description: She does her utmost to flawlessly carry out a person's last rites and preserve the world's balance of yin and yang.
  
  Hu Tao, being the little prankster she is, has tried to scare you with this graph problem! You are given a connected undirected graph of n nodes with m edges. You also have q queries. Each query consists of two nodes a and b.
  
  Initially, all edges in the graph have a weight of 0. For each query, you must choose a simple path starting from a and ending at b. Then you add 1 to every edge along this path. Determine if it's possible, after processing all q queries, for all edges in this graph to have an even weight. If so, output the choice of paths for each query. 
  
  If it is not possible, determine the smallest number of extra queries you could add to make it possible. It can be shown that this number will not exceed 10^{18} under the given constraints.
  
  A simple path is defined as any path that does not visit a node more than once.
  
  An edge is said to have an even weight if its value is divisible by 2.
  
  Input
  
  The first line contains two integers n and m (2 ≤ n ≤ 3 ⋅ 10^5, n-1 ≤ m ≤ min{\left((n(n-1))/(2), 3 ⋅ 10^5\right)}).
  
  Each of the next m lines contains two integers x and y (1 ≤ x, y ≤ n, x≠ y) indicating an undirected edge between node x and y. The input will not contain self-loops or duplicate edges, and the provided graph will be connected.
  
  The next line contains a single integer q (1 ≤ q ≤ 3 ⋅ 10^5).
  
  Each of the next q lines contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), the description of each query.
  
  It is guaranteed that nq ≤ 3 ⋅ 10^5.
  
  Output
  
  If it is possible to force all edge weights to be even, print "YES" on the first line, followed by 2q lines indicating the choice of path for each query in the same order the queries are given. For each query, the first line should contain a single integer x: the number of nodes in the chosen path. The next line should then contain x spaced separated integers p_i indicating the path you take (p_1 = a, p_x = b and all numbers should fall between 1 and n). This path cannot contain duplicate nodes and must be a valid simple path in the graph.
  
  If it is impossible to force all edge weights to be even, print "NO" on the first line and the minimum number of added queries on the second line.
  
  Examples
  
  Input
  
  
  6 7
  2 1
  2 3
  3 5
  1 4
  6 1
  5 6
  4 5
  3
  1 4
  5 1
  4 5
  
  
  Output
  
  
  YES
  2
  1 4
  4
  5 3 2 1
  5
  4 1 2 3 5
  
  
  Input
  
  
  5 7
  4 3
  4 5
  2 1
  1 4
  1 3
  3 5
  3 2
  4
  4 2
  3 5
  5 1
  4 5
  
  
  Output
  
  
  NO
  2
  
  Note
  
  Here is what the queries look like for the first test case (red corresponds to the 1st query, blue 2nd query, and green 3rd query): 
  
  <image> Notice that every edge in the graph is part of either 0 or 2 colored query edges.
  
  The graph in the second test case looks like this: 
  
  <image> There does not exist an assignment of paths that will force all edges to have even weights with the given queries. One must add at least 2 new queries to obtain a set of queries that can satisfy the condition.
solution: //package round749;
  import java.io.*;
  import java.util.*;
  
  public class E {
  	InputStream is;
  	FastWriter out;
  	String INPUT = "";
  	
  	void solve()
  	{
  		int n = ni(), m = ni();
  		int[][] es = new int[m][];
  		for(int i = 0;i < m;i++){
  			es[i] = new int[]{ni()-1, ni()-1};
  		}
  		DJSet ds = new DJSet(n);
  		int[] from = new int[n-1];
  		int[] to = new int[n-1];
  		int p = 0;
  		for(int[] e : es){
  			if(!ds.union(e[0], e[1])){
  				from[p] = e[0];
  				to[p] = e[1];
  				p++;
  			}
  		}
  		int[][] g = packU(n, from, to);
  		int[][] pars = parents(g, 0);
  		int[] par = pars[0];
  		LCAFast2 lcf = LCAFast2.build(g, 0);
  
  		int[] deg = new int[n];
  		StringBuilder sb = new StringBuilder();
  		for(int Q = ni();Q > 0;Q--){
  			int x = ni()-1, y = ni()-1;
  			int lca = lcf.lca(x, y);
  			Deque<Integer> routef = new ArrayDeque<>();
  			Deque<Integer> routeb = new ArrayDeque<>();
  			for(int u = x;u != lca;u = par[u]){
  				routef.addLast(u);
  			}
  			routef.addLast(lca);
  
  			for(int u = y;u != lca;u = par[u]){
  				routeb.addFirst(u);
  			}
  			sb.append(routef.size() + routeb.size() + "\n");
  			for(int u : routef){
  				sb.append(u+1).append(" ");
  			}
  			for(int u : routeb){
  				sb.append(u+1).append(" ");
  			}
  			sb.append("\n");
  			deg[x] ^= 1;
  			deg[y] ^= 1;
  		}
  
  		int dsu = 0;
  		for(int i = 0;i < n;i++){
  			dsu += deg[i];
  		}
  		if(dsu == 0){
  			out.println("YES");
  			out.print(sb.toString());
  		}else{
  			out.println("NO");
  			out.println(dsu/2);
  		}
  	}
  
  	public static class LCAFast2 {
  		public int n, h;
  		public int[][] bigst;
  		public int[][] bigind;
  		public long[][] smallb;
  		public int[] vs, first, deps;
  
  		public int lca(int a, int b)
  		{
  			return vs[rmqpos(Math.min(first[a], first[b]), Math.max(first[a], first[b]))];
  		}
  
  		public int pointOnPath(int a, int b, int dfroma)
  		{
  			int lca = lca(a, b);
  			if(dfroma <= dep(a) - dep(lca)){
  				return anc(a, dfroma);
  			}
  			int dfromb = dep(b) - dep(lca) - (dfroma - (dep(a) - dep(lca)));
  			if(dfromb < 0)return -1;
  
  			return anc(b, dfromb);
  		}
  
  		public int anc(int a, int d)
  		{
  			int da = dep(a);
  			if(da < d)return -1;
  			int danc = da - d;
  			int low = 0, high = first[a] + 1;
  			while(high - low > 1){
  				int h = high+low>>1;
  				if(rmqval(h, first[a]) <= danc){
  					low = h;
  				}else {
  					high = h;
  				}
  			}
  			return vs[low];
  		}
  
  		public int d(int a, int b)
  		{
  			return dep(a) + dep(b) - 2 * rmqval(Math.min(first[a], first[b]), Math.max(first[a], first[b]));
  		}
  
  		public int dep(int x)
  		{
  			return deps[first[x]];
  		}
  
  		public int rmqpos(int l, int r)
  		{
  			if(l > r)return -1;
  			int cl = l>>>6;
  			int cr = r>>>6;
  			if(cl == cr){
  				return argmax(smallb[l&63][cl], r-l+1) + l;
  			}else{
  				int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
  				int pos = argmax(smallb[l&63][cl], 63-(l&63)+1) + l;
  
  				{
  					int can = deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1);
  					if(can < min){
  						min = can;
  						pos = argmax(smallb[0][cr], (r&63)-0+1) + (r>>>6<<6);
  					}
  				}
  
  				if(cl+1 <= cr-1){
  					int len = (cr-1)-(cl+1)+1;
  					int h = 31-Integer.numberOfLeadingZeros(len);
  					{
  						int can = bigst[h][cl+1];
  						if(can < min){
  							min = can;
  							pos = bigind[h][cl+1];
  						}
  					}
  					{
  						int can = bigst[h][cr-1-(1<<h)+1];
  						if(can < min){
  							min = can;
  							pos = bigind[h][cr-1-(1<<h)+1];
  						}
  					}
  				}
  				return pos;
  			}
  		}
  
  		public int rmqval(int l, int r)
  		{
  			if(l > r)return -1;
  			int cl = l>>>6;
  			int cr = r>>>6;
  			if(cl == cr){
  				return deps[l] - max(smallb[l&63][cl], r-l+1);
  			}else{
  				int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
  				min = Math.min(min, deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1));
  
  				if(cl+1 <= cr-1){
  					int len = (cr-1)-(cl+1)+1;
  					int h = 31-Integer.numberOfLeadingZeros(len);
  					min = Math.min(min, bigst[h][cl+1]);
  					min = Math.min(min, bigst[h][cr-1-(1<<h)+1]);
  				}
  				return min;
  			}
  		}
  
  		public static LCAFast2 build(int[][] g, int root)
  		{
  			LCAFast2 ret = new LCAFast2();
  			int[][] et = eulerTour(g, root);
  			int[] vs = et[0], deps = et[1], first = et[2];
  			ret.vs = vs;
  			ret.first = first;
  			ret.deps = deps;
  
  			int n = deps.length;
  			int u = n+63>>>6;
  			int h = 31-Integer.numberOfLeadingZeros(u) + 1;
  			int[][] bigst = new int[h][];
  			int[][] bigind = new int[h][];
  			int[] cup = new int[u];
  			int[] cupind = new int[u];
  			Arrays.fill(cup, Integer.MAX_VALUE);
  			for(int i = 0;i < n;i++){
  				if(deps[i] < cup[i>>>6]){
  					cup[i>>>6] = deps[i];
  					cupind[i>>>6] = i;
  				}
  			}
  			bigst[0] = cup;
  			bigind[0] = cupind;
  			for(int i = 1;i < h;i++){
  				bigst[i] = new int[u-(1<<i)+1];
  				bigind[i] = new int[u-(1<<i)+1];
  				for(int j = 0;j + (1<<i) <= u;j++){
  					if(bigst[i-1][j] < bigst[i-1][j+(1<<i-1)]){
  						bigst[i][j] = bigst[i-1][j];
  						bigind[i][j] = bigind[i-1][j];
  					}else{
  						bigst[i][j] = bigst[i-1][j+(1<<i-1)];
  						bigind[i][j] = bigind[i-1][j+(1<<i-1)];
  					}
  				}
  			}
  
  			long[][] smallb = new long[64][u];
  			for(int i = 0;i < u;i++){
  				long x = 0;
  				for(int j = 0;j < 63 && (i<<6|j+1) < n;j++){
  					if(deps[i<<6|j] > deps[i<<6|j+1]){
  						x |= 1L<<j;
  					}
  				}
  				long val = 0;
  				for(int j = 63;j >= 0;j--){
  					val <<= 1;
  					if(x<<~j<0){
  						val |= 1L;
  					}else{
  						val &= val - 1;
  					}
  					smallb[j][i] = val;
  				}
  				//
  				//			for(int j = 0;j < 64;j++){
  				//				smallb[j][i] = make(x>>>j);
  				//			}
  			}
  
  			ret.n = n; ret.h = h;
  			ret.bigst = bigst;
  			ret.bigind = bigind;
  			ret.smallb = smallb;
  			return ret;
  		}
  
  		public static int[][] eulerTour(int[][] g, int root)
  		{
  			int n = g.length;
  			int[] vs = new int[2*n-1];
  			int[] deps = new int[2*n-1];
  			int[] first = new int[n];
  			Arrays.fill(first, -1);
  			int p = 0;
  
  			int[] stack = new int[n];
  			int[] inds = new int[n];
  			int sp = 0;
  			stack[sp++] = root;
  			outer:
  			while(sp > 0){
  				int cur = stack[sp-1], ind = inds[sp-1];
  				vs[p] = cur;
  				deps[p] = sp-1;
  				if(first[cur] == -1)first[cur] = p;
  				p++;
  				while(ind < g[cur].length){
  					int nex = g[cur][ind++];
  					if(first[nex] == -1){
  						inds[sp-1] = ind;
  						stack[sp] = nex;
  						inds[sp] = 0;
  						sp++;
  						continue outer;
  					}
  				}
  				inds[sp-1] = ind;
  				if(ind == g[cur].length)sp--;
  			}
  
  			return new int[][]{vs, deps, first};
  		}
  
  		// TinyRMQ
  		public static long make(long x)
  		{
  			int h = 0;
  			int max = 0;
  			long ret = 0;
  			for(int i = 0;i < 64;i++){
  				if(x<<~i<0){
  					h++;
  				}else{
  					h--;
  				}
  				if(h > max){
  					max = h;
  					ret |= 1L<<i;
  				}
  			}
  			return ret;
  		}
  
  		public static int max(long x, int r)
  		{
  			assert r > 0;
  			return Long.bitCount(x&(1L<<r-1)-1);
  		}
  
  		public static int argmax(long x, int r)
  		{
  			assert r > 0;
  			return 64-Long.numberOfLeadingZeros(x&(1L<<r-1)-1);
  		}
  
  	}
  
  
  		public static int[][] parents(int[][] g, int root) {
  		int n = g.length;
  		int[] par = new int[n];
  		Arrays.fill(par, -1);
  
  		int[] depth = new int[n];
  		depth[0] = 0;
  
  		int[] q = new int[n];
  		q[0] = root;
  		for (int p = 0, r = 1; p < r; p++) {
  			int cur = q[p];
  			for (int nex : g[cur]) {
  				if (par[cur] != nex) {
  					q[r++] = nex;
  					par[nex] = cur;
  					depth[nex] = depth[cur] + 1;
  				}
  			}
  		}
  		return new int[][]{par, q, depth};
  	}
  
  
  	public static int[][] packU(int n, int[] from, int[] to) {
  		return packU(n, from, to, from.length);
  	}
  
  	public static int[][] packU(int n, int[] from, int[] to, int sup) {
  		int[][] g = new int[n][];
  		int[] p = new int[n];
  		for (int i = 0; i < sup; i++) p[from[i]]++;
  		for (int i = 0; i < sup; i++) p[to[i]]++;
  		for (int i = 0; i < n; i++) g[i] = new int[p[i]];
  		for (int i = 0; i < sup; i++) {
  			g[from[i]][--p[from[i]]] = to[i];
  			g[to[i]][--p[to[i]]] = from[i];
  		}
  		return g;
  	}
  
  
  	public static class DJSet {
  		public int[] upper;
  
  		public DJSet(int n) {
  			upper = new int[n];
  			Arrays.fill(upper, -1);
  		}
  
  		public int root(int x) {
  			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
  		}
  
  		public boolean equiv(int x, int y) {
  			return root(x) == root(y);
  		}
  
  		public boolean union(int x, int y) {
  			x = root(x);
  			y = root(y);
  			if (x != y) {
  				if (upper[y] < upper[x]) {
  					int d = x;
  					x = y;
  					y = d;
  				}
  				upper[x] += upper[y];
  				upper[y] = x;
  			}
  			return x == y;
  		}
  
  		public int count() {
  			int ct = 0;
  			for (int u : upper) if (u < 0) ct++;
  			return ct;
  		}
  
  		public int[][] toBucket() {
  			int n = upper.length;
  			int[][] ret = new int[n][];
  			int[] rp = new int[n];
  			for (int i = 0; i < n; i++) if (upper[i] < 0) ret[i] = new int[-upper[i]];
  			for (int i = 0; i < n; i++) {
  				int r = root(i);
  				ret[r][rp[r]++] = i;
  			}
  			return ret;
  		}
  	}
  
  
  	void run() throws Exception
  	{
  		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
  		out = new FastWriter(System.out);
  		
  		long s = System.currentTimeMillis();
  		solve();
  		out.flush();
  		tr(System.currentTimeMillis()-s+"ms");
  	}
  	
  	public static void main(String[] args) throws Exception { new E().run(); }
  	
  	private byte[] inbuf = new byte[1024];
  	public int lenbuf = 0, ptrbuf = 0;
  	
  	private int readByte()
  	{
  		if(lenbuf == -1)throw new InputMismatchException();
  		if(ptrbuf >= lenbuf){
  			ptrbuf = 0;
  			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
  			if(lenbuf <= 0)return -1;
  		}
  		return inbuf[ptrbuf++];
  	}
  	
  	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
  	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
  	
  	private double nd() { return Double.parseDouble(ns()); }
  	private char nc() { return (char)skip(); }
  	
  	private String ns()
  	{
  		int b = skip();
  		StringBuilder sb = new StringBuilder();
  		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
  			sb.appendCodePoint(b);
  			b = readByte();
  		}
  		return sb.toString();
  	}
  	
  	private char[] ns(int n)
  	{
  		char[] buf = new char[n];
  		int b = skip(), p = 0;
  		while(p < n && !(isSpaceChar(b))){
  			buf[p++] = (char)b;
  			b = readByte();
  		}
  		return n == p ? buf : Arrays.copyOf(buf, p);
  	}
  
  	private int[] na(int n)
  	{
  		int[] a = new int[n];
  		for(int i = 0;i < n;i++)a[i] = ni();
  		return a;
  	}
  
  	private long[] nal(int n)
  	{
  		long[] a = new long[n];
  		for(int i = 0;i < n;i++)a[i] = nl();
  		return a;
  	}
  
  	private char[][] nm(int n, int m) {
  		char[][] map = new char[n][];
  		for(int i = 0;i < n;i++)map[i] = ns(m);
  		return map;
  	}
  
  	private int[][] nmi(int n, int m) {
  		int[][] map = new int[n][];
  		for(int i = 0;i < n;i++)map[i] = na(m);
  		return map;
  	}
  
  	private int ni() { return (int)nl(); }
  
  	private long nl()
  	{
  		long num = 0;
  		int b;
  		boolean minus = false;
  		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
  		if(b == '-'){
  			minus = true;
  			b = readByte();
  		}
  
  		while(true){
  			if(b >= '0' && b <= '9'){
  				num = num * 10 + (b - '0');
  			}else{
  				return minus ? -num : num;
  			}
  			b = readByte();
  		}
  	}
  
  	public static class FastWriter
  	{
  		private static final int BUF_SIZE = 1<<13;
  		private final byte[] buf = new byte[BUF_SIZE];
  		private final OutputStream out;
  		private int ptr = 0;
  
  		private FastWriter(){out = null;}
  
  		public FastWriter(OutputStream os)
  		{
  			this.out = os;
  		}
  
  		public FastWriter(String path)
  		{
  			try {
  				this.out = new FileOutputStream(path);
  			} catch (FileNotFoundException e) {
  				throw new RuntimeException("FastWriter");
  			}
  		}
  
  		public FastWriter write(byte b)
  		{
  			buf[ptr++] = b;
  			if(ptr == BUF_SIZE)innerflush();
  			return this;
  		}
  
  		public FastWriter write(char c)
  		{
  			return write((byte)c);
  		}
  
  		public FastWriter write(char[] s)
  		{
  			for(char c : s){
  				buf[ptr++] = (byte)c;
  				if(ptr == BUF_SIZE)innerflush();
  			}
  			return this;
  		}
  
  		public FastWriter write(String s)
  		{
  			s.chars().forEach(c -> {
  				buf[ptr++] = (byte)c;
  				if(ptr == BUF_SIZE)innerflush();
  			});
  			return this;
  		}
  
  		private static int countDigits(int l) {
  			if (l >= 1000000000) return 10;
  			if (l >= 100000000) return 9;
  			if (l >= 10000000) return 8;
  			if (l >= 1000000) return 7;
  			if (l >= 100000) return 6;
  			if (l >= 10000) return 5;
  			if (l >= 1000) return 4;
  			if (l >= 100) return 3;
  			if (l >= 10) return 2;
  			return 1;
  		}
  
  		public FastWriter write(int x)
  		{
  			if(x == Integer.MIN_VALUE){
  				return write((long)x);
  			}
  			if(ptr + 12 >= BUF_SIZE)innerflush();
  			if(x < 0){
  				write((byte)'-');
  				x = -x;
  			}
  			int d = countDigits(x);
  			for(int i = ptr + d - 1;i >= ptr;i--){
  				buf[i] = (byte)('0'+x%10);
  				x /= 10;
  			}
  			ptr += d;
  			return this;
  		}
  
  		private static int countDigits(long l) {
  			if (l >= 1000000000000000000L) return 19;
  			if (l >= 100000000000000000L) return 18;
  			if (l >= 10000000000000000L) return 17;
  			if (l >= 1000000000000000L) return 16;
  			if (l >= 100000000000000L) return 15;
  			if (l >= 10000000000000L) return 14;
  			if (l >= 1000000000000L) return 13;
  			if (l >= 100000000000L) return 12;
  			if (l >= 10000000000L) return 11;
  			if (l >= 1000000000L) return 10;
  			if (l >= 100000000L) return 9;
  			if (l >= 10000000L) return 8;
  			if (l >= 1000000L) return 7;
  			if (l >= 100000L) return 6;
  			if (l >= 10000L) return 5;
  			if (l >= 1000L) return 4;
  			if (l >= 100L) return 3;
  			if (l >= 10L) return 2;
  			return 1;
  		}
  
  		public FastWriter write(long x)
  		{
  			if(x == Long.MIN_VALUE){
  				return write("" + x);
  			}
  			if(ptr + 21 >= BUF_SIZE)innerflush();
  			if(x < 0){
  				write((byte)'-');
  				x = -x;
  			}
  			int d = countDigits(x);
  			for(int i = ptr + d - 1;i >= ptr;i--){
  				buf[i] = (byte)('0'+x%10);
  				x /= 10;
  			}
  			ptr += d;
  			return this;
  		}
  
  		public FastWriter write(double x, int precision)
  		{
  			if(x < 0){
  				write('-');
  				x = -x;
  			}
  			x += Math.pow(10, -precision)/2;
  			//		if(x < 0){ x = 0; }
  			write((long)x).write(".");
  			x -= (long)x;
  			for(int i = 0;i < precision;i++){
  				x *= 10;
  				write((char)('0'+(int)x));
  				x -= (int)x;
  			}
  			return this;
  		}
  
  		public FastWriter writeln(char c){
  			return write(c).writeln();
  		}
  
  		public FastWriter writeln(int x){
  			return write(x).writeln();
  		}
  
  		public FastWriter writeln(long x){
  			return write(x).writeln();
  		}
  
  		public FastWriter writeln(double x, int precision){
  			return write(x, precision).writeln();
  		}
  
  		public FastWriter write(int... xs)
  		{
  			boolean first = true;
  			for(int x : xs) {
  				if (!first) write(' ');
  				first = false;
  				write(x);
  			}
  			return this;
  		}
  
  		public FastWriter write(long... xs)
  		{
  			boolean first = true;
  			for(long x : xs) {
  				if (!first) write(' ');
  				first = false;
  				write(x);
  			}
  			return this;
  		}
  
  		public FastWriter writeln()
  		{
  			return write((byte)'\n');
  		}
  
  		public FastWriter writeln(int... xs)
  		{
  			return write(xs).writeln();
  		}
  
  		public FastWriter writeln(long... xs)
  		{
  			return write(xs).writeln();
  		}
  
  		public FastWriter writeln(char[] line)
  		{
  			return write(line).writeln();
  		}
  
  		public FastWriter writeln(char[]... map)
  		{
  			for(char[] line : map)write(line).writeln();
  			return this;
  		}
  
  		public FastWriter writeln(String s)
  		{
  			return write(s).writeln();
  		}
  
  		private void innerflush()
  		{
  			try {
  				out.write(buf, 0, ptr);
  				ptr = 0;
  			} catch (IOException e) {
  				throw new RuntimeException("innerflush");
  			}
  		}
  
  		public void flush()
  		{
  			innerflush();
  			try {
  				out.flush();
  			} catch (IOException e) {
  				throw new RuntimeException("flush");
  			}
  		}
  
  		public FastWriter print(byte b) { return write(b); }
  		public FastWriter print(char c) { return write(c); }
  		public FastWriter print(char[] s) { return write(s); }
  		public FastWriter print(String s) { return write(s); }
  		public FastWriter print(int x) { return write(x); }
  		public FastWriter print(long x) { return write(x); }
  		public FastWriter print(double x, int precision) { return write(x, precision); }
  		public FastWriter println(char c){ return writeln(c); }
  		public FastWriter println(int x){ return writeln(x); }
  		public FastWriter println(long x){ return writeln(x); }
  		public FastWriter println(double x, int precision){ return writeln(x, precision); }
  		public FastWriter print(int... xs) { return write(xs); }
  		public FastWriter print(long... xs) { return write(xs); }
  		public FastWriter println(int... xs) { return writeln(xs); }
  		public FastWriter println(long... xs) { return writeln(xs); }
  		public FastWriter println(char[] line) { return writeln(line); }
  		public FastWriter println(char[]... map) { return writeln(map); }
  		public FastWriter println(String s) { return writeln(s); }
  		public FastWriter println() { return writeln(); }
  	}
  
  	public void trnz(int... o)
  	{
  		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
  		System.out.println();
  	}
  
  	// print ids which are 1
  	public void trt(long... o)
  	{
  		Queue<Integer> stands = new ArrayDeque<>();
  		for(int i = 0;i < o.length;i++){
  			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
  		}
  		System.out.println(stands);
  	}
  
  	public void tf(boolean... r)
  	{
  		for(boolean x : r)System.out.print(x?'#':'.');
  		System.out.println();
  	}
  
  	public void tf(boolean[]... b)
  	{
  		for(boolean[] r : b) {
  			for(boolean x : r)System.out.print(x?'#':'.');
  			System.out.println();
  		}
  		System.out.println();
  	}
  
  	public void tf(long[]... b)
  	{
  		if(INPUT.length() != 0) {
  			for (long[] r : b) {
  				for (long x : r) {
  					for (int i = 0; i < 64; i++) {
  						System.out.print(x << ~i < 0 ? '#' : '.');
  					}
  				}
  				System.out.println();
  			}
  			System.out.println();
  		}
  	}
  
  	public void tf(long... b)
  	{
  		if(INPUT.length() != 0) {
  			for (long x : b) {
  				for (int i = 0; i < 64; i++) {
  					System.out.print(x << ~i < 0 ? '#' : '.');
  				}
  			}
  			System.out.println();
  		}
  	}
  
  	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
  	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
  }
  