Recently a tournament in k kinds of sports has begun in Berland. Vasya wants to make money on the bets.

The scheme of the tournament is very mysterious and not fully disclosed. Competitions are held back to back, each of them involves two sportsmen who have not left the tournament yet. Each match can be held in any of the k kinds of sport. Loser leaves the tournament. The last remaining sportsman becomes the winner. Apart of this, the scheme can be arbitrary, it is not disclosed in advance.

Vasya knows powers of sportsmen in each kind of sport. He believes that the sportsmen with higher power always wins.

The tournament is held every year, and each year one new participant joins it. In the first tournament, only one sportsman has participated, in the second there were two sportsmen, and so on. Vasya has been watching the tournament for the last n years. Help him to find the number of possible winners for each of the n tournaments.

Input

The first line contains two integers n and k (1 ≤ n ≤ 5·104, 1 ≤ k ≤ 10) — the number of tournaments and the number of kinds of sport, respectively.

Each of the next n lines contains k integers si1, si2, ..., sik (1 ≤ sij ≤ 109), where sij is the power of the i-th sportsman in the j-th kind of sport. The sportsman with higher powers always wins. It's guaranteed that for any kind of sport all of these powers are distinct.

Output

For each of the n tournaments output the number of contenders who can win.

Examples

Input

3 2
1 5
5 1
10 10


Output

1
2
1


Input

3 2
2 2
3 3
1 10


Output

1
1
3


Input

3 2
2 3
1 1
3 2


Output

1
1
2

Note

In the first sample:

In the first tournament there is only one sportsman, and he is the winner.

In the second tournament, there are two sportsmen, and everyone can defeat another, depending on kind of sports.

In the third tournament, the third sportsman in the strongest in both kinds of sports, so he is the winner regardless of the scheme.
//package round443;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;

public class C {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), K = ni();
		int[][] co = new int[n][];
		int[][] lower = new int[n][];
		int[][] upper = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = na(K);
			lower[i] = Arrays.copyOf(co[i], K);
			upper[i] = Arrays.copyOf(co[i], K);
		}
		
		Node[] nodes = new Node[n];
		for(int i = 0;i < n;i++)nodes[i] = new Node(i);
		
		Node root = null;
		
		for(int i = 0;i < n;i++){
			
			int L = -1, R = -1;
			{
				int lcount = 0;
				Node cur = root;
				while(cur != null){
					boolean oed = true;
					for(int j = 0;j < K;j++){
						if(upper[cur.v][j] >= co[i][j])oed = false;
					}
					
					if(!oed){
						cur = cur.left;
					}else{
						lcount += count(cur.left) + 1;
						cur = cur.right;
					}
				}
				L = lcount;
			}
			{
				int lcount = 0;
				Node cur = root;
				while(cur != null){
					boolean oed = true;
					for(int j = 0;j < K;j++){
						if(lower[cur.v][j] <= co[i][j])oed = false;
					}
					
					if(oed){
						cur = cur.left;
					}else{
						lcount += count(cur.left) + 1;
						cur = cur.right;
					}
				}
				R = lcount;
			}
			
			Node[] lm_r = split(root, R);
			Node[] l_m = split(lm_r[0], L);
			nodes[i].sum++;
			for(Node x : nodes(l_m[1])){
				nodes[i].sum += x.sum;
				for(int j = 0;j < K;j++){
					lower[i][j] = Math.min(lower[i][j], lower[x.v][j]);
					upper[i][j] = Math.max(upper[i][j], upper[x.v][j]);
				}
			}
			root = merge(l_m[0], nodes[i], lm_r[1]);
			out.println(get(root, count(root)-1).sum);
		}
	}
	
	
	public static Random gen = new Random();
	
	static public class Node
	{
		public int v; // value
		public int sum = 0;
		public long priority;
		public Node left, right, parent;
		
		public int count;
		
		public Node(int v)
		{
			this.v = v;
			priority = gen.nextLong();
			update(this);
		}

		@Override
		public String toString() {
			StringBuilder builder = new StringBuilder();
			builder.append("Node [v=");
			builder.append(v);
			builder.append(", count=");
			builder.append(count);
			builder.append(", parent=");
			builder.append(parent != null ? parent.v : "null");
			builder.append("]");
			return builder.toString();
		}
	}

	public static Node update(Node a)
	{
		if(a == null)return null;
		a.count = 1;
		if(a.left != null)a.count += a.left.count;
		if(a.right != null)a.count += a.right.count;
		
		// TODO
		return a;
	}
	
	public static void propagate(Node x)
	{
		for(;x != null;x = x.parent)update(x);
	}
	
	public static Node disconnect(Node a)
	{
		if(a == null)return null;
		a.left = a.right = a.parent = null;
		return update(a);
	}
	
	public static Node root(Node x)
	{
		if(x == null)return null;
		while(x.parent != null)x = x.parent;
		return x;
	}
	
	public static int count(Node a)
	{
		return a == null ? 0 : a.count;
	}
	
	public static void setParent(Node a, Node par)
	{
		if(a != null)a.parent = par;
	}
	
	public static Node merge(Node a, Node b, Node... c)
	{
		Node x = merge(a, b);
		for(Node n : c)x = merge(x, n);
		return x;
	}
	
	public static Node merge(Node a, Node b)
	{
		if(b == null)return a;
		if(a == null)return b;
		if(a.priority > b.priority){
			setParent(a.right, null);
			setParent(b, null);
			a.right = merge(a.right, b);
			setParent(a.right, a);
			return update(a);
		}else{
			setParent(a, null);
			setParent(b.left, null);
			b.left = merge(a, b.left);
			setParent(b.left, b);
			return update(b);
		}
	}
	
	public static Node[] split(Node x)
	{
		if(x == null)return new Node[]{null, null};
		if(x.left != null)x.left.parent = null;
		Node[] sp = new Node[]{x.left, x};
		x.left = null;
		update(x);
		while(x.parent != null){
			Node p = x.parent;
			x.parent = null;
			if(x == p.left){
				p.left = sp[1];
				if(sp[1] != null)sp[1].parent = p;
				sp[1] = p;
			}else{
				p.right = sp[0];
				if(sp[0] != null)sp[0].parent = p;
				sp[0] = p;
			}
			update(p);
			x = p;
		}
		return sp;
	}
	
	public static Node[] split(Node a, int... ks)
	{
		int n = ks.length;
		if(n == 0)return new Node[]{a};
		for(int i = 0;i < n-1;i++){
			if(ks[i] > ks[i+1])throw new IllegalArgumentException(Arrays.toString(ks));
		}
		
		Node[] ns = new Node[n+1];
		Node cur = a;
		for(int i = n-1;i >= 0;i--){
			Node[] sp = split(cur, ks[i]);
			cur = sp[0];
			ns[i] = sp[0];
			ns[i+1] = sp[1];
		}
		return ns;
	}
	
	// [0,K),[K,N)
	public static Node[] split(Node a, int K)
	{
		if(a == null)return new Node[]{null, null};
		if(K <= count(a.left)){
			setParent(a.left, null);
			Node[] s = split(a.left, K);
			a.left = s[1];
			setParent(a.left, a);
			s[1] = update(a);
			return s;
		}else{
			setParent(a.right, null);
			Node[] s = split(a.right, K-count(a.left)-1);
			a.right = s[0];
			setParent(a.right, a);
			s[0] = update(a);
			return s;
		}
	}
	
	public static Node insertb(Node root, Node x)
	{
		int ind = lowerBound(root, x.v);
		return insert(root, ind, x);
	}
	
	public static Node insert(Node a, int K, Node b)
	{
		if(a == null)return b;
		if(b.priority < a.priority){
			if(K <= count(a.left)){
				a.left = insert(a.left, K, b);
				setParent(a.left, a);
			}else{
				a.right = insert(a.right, K-count(a.left)-1, b);
				setParent(a.right, a);
			}
			return update(a);
		}else{
			Node[] ch = split(a, K);
			b.left = ch[0]; b.right = ch[1];
			setParent(b.left, b);
			setParent(b.right, b);
			return update(b);
		}
	}
	
	// delete K-th
	public static Node erase(Node a, int K)
	{
		if(a == null)return null;
		if(K < count(a.left)){
			a.left = erase(a.left, K);
			setParent(a.left, a);
			return update(a);
		}else if(K == count(a.left)){
			setParent(a.left, null);
			setParent(a.right, null);
			Node aa = merge(a.left, a.right);
			disconnect(a);
			return aa;
		}else{
			a.right = erase(a.right, K-count(a.left)-1);
			setParent(a.right, a);
			return update(a);
		}
	}
	
	public static Node get(Node a, int K)
	{
		while(a != null){
			if(K < count(a.left)){
				a = a.left;
			}else if(K == count(a.left)){
				break;
			}else{
				K = K - count(a.left)-1;
				a = a.right;
			}
		}
		return a;
	}
	
	public static int index(Node a)
	{
		if(a == null)return -1;
		int ind = count(a.left);
		while(a != null){
			Node par = a.parent;
			if(par != null && par.right == a){
				ind += count(par.left) + 1;
			}
			a = par;
		}
		return ind;
	}
	
	public static Node mergeTechnically(Node x, Node y)
	{
		if(count(x) > count(y)){
			Node d = x; x = y; y = d;
		}
		// |x|<=|y|
		for(Node cur : nodesdfs(x))y = insertb(y, disconnect(cur));
		return y;
	}
	
	public static int lowerBound(Node a, int q)
	{
		int lcount = 0;
		while(a != null){
			if(a.v >= q){
				a = a.left;
			}else{
				lcount += count(a.left) + 1;
				a = a.right;
			}
		}
		return lcount;
	}
	
	public static int search(Node a, int q)
	{
		int lcount = 0;
		while(a != null){
			if(a.v == q){
				lcount += count(a.left);
				break;
			}
			if(q < a.v){
				a = a.left;
			}else{
				lcount += count(a.left) + 1;
				a = a.right;
			}
		}
		return a == null ? -(lcount+1) : lcount;
	}
	
	public static Node next(Node x)
	{
		if(x == null)return null;
		if(x.right != null){
			x = x.right;
			while(x.left != null)x = x.left;
			return x;
		}else{
			while(true){
				Node p = x.parent;
				if(p == null)return null;
				if(p.left == x)return p;
				x = p;
			}
		}
	}
	
	public static Node prev(Node x)
	{
		if(x == null)return null;
		if(x.left != null){
			x = x.left;
			while(x.right != null)x = x.right;
			return x;
		}else{
			while(true){
				Node p = x.parent;
				if(p == null)return null;
				if(p.right == x)return p;
				x = p;
			}
		}
	}
	
	public static Node[] nodes(Node a) { return nodes(a, new Node[count(a)], 0, count(a)); }
	public static Node[] nodes(Node a, Node[] ns, int L, int R)
	{
		if(a == null)return ns;
		nodes(a.left, ns, L, L+count(a.left));
		ns[L+count(a.left)] = a;
		nodes(a.right, ns, R-count(a.right), R);
		return ns;
	}
	
	// faster than nodes but inconsistent
	public static Node[] nodesdfs(Node a) { return nodesdfs(a, new Node[a.count], new int[]{0}); }
	public static Node[] nodesdfs(Node a, Node[] ns, int[] pos)
	{
		if(a == null)return ns;
		ns[pos[0]++] = a;
		nodesdfs(a.left, ns, pos);
		nodesdfs(a.right, ns, pos);
		return ns;
	}
	
	public static String toString(Node a, String indent)
	{
		if(a == null)return "";
		StringBuilder sb = new StringBuilder();
		sb.append(toString(a.left, indent + "  "));
		sb.append(indent).append(a).append("\n");
		sb.append(toString(a.right, indent + "  "));
		return sb.toString();
	}

	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new C().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 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[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, 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();
		}
	}
	
	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();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
