Problem: You are given a tree with N vertices 1,2,\ldots,N, and positive integers c_1,c_2,\ldots,c_N. The i-th edge in the tree (1 \leq i \leq N-1) connects Vertex a_i and Vertex b_i.

We will write a positive integer on each vertex in T and calculate our score as follows:

* On each edge, write the smaller of the integers written on the two endpoints.
* Let our score be the sum of the integers written on all the edges.



Find the maximum possible score when we write each of c_1,c_2,\ldots,c_N on one vertex in T, and show one way to achieve it. If an integer occurs multiple times in c_1,c_2,\ldots,c_N, we must use it that number of times.

Constraints

* 1 \leq N \leq 10000
* 1 \leq a_i,b_i \leq N
* 1 \leq c_i \leq 10^5
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 \ldots c_N


Output

Use the following format:


M
d_1 \ldots d_N


where M is the maximum possible score, and d_i is the integer to write on Vertex i. d_1,d_2,\ldots,d_N must be a permutation of c_1,c_2,\ldots,c_N. If there are multiple ways to achieve the maximum score, any of them will be accepted.

Examples

Input

5
1 2
2 3
3 4
4 5
1 2 3 4 5


Output

10
1 2 3 4 5


Input

5
1 2
1 3
1 4
1 5
3141 59 26 53 59


Output

197
59 26 3141 59 53

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {static int nn=0;
	private static void solve() {
		int n = nei();
		int[][] ab = nis2(n - 1, 2);
		long[] cs = nls(n);
		for (int i = 0; i < n; i++) {
			cs[i] = -cs[i];
		}
		Arrays.sort(cs);
		for (int i = 0; i < n; i++) {
			cs[i] = -cs[i];
		}
		G<Long, Long> g = new G<Long, Long>();
		for (int i = 0; i < n; i++) {
			g.addV(i + 1, 0l);
		}
		for (int i = 0; i < n - 1; i++) {
			g.addUE(ab[i][0], ab[i][1], 0l);
		}
		g.bfs(1, 0, (s, i, j, edg) -> s + 1, (s, v, vs) -> {
			g.setV(v, cs[nn++]);
		});
		long ans = 0;
		for (int i = 1; i < n; i++) {
			ans += cs[i];
		}
		StringBuilder sb = new StringBuilder();
		out(ans);
		for (long l : g.getSortedVs()) {
			if (sb.length() != 0)
				sb.append(" ");
			sb.append(l);
		}
		out(sb);
	}

	// returns (x, y, d) s.t. ax + by = d
	static long[] exgcd(long a, long b) {
		int sa = a < 0 ? -1 : 1;
		int sb = b < 0 ? -1 : 1;
		a *= sa;
		b *= sb;
		long x = 1;
		long y = 0;
		long z = 0;
		long w = 1;
		while (b > 0) {
			long q = a / b;
			long t = z;
			z = x - q * z;
			x = t;
			t = w;
			w = y - q * w;
			y = t;
			t = b;
			b = a - q * b;
			a = t;
		}
		return new long[] { x * sa, y * sb, a };
	}

	static int[] lis(int[] s) {
		int n = s.length;
		int[] dp = new int[n];
		int[] ids = new int[n];
		int[] pids = new int[n];
		dp[0] = s[0];
		int len = 1;
		int lidx = 0;
		for (int i = 1; i < n; i++) {
			int idx = bs(s[i], dp, 0, len);
			dp[idx] = s[i];
			ids[idx] = i;
			if (idx == len) {
				lidx = i;
				len++;
			}
			if (idx > 0)
				pids[i] = ids[idx - 1];
		}
		int[] lis = new int[len];
		lis[len - 1] = s[lidx];
		for (int i = len - 1; i >= 0; i--) {
			lis[i] = s[lidx];
			lidx = pids[lidx];
		}
		return lis;
	}

	static int bs(int a, int[] as, int from, int num) {
		int min = from;
		int max = from + num - 1;
		while (min < max) {
			int mid = min + max >> 1;
			if (as[mid] < a)
				min = mid + 1;
			else if (as[mid] > a)
				max = mid;
			else
				return mid;
		}
		return as[min] < a ? min + 1 : min;
	}

	static int gcd(int x, int y) {
		x = (x ^ x >> 31) - (x >> 31);
		y = (y ^ y >> 31) - (y >> 31);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long gcd(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		long z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long modinv(long a, long mod) {
		return modpow(a, mod - 2, mod);
	}

	static long modpow(long a, long b, long mod) {
		if (b == 0)
			return 1;
		if ((b & 1) == 0) {
			long sqrt = modpow(a, b >> 1, mod);
			return sqrt * sqrt % mod;
		}
		return a * modpow(a, b - 1, mod) % mod;
	}

	static long fact(long n) {
		if (n <= 1)
			return 1;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
		}
		return res;
	}

	static long modfact(long n, long mod) {
		if (n <= 1)
			return 1 % mod;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
			res %= mod;
		}
		return res % mod;
	}

	// returns facts([0]) and invfacts([1])
	static long[][] enumfacts(int n, long mod) {
		int num = n + 10;
		long[][] res = new long[2][num];
		long[] facts = res[0];
		long[] invfacts = res[1];
		for (int i = 0; i < num; i++) {
			if (i <= 1) {
				facts[i] = 1;
				invfacts[i] = 1;
			} else {
				facts[i] = facts[i - 1] * i % mod;
				invfacts[i] = modinv(facts[i], mod);
			}
		}
		return res;
	}

	static long modcomb(long n, long m, long mod) {
		if (m > n)
			return 0;
		if (m > n - m) {
			m = n - m;
		}
		long numer = 1;
		for (int i = 0; i < m; i++) {
			numer = numer * (n - i) % mod;
		}
		long denom = modfact(m, mod);
		return numer * modinv(denom, mod) % mod;
	}

	static long modcomb(int n, int m, long[] facts, long[] invfacts, long mod) {
		if (m > n)
			return 0;
		long numer = facts[n];
		long denom = invfacts[m] * invfacts[n - m] % mod;
		return numer * denom % mod;
	}

	// res[i][0]: prime factor, res[i][1]: exponent
	static int[][] factorize(int n) {
		int[][] pfs = new int[32][2];
		int num = 0;
		for (int i = 2; i * i <= n; i++) {
			int count = 0;
			while (n % i == 0) {
				n /= i;
				count++;
			}
			if (count > 0) {
				pfs[num][0] = i;
				pfs[num][1] = count;
				num++;
			}
		}
		if (n > 1) {
			pfs[num][0] = n;
			pfs[num][1] = 1;
			num++;
		}
		int[][] res = new int[num][2];
		for (int i = 0; i < num; i++) {
			res[i][0] = pfs[i][0];
			res[i][1] = pfs[i][1];
		}
		return res;
	}

	static long lcm(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		return x / gcd(x, y) * y;
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static long abs(long x) {
		return x < 0 ? -x : x;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static double clamp(double a, double min, double max) {
		return a < min ? min : a > max ? max : a;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(Object val) {
		IO.out(String.valueOf(val));
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(val ? "true" : "false");
	}

	static void kil(String val) {
		IO.out(val);
		IO.flush();
		System.exit(0);
	}

	static void kil(Object val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(int val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(long val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(char val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(boolean val) {
		IO.out(val ? "true" : "false");
		IO.flush();
		System.exit(0);
	}

	static String nes() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static double ned() {
		return IO.nextDouble();
	}

	static char nec() {
		return IO.nextChar();
	}

	static String[] nss(int n) {
		String[] as = new String[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.next();
		}
		return as;
	}

	static int[] nis(int n) {
		int[] as = new int[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextInt();
		}
		return as;
	}

	static long[] nls(int n) {
		long[] as = new long[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextLong();
		}
		return as;
	}

	static double[] nds(int n) {
		double[] as = new double[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextDouble();
		}
		return as;
	}

	static char[] ncs(int n) {
		char[] as = new char[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextChar();
		}
		return as;
	}

	static String[][] nss2(int n, int m) {
		String[][] as = new String[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.next();
			}
		}
		return as;
	}

	static int[][] nis2(int n, int m) {
		int[][] as = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextInt();
			}
		}
		return as;
	}

	static long[][] nls2(int n, int m) {
		long[][] as = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextLong();
			}
		}
		return as;
	}

	static double[][] nds2(int n, int m) {
		double[][] as = new double[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextDouble();
			}
		}
		return as;
	}

	static char[][] ncs2(int n, int m) {
		char[][] as = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextChar();
			}
		}
		return as;
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		try {
			solve();
			IO.flush();
		} catch (NumberFormatException e) {
			e.printStackTrace();
		}
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		return (char) readByte();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}

class Rev<A extends Comparable<A>> implements Comparable<Rev<A>> {
	A a;

	Rev(A a) {
		this.a = a;
	}

	static <A extends Comparable<A>> Rev<A> make(A a) {
		return new Rev<A>(a);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof Rev))
			return false;
		Rev<?> r = (Rev<?>) o;
		return a == null ? r.a == null : a.equals(r.a);
	}

	public int compareTo(Rev<A> o) {
		return -a.compareTo(o.a);
	}

	public String toString() {
		return "-(" + a.toString() + ")";
	}
}

class Flat<A> implements Comparable<Flat<A>> {
	A a;

	Flat(A a) {
		this.a = a;
	}

	static <A> Flat<A> make(A a) {
		return new Flat<A>(a);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof Flat))
			return false;
		Flat<?> r = (Flat<?>) o;
		return a == null ? r.a == null : a.equals(r.a);
	}

	public int compareTo(Flat<A> o) {
		return 0;
	}

	public String toString() {
		return "0(" + a.toString() + ")";
	}
}

class UP<A, B> { // Unordered Pair
	A a;
	B b;

	UP(A a, B b) {
		this.a = a;
		this.b = b;
	}

	static <A, B> UP<A, B> make(A a, B b) {
		return new UP<A, B>(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UP))
			return false;
		UP<?, ?> p = (UP<?, ?>) o;
		boolean aok = a == null ? p.a == null : a.equals(p.a);
		boolean bok = b == null ? p.b == null : b.equals(p.b);
		return aok && bok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ")";
	}
}

class P<A extends Comparable<A>, B extends Comparable<B>> extends UP<A, B> implements Comparable<P<A, B>> { // Pair
	P(A a, B b) {
		super(a, b);
	}

	static <A extends Comparable<A>, B extends Comparable<B>> P<A, B> make(A a, B b) {
		return new P<A, B>(a, b);
	}

	public int compareTo(P<A, B> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		return sa != 0 ? sa : sb;
	}
}

class UT<A, B, C> { // Unordered Tuple
	A a;
	B b;
	C c;

	UT(A a, B b, C c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static <A, B, C> UT<A, B, C> make(A a, B b, C c) {
		return new UT<A, B, C>(a, b, c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UT))
			return false;
		UT<?, ?, ?> t = (UT<?, ?, ?>) o;
		boolean aok = a == null ? t.a == null : a.equals(t.a);
		boolean bok = b == null ? t.b == null : b.equals(t.b);
		boolean cok = c == null ? t.c == null : c.equals(t.c);
		return aok && bok && cok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ", " + c.toString() + ")";
	}
}

class T<A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> extends UT<A, B, C> implements
		Comparable<T<A, B, C>> { // Tuple
	T(A a, B b, C c) {
		super(a, b, c);
	}

	static <A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> T<A, B, C> make(A a, B b, C c) {
		return new T<A, B, C>(a, b, c);
	}

	public int compareTo(T<A, B, C> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		int sc = c.compareTo(o.c);
		return sa != 0 ? sa : sb != 0 ? sb : sc;
	}
}

interface F1<A> {
	A f();
}

interface F2<A, B> {
	B f(A a);
}

interface F3<A, B, C> {
	C f(A a, B b);
}

interface F4<A, B, C, D> {
	D f(A a, B b, C c);
}

interface F5<A, B, C, D, E> {
	E f(A a, B b, C c, D d);
}

interface F1V<A> {
	void f(A a);
}

interface F2V<A, B> {
	void f(A a, B b);
}

interface F3V<A, B, C> {
	void f(A a, B b, C c);
}

interface F4V<A, B, C, D> {
	void f(A a, B b, C c, D d);
}

interface F5V<A, B, C, D, E> {
	void f(A a, B b, C c, D d, E e);
}

class U { // Utilities
	static <A> ArrayList<A> make(int n, F2<Integer, A> maker) {
		ArrayList<A> res = new ArrayList<A>();
		for (int i = 0; i < n; i++)
			res.add(maker.f(i));
		return res;
	}

	static <A> ArrayList<A> filter(ArrayList<A> as, F2<A, Boolean> pred) {
		ArrayList<A> res = new ArrayList<A>();
		for (A a : as)
			if (pred.f(a))
				res.add(a);
		return res;
	}

	static <A> int count(ArrayList<A> as, F2<A, Boolean> pred) {
		int res = 0;
		for (A a : as)
			if (pred.f(a))
				res++;
		return res;
	}

	static <A> ArrayList<A> concat(ArrayList<A> as, ArrayList<A> bs) {
		ArrayList<A> res = new ArrayList<A>();
		res.addAll(as);
		res.addAll(bs);
		return res;
	}

	static <A> boolean any(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (pred.f(a))
				return true;
		return false;
	}

	static <A> boolean all(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (!pred.f(a))
				return false;
		return true;
	}

	static <A> ArrayList<A> flatten(ArrayList<ArrayList<A>> ass) {
		ArrayList<A> res = new ArrayList<A>();
		for (ArrayList<A> as : ass)
			res.addAll(as);
		return res;
	}

	static <A, B> B foldl(ArrayList<A> as, F3<B, A, B> f, B e) {
		B res = e;
		for (A a : as)
			res = f.f(res, a);
		return res;
	}

	static <A, B> B foldr(ArrayList<A> as, F3<A, B, B> f, B e) {
		B res = e;
		for (int i = as.size() - 1; i >= 0; i--)
			res = f.f(as.get(i), res);
		return res;
	}

	static <A> ArrayList<A> reverse(ArrayList<A> as) {
		int size = as.size();
		return make(size, i -> as.get(size - 1 - i));
	}

	static <A> void forEach(ArrayList<A> as, F1V<A> f) {
		for (A a : as)
			f.f(a);
	}

	static <A extends Comparable<A>> UP<TreeMap<A, Integer>, ArrayList<A>> compress(ArrayList<A> as) {
		TreeSet<A> set = new TreeSet<A>(as);
		TreeMap<A, Integer> map = new TreeMap<A, Integer>();
		ArrayList<A> imap = new ArrayList<A>();
		int i = 0;
		for (A a : set) {
			map.put(a, i++);
			imap.add(a);
		}
		return UP.make(map, imap);
	}

	static <A, B> ArrayList<B> map(ArrayList<A> as, F2<A, B> f) {
		return make(as.size(), (i) -> f.f(as.get(i)));
	}

	static <A, B> ArrayList<UP<A, B>> zip(ArrayList<A> as, ArrayList<B> bs) {
		return make(min(as.size(), bs.size()), (i) -> UP.make(as.get(i), bs.get(i)));
	}

	static <A extends Comparable<A>> A min(A a, A b) {
		return a.compareTo(b) < 0 ? a : b;
	}

	static <A extends Comparable<A>> A max(A a, A b) {
		return a.compareTo(b) > 0 ? a : b;
	}

	static <A extends Comparable<A>> A clamp(A a, A min, A max) {
		return a.compareTo(min) < 0 ? min : a.compareTo(max) > 0 ? max : a;
	}

	static <A> A[] doubleSize(A[] as) {
		return Arrays.copyOf(as, as.length << 1);
	}
}

@SuppressWarnings("unchecked")
class G<V, E> { // Graph
	private int vSize;
	private Object[] vs; // V
	private Object[] esFrom; // EdgeSet
	private Object[] esTo; // EdgeSet
	private Object[] pool; // UP<Object, Integer>
	private Integer[] ints;
	private int poolCounter;

	private class EdgeSet {
		HashMap<Integer, E> map;
		Integer[] is;
		Object[] es;
		int size;

		EdgeSet() {
			is = new Integer[2];
			es = new Object[2];
			size = 0;
		}

		void add(Integer i, E e) {
			if (size > 16) {
				map.put(i, e);
				size++;
				return;
			}
			if (size == is.length) {
				is = Arrays.copyOf(is, size << 1);
				es = Arrays.copyOf(es, size << 1);
			}
			is[size] = i;
			es[size] = e;
			if (++size > 16) {
				map = new HashMap<Integer, E>();
				for (int j = 0; j < size; j++) {
					map.put(is[j], (E) es[j]);
				}
				is = null;
				es = null;
			}
		}

		void iter(F2V<Integer, E> f) {
			if (map == null)
				for (int i = 0; i < size; i++)
					f.f(is[i], (E) es[i]);
			else
				for (Entry<Integer, E> e : map.entrySet())
					f.f(e.getKey(), e.getValue());
		}
	}

	G() {
		vs = new Object[64];
		esFrom = new Object[64];
		esTo = new Object[64];
		pool = new Object[64];
		ints = new Integer[64];
		vSize = 0;
	}

	V getV(int i) {
		return i < 0 || i >= vs.length ? null : (V) vs[i];
	}

	ArrayList<V> getSortedVs() {
		ArrayList<V> res = new ArrayList<V>();
		for (int i = 0; i < vs.length; i++) {
			if (vs[i] != null)
				res.add((V) vs[i]);
		}
		return res;
	}

	void addV(int i, V v) {
		if (getV(i) != null)
			throw new RuntimeException("duplicate vtx: " + i);
		while (vs.length <= i) {
			vs = U.doubleSize(vs);
			ints = U.doubleSize(ints);
			esFrom = U.doubleSize(esFrom);
			esTo = U.doubleSize(esTo);
			pool = U.doubleSize(pool);
		}
		vSize = U.max(vSize, i + 1);
		vs[i] = v;
		ints[i] = Integer.valueOf(i);
		esFrom[i] = new EdgeSet();
		esTo[i] = new EdgeSet();
		pool[i] = UP.make(null, 0);
	}

	void setV(int i, V v) {
		if (getV(i) == null)
			throw new RuntimeException("no such vtx: " + i);
		vs[i] = v;
	}

	void addE(int from, int to, E e) {
		((EdgeSet) esFrom[from]).add(ints[to], e);
		((EdgeSet) esTo[to]).add(ints[from], e);
	}

	void addUE(int i, int j, E e) {
		addE(i, j, e);
		addE(j, i, e);
	}

	<State> void dfs(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit) {
		ArrayDeque<UP<Object, Integer>> deque = new ArrayDeque<UP<Object, Integer>>();
		search(firstIdx, firstS, nextState, visit, deque::push, deque::pop, deque::isEmpty);
	}

	<State> void bfs(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit) {
		ArrayDeque<UP<Object, Integer>> deque = new ArrayDeque<UP<Object, Integer>>();
		search(firstIdx, firstS, nextState, visit, deque::addLast, deque::pollFirst, deque::isEmpty);
	}

	private <State> void search(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit, F1V<UP<Object, Integer>> push, F1<UP<Object, Integer>> pop,
			F1<Boolean> isEmpty) {
		boolean[] visited = new boolean[vSize];
		ArrayList<Integer> movedTo = new ArrayList<Integer>();
		push.f(UP.make(firstS, firstIdx));
		visited[firstIdx] = true;
		while (!isEmpty.f()) {
			UP<Object, Integer> si = pop.f();
			State s = (State) si.a;
			Integer i = si.b;
			movedTo.clear();
			((EdgeSet) esFrom[i]).iter((j, e) -> {
				if (visited[j])
					return;
				State ns = nextState.f(s, i, j, e);
				if (ns != null) {
					movedTo.add(j);
					push.f(pick(ns, j));
					visited[j] = true;
				}
			});
			visit.f(s, i, movedTo);
		}
	}

	private UP<Object, Integer> pick(Object o, Integer i) {
		return UP.make(o, i);
	}
}