
	return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
	pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
	pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
	cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
	DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
	unsyncIO();
	// cin.exceptions(cin.failbit); 
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

/**
 * Description: Minimum-cost maximum flow, assumes no negative cycles. 
 	* Edges may be negative only during first run of SPFA.
 * Time: $O(FM\log M)$ if caps are integers and $F$ is max flow
 * Source: GeeksForGeeks
 	* https://courses.csail.mit.edu/6.854/06/scribe/s12-minCostFlowAlg.pdf
 	* running time is only pseudo-polynomial; see https://codeforces.com/blog/entry/70740
 * Verification: https://codeforces.com/contest/164/problem/C
 */

template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
template<class T> T poll(pqg<T>& x) {
	T y = x.top(); x.pop(); return y; }

template<int SZ> struct MCMF { 
	typedef ll F; typedef ll C;
	struct Edge { int to, rev; F flow, cap; C cost; };
	vector<Edge> adj[SZ];
	void ae(int u, int v, F cap, C cost) {
		ckmax(N,max(u,v)+1);
		assert(cap >= 0);
		Edge a{v,sz(adj[v]),0,cap,cost}, b{u,sz(adj[u]),0,0,-cost};
		adj[u].pb(a), adj[v].pb(b);
	}
	int N, s, t;
	pi pre[SZ]; // previous vertex, edge label on path
	pair<C,F> cost[SZ]; // tot cost of path, amount of flow
	C totCost, curCost; F totFlow; 
	bool spfa() { // find lowest cost path to send flow through
		F0R(i,N) cost[i] = {numeric_limits<C>::max(),0}; 
		cost[s] = {0,numeric_limits<F>::max()};
		pqg<pair<C,int>> todo; todo.push({0,s});
		while (sz(todo)) {
			auto x = poll(todo); if (x.f > cost[x.s].f) continue;
			trav(a,adj[x.s]) if (a.flow < a.cap 
				&& ckmin(cost[a.to].f,x.f+a.cost)) { 
				// if costs are doubles, add some small constant so
				// you don't traverse some ~0-weight cycle repeatedly
				pre[a.to] = {x.s,a.rev};
				cost[a.to].s = min(a.cap-a.flow,cost[x.s].s);
				todo.push({cost[a.to].f,a.to});
			}
		}
		return cost[t].s;
	}
	vpl paths;
	void backtrack() {
		F df = cost[t].s; totFlow += df;
		curCost += cost[t].f; totCost += curCost*df;
		paths.pb({curCost,df});
		for (int x = t; x != s; x = pre[x].f) {
			adj[x][pre[x].s].flow -= df;
			adj[pre[x].f][adj[x][pre[x].s].rev].flow += df;
		}
		F0R(i,N) trav(p,adj[i]) p.cost += cost[i].f-cost[p.to].f;
		// all reduced costs non-negative
		// edges on shortest path become 0
	}
	vpl calc(int _s, int _t) {
		s = _s, t = _t; totFlow = totCost = curCost = 0;
		while (spfa()) {
			backtrack();
			if (paths.bk.s >= INF/2) break;
		}
		return paths;
	}
};

MCMF<1000> D;

int N,M;
vector<array<ll,3>> todo[31];
map<pi,int> m;
int nex = 2;

int label(int x, int y) {
	if (!m.count({x,y})) m[{x,y}] = nex++;
	return m[{x,y}];
}

int main() {
	setIO(); re(N); // help I don't remember how duality works D:
	int SRC = 0, SNK = 1;
	FOR(i,1,N+1) {
		int K; re(K); // dbg(i,K);
		F0R(j,K) {
			ll S,P,C; re(S,P,C);
			todo[i].pb({S,P,C});
		}
		sort(all(todo[i]));
		F0R(j,K) {
			D.ae(label(i,j),label(i,j+1),todo[i][j][1],0);
			D.ae(label(i,j),label(i,j+1),INF,todo[i][j][2]);
		}
		D.ae(SRC,label(i,0),INF,0);
		D.ae(label(i,K),SNK,INF,0);
		// x(i,0)=0, x(i,K)=A
		// x(i,ind+1) <= x(i,ind)+C_{ind}
		// x(i,ind+1)-x(i,ind) <= C_{ind} EDGE
		// x(i,ind)-x(i,ind+1) >= -C_{ind} 
		// x(i,k)-D <= A
		// D-x(i,k) <= -A // minimize
		// x(i,0)-D <= 0
	}
	// original problem: you want to MINIMIZE sum(p_?*x_i)
	re(M); // dbg(M);
	F0R(i,M) {
		int U,V,W; re(U,V,W); // dbg(U,V,W);
		int ind = 0;
		F0R(j,sz(todo[V])) {
			while (ind < sz(todo[U]) && todo[U][ind][0] < todo[V][j][0]-W)
				ind ++;
			//ps("HUH",mp(U,ind),mp(V,j));
			D.ae(label(V,j),label(U,ind),INF,0);
			// dbg(U,ind,V,j);
			// x(U,ind) <= x(V,j)
			// x(U,ind)-x(V,j) <= 0 EDGE
			// x(V,j)-x(U,ind) >= 0 **
		}
	}
	// ps(D.calc(0,1));
	// want to minimize sum(P(i,ind)*(x(i,ind+1)-x(i,ind)))
	// = (P_{i,ind-1}-P_{i,ind})*x(i,ind)
	auto p = D.calc(0,1); // cost, flow
	vpl stor;
	ll x = 0, y = 0;
	trav(t,p) {
		stor.pb({x,y});
		x += t.s; y += t.f*t.s;
	}
	// dbg(p);
	// ps("WUT",p);
	int Q; re(Q); dbg(Q);
	vl A(Q); re(A);
	trav(t,A) {
		auto ind = lb(all(p),mp(t,-INF))-begin(p);
		if (ind == sz(p)) ps(-1);
		else ps(stor[ind].f*t-stor[ind].s);
	}
	// you should actually read the stuff at the bottom
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
	* do smth instead of nothing and stay organized
	* WRITE STUFF DOWN
*/