SaMer has written the greatest test case of all time for one of his problems. For a given array of integers, the problem asks to find the minimum number of groups the array can be divided into, such that the product of any pair of integers in the same group is a perfect square. 

Each integer must be in exactly one group. However, integers in a group do not necessarily have to be contiguous in the array.

SaMer wishes to create more cases from the test case he already has. His test case has an array A of n integers, and he needs to find the number of contiguous subarrays of A that have an answer to the problem equal to k for each integer k between 1 and n (inclusive).

Input

The first line of input contains a single integer n (1 ≤ n ≤ 5000), the size of the array.

The second line contains n integers a_1,a_2,...,a_n (-10^8 ≤ a_i ≤ 10^8), the values of the array.

Output

Output n space-separated integers, the k-th integer should be the number of contiguous subarrays of A that have an answer to the problem equal to k.

Examples

Input

2
5 5


Output

3 0


Input

5
5 -4 2 1 8


Output

5 5 3 2 0


Input

1
0


Output

1
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	static PrintWriter out;
	static InputReader ir;

	static void solve() {
		int n = ir.nextInt();
		int[] a = ir.nextIntArray(n);
		boolean[] p = new boolean[1001];
		Arrays.fill(p, true);
		p[0] = p[1] = false;
		for (int i = 2; i <= 1000; i++) {
			if (p[i]) {
				for (int j = i * 2; j <= 1000; j += i)
					p[j] = false;
			}
		}
		for (int i = 0; i < n; i++) {
			int ret = 1;
			if(a[i]==0)
				continue;
			for (int j = 2; j <= 1000; j++) {
				if (!p[j])
					continue;
				int m = -1;
				while (Math.abs(a[i]) % j == 0) {
					if (m < 0)
						m = 0;
					a[i] /= j;
					m ^= 1;
				}
				if (m == 1)
					ret *= j;
			}
			a[i] *= ret;
		}
		int[] ret = new int[n];
		HashSet<Integer> st = new HashSet<>();
		for (int i = 0; i < n; i++) {
			for (int j = i; j < n; j++) {
				if(a[j]!=0)
					st.add(a[j]);
				ret[Math.max(0, st.size() - 1)]++;
			}
			st.clear();
		}
		for (int i = 0; i < n; i++)
			out.print(ret[i] + (i == n - 1 ? "\n" : " "));
	}

	public static void main(String[] args) throws Exception {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

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

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

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

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}