Problem: A maze is composed of a grid of H \times W squares - H vertical, W horizontal.

The square at the i-th row from the top and the j-th column from the left - (i,j) - is a wall if S_{ij} is `#` and a road if S_{ij} is `.`.

There is a magician in (C_h,C_w). He can do the following two kinds of moves:

* Move A: Walk to a road square that is vertically or horizontally adjacent to the square he is currently in.
* Move B: Use magic to warp himself to a road square in the 5\times 5 area centered at the square he is currently in.



In either case, he cannot go out of the maze.

At least how many times does he need to use the magic to reach (D_h, D_w)?

Constraints

* 1 \leq H,W \leq 10^3
* 1 \leq C_h,D_h \leq H
* 1 \leq C_w,D_w \leq W
* S_{ij} is `#` or `.`.
* S_{C_h C_w} and S_{D_h D_w} are `.`.
* (C_h,C_w) \neq (D_h,D_w)

Input

Input is given from Standard Input in the following format:


H W
C_h C_w
D_h D_w
S_{11}\ldots S_{1W}
\vdots
S_{H1}\ldots S_{HW}


Output

Print the minimum number of times the magician needs to use the magic. If he cannot reach (D_h,D_w), print `-1` instead.

Examples

Input

4 4
1 1
4 4
..#.
..#.
.#..
.#..


Output

1


Input

4 4
1 4
4 1
.##.


.##.


Output

-1


Input

4 4
2 2
3 3
....
....
....
....


Output

0


Input

4 5
1 2
2 5
.###
.
..##
..##


Output

2

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.NoSuchElementException;

public class Main {

	//PriorityQueueは拡張for文で出すとsortされてない順番で出てくる
	//longのbit演算は1L<<posに注意
	//long long
	//JOIはMLEが厳しい。shortを使う。rrayListはオートボクシングが遅いから、自作listが早い

	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);

		int h = sc.nexI();
		int w = sc.nexI();
		int sy = sc.nexI()-1;
		int sx = sc.nexI()-1;
		int gy = sc.nexI()-1;
		int gx = sc.nexI()-1;

		boolean[][] moval = new boolean[h][w];
		
		for(int i=0; i<h; i++){
		    String line = sc.next();
		    for(int j=0; j<w; j++){
		        moval[i][j] = (line.charAt(j)=='.');
		    }
		}

		int[][] seen = new int[h][w];
		fill(seen, -1);
		
		int moving = -1;	//0-indexedにするため
		ArrayDeque<Vector> bfs = new ArrayDeque<>();
		for(int i=0; i<h; i++) {
			for(int j=0; j<w; j++) {
				if(moval[i][j] && (seen[i][j]<0)) {
					moving++;
					seen[i][j]=moving;
					bfs.add(new Vector(j, i));
					while (bfs.size()>0) {
						Vector dw = bfs.poll();
						for(int k=0; k<4; k++) {
							int neX = dw.x+Xdir4[k];
							int neY = dw.y+Ydir4[k];
							if(is_in_area(neY, neX, h, w)) {
								if(moval[neY][neX] && (seen[neY][neX]<0)) {
									seen[neY][neX] = moving;
									bfs.add(new Vector(neX, neY));
								}
							}
						}
					}
				}
			}
		}
		ArrayList<HashSet<Integer>> graph = new ArrayList<>();
		for (int i = 0; i <= moving; i++) {
			graph.add(new HashSet<Integer>());
		}
		
		for(int i=0; i<h; i++) {
			for(int j=0; j<w; j++) {
				if(!moval[i][j]) continue;
				for(int dx=-2; dx<=2; dx++) {
					for(int dy=-2; dy<=2; dy++) {
						if(is_in_area(i+dy, j+dx, h, w)) {
							if(moval[i+dy][j+dx] && (seen[i][j] != seen[i+dy][j+dx])) {
								int a1 = seen[i][j], b1 = seen[i+dy][j+dx];
								if(!graph.get(a1).contains(b1)) {
									graph.get(a1).add(b1);
									graph.get(b1).add(a1);
								}
							}
						}
					}
				}
			}
		}
		
		int[] d8s = new int[moving+1];
		fill(d8s, INF);
		d8s[seen[sy][sx]]=0;
		
		ArrayDeque<Integer> todo = new ArrayDeque<>();
		todo.add(seen[sy][sx]);
		while(todo.size()>0) {
			int dw = todo.poll();
			int disnew = d8s[dw]+1;
			for(int e: graph.get(dw)) {
				if(d8s[e]>disnew) {
					d8s[e]= disnew;
					todo.add(e);
				}
			}
		}
		
		int ans = d8s[seen[gy][gx]];
		if(ans==INF) out.println(-1);
		else out.println(ans);
		
		out.flush();
		return;
	}
    
	private static int INF = 100000000;
	private static long INFL = 100000000000000000L;
	private static long e97 = 1000000007L;
	private static long e99 = 998244353L;

	private static void assertion(boolean b) {
		if(!b) throw new AssertionError();
	}

	private static int pow2(int in) {
		return in*in;
	}
	private static long pow2(long in) {
		return in*in;
	}
	private static double pow2(double in) {
		return in*in;
	}

	private static int getDigit2(long num) {
		long cf = 1;
		int d = 0;
		while(num > cf) {
			d ++;
			cf = (1L<<d);
		}
		return d; //numは2^d以下
	}
	private static int getDigit10(long num) {
		long cf = 1L;
		int d = 0;
		while(num >= cf) {
			d ++;
			cf *= 10L;
		}
		return d; //numはd桁の数で、10^dより小さい

	}

	private static int divceil(int nume, int deno) {
		return (nume+deno-1)/deno;
	}
	private static long divceil(long nume, long deno) {
		return (nume+deno-1L)/deno;
	}

	private static boolean isINF(long in) {
		if((in*20L)>INF) return true;
		else return false;
	}
	private static boolean isINFL(long in) {
		if((in*10L)>INFL) return true;
		else return false;
	}

	public static int biSearchMax(long[] dt, long target) {
		int left=-1, right=dt.length, mid=-1;
		while((right-left)>1) {
			mid = (right+left)/2;
			if(dt[mid] < target) left=mid;
			else right=mid;
		}
		return left;	//target未満の最大のaddress
	}
	public static int biSearchmin(long[] dt, long target) {	//単調減少文字列
		int left=-1, right=dt.length, mid=-1;
		while((right-left)>1) {
			mid = (right+left)/2;
			if(dt[mid] > target) left=mid;
			else right=mid;
		}
		return left;	//targetより大きい最大のaddress
	}
	public static int biSearchMaxAL(ArrayList<Long> dt, long target) {
		int left=-1, right=dt.size(), mid=-1;
		while((right-left)>1) {
			mid = (right+left)/2;
			if(dt.get(mid) <= target) left=mid;
			else right=mid;
		}
		return left;//target以下の最大のaddress
	}

	private static int[] Xdir4 = {1,0,0,-1};
	private static int[] Ydir4 = {0,1,-1,0};
	private static int[] Xdir8 = {1,1,1,0,0,-1,-1,-1};
	private static int[] Ydir8 = {1,0,-1,1,-1,1,0,-1};

	private static boolean is_in_area(int y, int x, int h, int w) {
		if(y < 0) return false;
		if(x < 0) return false;
		if(y >= h) return false;
		if(x >= w) return false;
		return true;
	}

	private static int abs(int a) {
		return (a>=0) ? a: -a;
	}
	private static long abs(long a) {
		return (a>=0) ? a: -a;
	}
	private static double abs(double a) {
		return (a>=0) ? a: -a;
	}

	private static int min(int a, int b) {
		return (a>b) ? b : a;
	}
	private static long min(long a, long b) {
		return (a>b) ? b : a;
	}
	private static double min(double a, double b) {
		return (a>b) ? b : a;
	}

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

	private static int minN(int... ins) {
		int min = ins[0];
		for(int i=1; i<ins.length; i++) {
			if(ins[i] < min) min = ins[i];
		}
		return min;
	}
	private static long minN(long... ins) {
		long min = ins[0];
		for(int i=1; i<ins.length; i++) {
			if(ins[i] < min) min = ins[i];
		}
		return min;
	}
	private static int maxN(int... ins) {
		int max = ins[0];
		for(int i=1; i<ins.length; i++) {
			if(ins[i] > max) max = ins[i];
		}
		return max;
	}
	private static long maxN(long... ins) {
		long max = ins[0];
		for(int i=1; i<ins.length; i++) {
			if(ins[i] > max) max = ins[i];
		}
		return max;
	}

	private static int minExAd(int[] dt, int ad) {
		int min = Integer.MAX_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((i!=ad) && (dt[i]<min)) min = dt[i];
		}
		return min;
	}
	private static long minExAd(long[] dt, int ad) {
		long min = Long.MAX_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((i!=ad) && (dt[i]<min)) min = dt[i];
		}
		return min;
	}
	private static int minExVal(int[] dt, int ex_val) {
		int min = Integer.MAX_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((dt[i]!=ex_val) && (dt[i]<min)) min = dt[i];
		}
		return min;
	}
	private static long minExVal(long[] dt, long ex_val) {
		long min = Long.MAX_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((dt[i]!=ex_val) && (dt[i]<min)) min = dt[i];
		}
		return min;
	}
	private static int maxExAd(int[] dt, int ad) {
		int max = Integer.MIN_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((i!=ad) && (dt[i]>max)) max = dt[i];
		}
		return max;
	}
	private static long maxExAd(long[] dt, int ad) {
		long max = Long.MIN_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((i!=ad) && (dt[i]>max)) max = dt[i];
		}
		return max;
	}
	private static int maxExVal(int[] dt, int ex_val) {
		int max = Integer.MIN_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((dt[i]!=ex_val) && (dt[i]>max)) max = dt[i];
		}
		return max;
	}
	private static long maxExVal(long[] dt, long ex_val) {
		long max = Long.MIN_VALUE;
		for(int i=0; i<dt.length; i++) {
			if((dt[i]!=ex_val) && (dt[i]>max)) max = dt[i];
		}
		return max;
	}

	private static int sumA(int[] dt) {
		int sum = 0;
		for(int e: dt) {
			sum += e;
		}
		return sum;
	}
	private static long sumA(long[] dt) {
		long sum = 0L;
		for(long e: dt) {
			sum += e;
		}
		return sum;
	}
	private static long sumA(ArrayList<Long> dt) {
		long sum =0L;
		for(long e: dt) {
			sum += e;
		}
		return sum;
	}

	private static int pow(int n, int k) {
		int ans = 1;
		for(int i=0; i<k; i++) {
			ans *= n;
			assertion(n>=0);
		}
		return ans;
	}
	private static long pow(long n, int k) {
		long ans = 1L;
		for(int i=0; i<k; i++) {
			ans *= n;
			assertion(n>=0L);
		}
		return ans;
	}

	private static double hypod(double a, double b) {
		return Math.sqrt(a*a+b*b);
	}

	private static long factorial(int n) {
		long ans=1L;
		for(long i=n; i>0; i--) {
			ans *= i;
			assertion(ans>=0L);
		}
		return ans;
	}
	private static long facP(int n, long p) {
		long ans=1L;
		for(long i=n; i>0; i--) {
			ans *= i;
			ans %= p;
		}
		return ans;
	}

	private static long lcm(long m, long n) {
		assertion((m>0L) && (n>0L));
		long ans = m/gcd(m,n);
		ans *= n;
		return ans;
	}
	private static long gcd(long m, long n) {
		if(isINFL(-m)) return n;
		assertion((m>=0L) && (n>=0L));
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}

	private static boolean is_prime(long a) {
		if(a==1) return false;
		for(long i=2L; i<=Math.sqrt(a); i++) {
			if(a%i == 0) return false;
		}
		return true;
	}

	private static long modinv(long a, long p) {
		assertion((a>0)&&(p>1)&&(a%p != 0));
		//a|p, >1に注意
		long b = p, u = 1L, v = 0L;
		while (b > 0) {
			long t = a / b;
			long pe = a%b;
			a = b;
			b = pe;
			pe = u-t*v;
			u = v;
			v = pe;
		}
		u %= p;
		if(u < 0L) u += p;
		return u;
	}

	private static long pow10E97(long ob, long soeji, long p) {		//繰り返し二乗法
		if(ob==0) return 0L;
		if(soeji==0) return 1L;
		if(soeji==2) return (ob*ob)%p;

		long cf = 1L;
		int d = 0;
		while(soeji >= cf) {
			d ++;
			cf = (1L<<d);
		}

		long[] ob_pow_2pow = new long[d];
		ob_pow_2pow[0] = ob;
		for(int i=1; i<d; i++) {
			ob_pow_2pow[i] = (ob_pow_2pow[i-1]*ob_pow_2pow[i-1])%p;
		}
		long ans=1L;
		for(long i=(d-1); i>=0L; i--) {
			if(soeji >= (1L<<i)) {
				soeji -= (1L<<i);
				ans = (ans*ob_pow_2pow[(int)i])%p;
			}
 		}
		return ans%p;
	}

	private static int inC2(int n) {
		return ((n*(n-1))/2);
	}
	private static long nC2(long n) {
		return ((n*(n-1L))/2L);
	}

	private static int intflag(int pos) {
		assertion(pos<31);
		return (1<<pos);
	}
	private static long flag(long pos) {
		assertion(pos<63);
		return (1L<<pos);
	}
	private static boolean isFlaged(int bit, int pos) {
		if((bit&(1<<pos)) > 0) return true;
		else return false;
	}
	private static boolean isFlaged(long bit, int pos) {
		if((bit&(1L<<pos)) > 0L) return true;
		else return false;
	}
	private static int ideflag(int bit, int pos) {
		return bit&~(1<<pos);
	}
	private static int countFlaged(int bit) {
		int ans=0;
		for(int i=0; i<31; i++) {
			if((bit&(1<<i)) > 0) ans++;
		}
		return ans;
	}
	private static int countFlaged(long bit) {
		int ans=0;
		for(long i=0; i<63; i++) {
			if((bit&(1L<<i)) > 0) ans++;
		}
		return ans;
	}

	public static int biSearch(int[] dt, int target) {
		int left=0, right=dt.length-1;
		int mid=-1;
		while(left<=right) {
			mid = (right+left)/2;
			if(dt[mid] == target) return mid;
			if(dt[mid] < target) left=mid+1;
			else right=mid-1;
		}
		return -1;
	}

	private static void show2(int bit) {
		for(int i=0; i<getDigit2(bit); i++) {
			if(isFlaged(bit,i)) System.out.print("O");
			else System.out.print(".");
		}
		System.out.println();
	}
	static void show2(boolean[][] dt, int lit_x, int lit_y) {
		for(int j=0; j<dt.length; j++) {
			for(int i=0; i<dt[j].length; i++) {
				if((i==lit_y) && (j==lit_x)) System.out.print("X");
				else if(dt[j][i]) System.out.print("O");
				else System.out.print(".");
			}
			System.out.println();
		}
	}
	static void show2(int[][] dt, String cmnt) {
		for(int i=0; i<dt.length; i++) {
			for(int j=0; j<dt[i].length; j++) {
				System.out.print(dt[i][j]+",");
			}
			System.out.println("<-"+cmnt+":"+i);
		}
	}
	static void show2(long[][] dt, String cmnt) {
		for(int i=0; i<dt.length; i++) {
			for(int j=0; j<dt[i].length; j++) {
				System.out.print(dt[i][j]+",");
			}
			System.out.println("<-"+cmnt+":"+i);
		}
	}
	static void show2(ArrayDeque<Long> dt) {		//上手くいかなかった時用
		long a=0;
		while(dt.size()>0) {
			a=dt.removeFirst();
			System.out.print(a);
		}
		System.out.println("\n");
	}
	static void show2(List dt) {		//上手くいかなかった時用
	 	for(int i=0; i<dt.size(); i++) {
			System.out.print(dt.get(i)+",");
		}
		System.out.println("\n");
	}

	private static void prtlnas(int[] as) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<as.length; i++) {
			out.println(as[i]);
		}
		out.flush();
	}
	private static void prtlnas(long[] as) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<as.length; i++) {
			out.println(as[i]);
		}
		out.flush();
	}private static void prtlnas(ArrayList as) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<as.size(); i++) {
			out.println(as.get(i));
		}
		out.flush();
	}
	private static void prtspas(int[] as) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
		for(int i=1; i<as.length; i++) {
			out.print(" "+as[i]);
		}
		out.println();
		out.flush();
	}
	private static void prtspas(long[] as) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
		for(int i=1; i<as.length; i++) {
			out.print(" "+as[i]);
		}
		out.println();
		out.flush();
	}
	private static void prtspas(ArrayList as) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(as.get(0));
		for(int i=1; i<as.size(); i++) {
			out.print(" "+as.get(i));
		}
		out.println();
		out.flush();
	}

	private static void fill(boolean[] ob, boolean res) {
		for(int i=0; i<ob.length; i++) {
			ob[i] = res;
		}
	}
	private static void fill(int[] ob, int res) {
		for(int i=0; i<ob.length; i++) {
			ob[i] = res;
		}
	}
	private static void fill(long[] ob, long res) {
		for(int i=0; i<ob.length; i++) {
			ob[i] = res;
		}
	}
	private static void fill(char[] ob, char res) {
		for(int i=0; i<ob.length; i++) {
			ob[i] = res;
		}
	}
	private static void fill(double[] ob, double res) {
		for(int i=0; i<ob.length; i++) {
			ob[i] = res;
		}
	}
	private static void fill(boolean[][] ob,boolean res) {
		for(int i=0;i<ob.length; i++) {
			for(int j=0; j<ob[0].length; j++) {
				ob[i][j] = res;
			}
		}
	}
	private static void fill(int[][] ob, int res) {
		for(int i=0; i<ob.length; i++) {
			for(int j=0; j<ob[0].length; j++) {
				ob[i][j] = res;
			}
		}
	}
	private static void fill(long[][] ob, long res) {
		for(int i=0; i<ob.length; i++) {
			for(int j=0; j<ob[0].length; j++) {
				ob[i][j] = res;
			}
		}
	}
	private static void fill(char[][] ob, char res) {
		for(int i=0; i<ob.length; i++) {
			for(int j=0; j<ob[0].length; j++) {
				ob[i][j] = res;
			}
		}
	}
	private static void fill(double[][] ob, double res) {
		for(int i=0; i<ob.length; i++) {
			for(int j=0; j<ob[0].length; j++) {
				ob[i][j] = res;
			}
		}
	}
	private static void fill(int[][][] ob,int res) {
		for(int i=0;i<ob.length;i++) {
			for(int j=0;j<ob[0].length;j++) {
				for(int k=0;k<ob[0][0].length;k++) {
					ob[i][j][k]=res;
				}
			}
		}
	}
	private static void fill(long[][][] ob,long res) {
		for(int i=0;i<ob.length;i++) {
			for(int j=0;j<ob[0].length;j++) {
				for(int k=0;k<ob[0][0].length;k++) {
					ob[i][j][k]=res;
				}
			}
		}
	}
	static class FastScanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
			if(ptr < buflen) {
				return true;
			}else{
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if(buflen <= 0) {
					return false;
				}
			}
			return true;
		}
		private int readByte() {
			if(hasNextByte()) return buffer[ptr++];
			else return -1;
		}
		private static boolean isPrintableChar(int c) {
			return (33 <= c) && (c <= 126);
		}
		public boolean hasNext() {
			while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
			return hasNextByte();
		}
		public String next() {
			if(!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while(isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		public long nexL() {
			if(!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if(b == '-') {
				minus = true;
				b = readByte();
			}
			if(b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while(true) {
				if('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				}else if(b == -1 || !isPrintableChar(b) || b == ':') {
					return minus ? -n : n;
				}else{
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
		public int nexI() {
			long nl = nexL();
			if(nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
			return (int) nl;
		}
		public double nexD() { return Double.parseDouble(next());}
		public void al(long[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexL();
		 	}
		 	return;
		}
		public void ai(int[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexI();
		 	}
		 	return;
		}
		public void aimin1(int[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexI()-1;
		 	}
		 	return;
		}
		public void aD(double[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexD();
		 	}
		 	return;
		}
		public void ai2(int[] as, int[] bs) {
		 	for(int i=0; i<as.length; i++) {
				as[i] = nexI();
				bs[i] = nexI();
		 	}
		 	return;
		}
		public void al2(long[] as, long[] bs) {
		 	for(int i=0; i<as.length; i++) {
				as[i] = nexL();
				bs[i] = nexL();
		 	}
		 	return;
		}
		public void ai3(int[] as, int[] bs, int[] cs) {
		 	for(int i=0; i<as.length; i++) {
				as[i] = nexI();
				bs[i] = nexI();
				cs[i] = nexI();
		 	}
		 	return;
		}
		public void ad2i(int[][] as) {
			for(int i=0; i<as.length; i++) {
				for(int j=0; j<as[0].length; j++) {
					as[i][j] = nexI();
				}
			}
			return;
		}
		public void ain(int[]... as) {
			for(int i=0; i<as[0].length; i++) {
				for(int j=0; j<as.length; j++) {
					as[j][i] = nexI();
				}
			}
			return;
		}
		public void aln(long[]... as) {
			for(int i=0; i<as[0].length; i++) {
				for(int j=0; j<as.length; j++) {
					as[j][i] = nexL();
				}
			}
			return;
		}
	}

	static class Graph0n {
		private ArrayList<Node0n> dt = new ArrayList<>();
		Graph0n(int sz) {
			for(int i = 0; i < sz; i++) {
				Node0n node1 = new Node0n();
				dt.add(node1);
			}
		}
		public void add(int vn, int val) {
			dt.get(vn).add(val);
		}
		public void add2(int vn, int val) {
			dt.get(vn).add(val);
			dt.get(val).add(vn);
		}
		public int get(int vn, int index) {
			return dt.get(vn).get(index);
		}
		public ArrayList<Integer> get(int vn) {
			return dt.get(vn).getAll();
		}
		public int size() {
			return dt.size();
		}
		public int sizeOf(int vn) {
			return dt.get(vn).size();
		}
		public void clear() {
			for(int i = 0; i < dt.size(); i++) {
				dt.get(i).clear();
			}
		}
		public void clear(int i) {
			dt.get(i).clear();
		}
		public static Graph0n make_tree(int vn, FastScanner sc) {
			Graph0n tree = new Graph0n(vn);
			for(int i = 1; i < vn; i++) {
				int s1 = sc.nexI() - 1;
				int g1 = sc.nexI() - 1;
				tree.add2(s1, g1);
			}
			return tree;
		}
		private void add_Vertex(Node0n vnew) {
			dt.add(vnew);
		}
	}

	static class Node0n { // 重みなし無向・有向グラフの頂点
		private ArrayList<Integer> next_vs = new ArrayList<>();
		public void add(int val) {
			next_vs.add(val);
		}
		public int get(int ad) {
			return next_vs.get(ad);
		}
		public ArrayList<Integer> getAll() {
			return next_vs;
		}
		public int size() {
			return next_vs.size();
		}
		public void clear() {
			next_vs.clear();
		}
		public void addAll(Node0n vnew) {
			this.next_vs.addAll(vnew.next_vs);
		}
	}

	static class Edge {
		int from=-1, v2=-1;
		long weight;
		public Edge(int vn, long w) {
			this.v2 = vn;
			this.weight = w;
		}
		public Edge(int cm, int vn, long w) {
			this.from = cm;
			this.v2 = vn;
			this.weight = w;
		}
	}

	static class Edge2 {
		int v2;
		long cost1,cost2;
		public Edge2(int vn, long w1, long w2) {
			this.v2 = vn;
			this.cost1 = w1;
			this.cost2 = w2;
		}
	}

	static class CompEdge_float implements Comparator<Edge>{
		//今は小さいのが前に出てくる
		public int compare(Edge a, Edge b) {
			if(a.weight>b.weight) return 1;
			else if(a.weight<b.weight) return -1;
			else return a.v2-b.v2;
		}
	}
	static class Vector {
		int x,y;
		public Vector(int sx, int sy) {
			this.x=sx;
			this.y=sy;
		}
	}
}