Problem: There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.

You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.

What is the lexicographically smallest sequence of volumes of water that you can achieve?

As a reminder:

A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.

Input

The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.

Because of large input, reading input as doubles is not recommended.

Output

Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.

Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.

Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.

Examples

Input


4
7 5 5 7


Output


5.666666667
5.666666667
5.666666667
7.000000000


Input


5
7 8 8 10 12


Output


7.000000000
8.000000000
8.000000000
10.000000000
12.000000000


Input


10
3 9 5 5 1 7 5 3 8 7


Output


3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000

Note

In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].

In the second sample, you can't get any lexicographically smaller sequence.

Solution (in JAVA):

Solution:
//package round618;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Queue;

public class C3 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n);
		
		long[] sums = new long[n];
		LST lst = new LST(n+1);
		lst.setRange(n+1);
		for(int i = 0;i < n;i++){
			sums[i] = a[i];
		}
		Queue<Integer> q = new ArrayDeque<>();
		for(int i = 0;i < n;i++){
			q.add(i);
		}
		while(!q.isEmpty()){
			int cur = q.poll();
			int nex = lst.next(cur+1);
			if(nex == n)continue;
			int nnex = lst.next(nex+1);
//			if(sums[cur] / (nex-cur) > sums[nex] / (nnex - nex)){
			if(sums[cur] * (nnex - nex) > sums[nex] * (nex-cur)){
//				tr(cur, nex, sums[cur], sums[nex]);
				sums[cur] += sums[nex];
				sums[nex] = 0;
				lst.unset(nex);
				q.add(cur);
				int pre = lst.prev(cur-1);
				if(pre != -1)q.add(pre);
			}
		}
		for(int i = 0;i < n;i++){
			if(lst.get(i)){
				int nex = lst.next(i+1);
				double ave = (double)sums[i] / (nex-i);
				String d = dtos(ave, 11);
				for(int j = 0;j < nex-i;j++){
					out.println(d);
				}
			}
		}
	}
	
	public static class LST {
		public long[][] set;
		public int n;
//		public int size;
		
		public LST(int n) {
			this.n = n;
			int d = 1;
			for(int m = n;m > 1;m>>>=6, d++);
			
			set = new long[d][];
			for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){
				set[i] = new long[m+1];
			}
//			size = 0;
		}
		
		// [0,r)
		public LST setRange(int r)
		{
			for(int i = 0;i < set.length;i++, r=r+63>>>6){
				for(int j = 0;j < r>>>6;j++){
					set[i][j] = -1L;
				}
				if((r&63) != 0)set[i][r>>>6] |= (1L<<r)-1;
			}
			return this;
		}
		
		// [0,r)
		public LST unsetRange(int r)
		{
			if(r >= 0){
				for(int i = 0;i < set.length;i++, r=r+63>>>6){
					for(int j = 0;j < r+63>>>6;j++){
						set[i][j] = 0;
					}
					if((r&63) != 0)set[i][r>>>6] &= ~((1L<<r)-1);
				}
			}
			return this;
		}
		
		public LST set(int pos)
		{
			if(pos >= 0 && pos < n){
//				if(!get(pos))size++;
				for(int i = 0;i < set.length;i++, pos>>>=6){
					set[i][pos>>>6] |= 1L<<pos;
				}
			}
			return this;
		}
		
		public LST unset(int pos)
		{
			if(pos >= 0 && pos < n){
//				if(get(pos))size--;
				for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){
					set[i][pos>>>6] &= ~(1L<<pos);
				}
			}
			return this;
		}
		
		public boolean get(int pos)
		{
			return pos >= 0 && pos < n && set[0][pos>>>6]<<~pos<0;
		}
		
		public LST toggle(int pos)
		{
			return get(pos) ? unset(pos) : set(pos);
		}
		
		public int prev(int pos)
		{
			for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){
				int pre = prev(set[i][pos>>>6], pos&63);
				if(pre != -1){
					pos = pos>>>6<<6|pre;
					while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}
		
		public int next(int pos)
		{
			for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){
				int nex = next(set[i][pos>>>6], pos&63);
				if(nex != -1){
					pos = pos>>>6<<6|nex;
					while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}
		
		private static int prev(long set, int n)
		{
			long h = set<<~n;
			if(h == 0L)return -1;
			return -Long.numberOfLeadingZeros(h)+n;
		}
		
		private static int next(long set, int n)
		{
			long h = set>>>n;
			if(h == 0L)return -1;
			return Long.numberOfTrailingZeros(h)+n;
		}
		
		@Override
		public String toString()
		{
			List<Integer> list = new ArrayList<Integer>();
			for(int pos = next(0);pos != -1;pos = next(pos+1)){
				list.add(pos);
			}
			return list.toString();
		}
	}

	
	public static String dtos(double x, int n) {
		StringBuilder sb = new StringBuilder();
		if(x < 0){
			sb.append('-');
			x = -x;
		}
		x += Math.pow(10, -n)/2;
//		if(x < 0){ x = 0; }
		sb.append((long)x);
		sb.append(".");
		x -= (long)x;
		for(int i = 0;i < n;i++){
			x *= 10;
			sb.append((int)x);
			x -= (int)x;
		}
		return sb.toString();
	}

	
	void run() throws Exception
	{
//		int n = 1000000, m = 99999;
//		Random gen = new Random();
//		StringBuilder sb = new StringBuilder();
//		sb.append(n + " ");
//		for (int i = 0; i < n; i++) {
////			sb.append(gen.nextInt(1000000)+1 + " ");
//			sb.append(i + " ");
//		}
//		INPUT = sb.toString();
//
		
		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 C3().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)); }
}