Rick and Morty want to find MR. PBH and they can't do it alone. So they need of Mr. Meeseeks. They Have generated n Mr. Meeseeks, standing in a line numbered from 1 to n. Each of them has his own color. i-th Mr. Meeseeks' color is ai. 

Rick and Morty are gathering their army and they want to divide Mr. Meeseeks into some squads. They don't want their squads to be too colorful, so each squad should have Mr. Meeseeks of at most k different colors. Also each squad should be a continuous subarray of Mr. Meeseeks in the line. Meaning that for each 1 ≤ i ≤ e ≤ j ≤ n, if Mr. Meeseeks number i and Mr. Meeseeks number j are in the same squad then Mr. Meeseeks number e should be in that same squad.

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Also, each squad needs its own presidio, and building a presidio needs money, so they want the total number of squads to be minimized.

Rick and Morty haven't finalized the exact value of k, so in order to choose it, for each k between 1 and n (inclusive) need to know the minimum number of presidios needed.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 105) — number of Mr. Meeseeks.

The second line contains n integers a1, a2, ..., an separated by spaces (1 ≤ ai ≤ n) — colors of Mr. Meeseeks in order they standing in a line.

Output

In the first and only line of input print n integers separated by spaces. i-th integer should be the minimum number of presidios needed if the value of k is i.

Examples

Input

5
1 3 4 3 3


Output

4 2 1 1 1 


Input

8
1 5 7 8 1 7 6 1


Output

8 4 3 2 1 1 1 1 

Note

For the first sample testcase, some optimal ways of dividing army into squads for each k are:

  1. [1], [3], [4], [3, 3]
  2. [1], [3, 4, 3, 3]
  3. [1, 3, 4, 3, 3]
  4. [1, 3, 4, 3, 3]
  5. [1, 3, 4, 3, 3]



For the second testcase, some optimal ways of dividing army into squads for each k are:

  1. [1], [5], [7], [8], [1], [7], [6], [1]
  2. [1, 5], [7, 8], [1, 7], [6, 1]
  3. [1, 5, 7], [8], [1, 7, 6, 1]
  4. [1, 5, 7, 8], [1, 7, 6, 1]
  5. [1, 5, 7, 8, 1, 7, 6, 1]
  6. [1, 5, 7, 8, 1, 7, 6, 1]
  7. [1, 5, 7, 8, 1, 7, 6, 1]
  8. [1, 5, 7, 8, 1, 7, 6, 1]
import java.util.*;
import java.io.*;

public class _0786_C_TillICollapse {

	static class Node{
		int l, r, val, idx; Node left, right;
		public Node(int l, int r) {
			this.l = l; this.r = r;
		}
		Node copy() {
			Node x = new Node(l, r);
			x.val = val;
			x.left = left; x.right = right;
			return x;
		}
	}
		
	static Node build(int l, int r) {
		Node n = new Node(l, r);
		if(l == r) return n;
		int mid = (l+r)/2; 
		n.left = build(l, mid);
		n.right = build(mid+1, r);
		return n;
	}
	
	static Node upd(Node x, int p, int val) {
		Node n = x.copy();
		if(n.l == p && n.r == p) {
			n.val = val;
			return n;
		}
		int mid = (n.l + n.r)/2;
		if(p <= mid) n.left = upd(x.left, p, val);
		else n.right = upd(x.right, p, val);
		n.val = n.left.val + n.right.val;
		return n;
	}
	
	static int query(Node n, int val, int sum) {
		if(n.l == n.r) return n.l;
//		println(n.left.val + " " + n.left.l + " " + n.left.r + " " + val);
		if(sum + n.left.val >= val) return query(n.left, val, sum);
		else return query(n.right, val, sum + n.left.val);
	}
	
	public static void main(String[] args) throws IOException {
		int N = readInt();
		int arr[] = new int[N+1];
		for(int i = 1; i<=N; i++) arr[i] = readInt();
		Node seg[] = new Node[N+2];
		seg[N+1] = build(1, N+1);
		int occ[] = new int[N+1]; 
		for(int i = N; i>=1; i--) {
			seg[i] = seg[i+1];
			if(occ[arr[i]] != 0) seg[i] = upd(seg[i], occ[arr[i]], 0);
			seg[i] = upd(seg[i], occ[arr[i]] = i, 1);
		}
		for(int len = 1; len<=N; len++) {
			int idx = 1, cnt = 0;
			while(idx <= N) {
				idx = query(seg[idx], len + 1, 0);
				cnt++;
			}
			print(cnt + " ");
		}
		exit();
	}

	final private static int BUFFER_SIZE = 1 << 16;
	private static DataInputStream din = new DataInputStream(System.in);
	private static byte[] buffer = new byte[BUFFER_SIZE];
	private static int bufferPointer = 0, bytesRead = 0;
	static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

	public static String readLine() throws IOException {
		byte[] buf = new byte[64]; // line length
		int cnt = 0, c;
		while ((c = Read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}

	public static String read() throws IOException {
		byte[] ret = new byte[1024];
		int idx = 0;
		byte c = Read();
		while (c <= ' ') {
			c = Read();
		}
		do {
			ret[idx++] = c;
			c = Read();
		} while (c != -1 && c != ' ' && c != '\n' && c != '\r');
		return new String(ret, 0, idx);
	}

	public static int readInt() throws IOException {
		int ret = 0;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');

		if (neg)
			return -ret;
		return ret;
	}

	public static long readLong() throws IOException {
		long ret = 0;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}

	public static double readDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = Read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg)
			return -ret;
		return ret;
	}

	private static void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private static byte Read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	static void print(Object o) {
		pr.print(o);
	}

	static void println(Object o) {
		pr.println(o);
	}

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

	static void println() {
		pr.println();
	}

	static void exit() throws IOException {
		din.close();
		pr.close();
		System.exit(0);
	}
}
