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:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.*;
import java.util.*;
import java.util.function.*;

public class E {

    private static final FastReader in = new FastReader();
    private static final FastWriter out = new FastWriter();

    public static void main(String[] args) {
        new E().run();
    }

    private void run() {
        var t = 1;
        while (t-- > 0) {
            solve();
        }

        out.flush();
    }

    private void solve() {
        var n = in.nextInt();
        var a = in.nextLongArray(n);

        var sum = new long[n + 1];
        sum[0] = 0;
        for (var i = 1; i <= n; i++) {
            sum[i] = sum[i - 1] + a[i - 1];
        }

        var q = new int[n + 1];
        var top = 0;
        for (var i = 1; i <= n; i++) {
            while (top > 0) {
                var j = q[top];
                var k = q[top - 1];
                double topAvg = (double) (sum[j] - sum[k]) / (j - k);
                double nowAvg = (double) (sum[i] - sum[k]) / (i - k);
                if (EPS_COMPARATOR.compare(topAvg, nowAvg) >= 0) {
                    top--;
                } else {
                    break;
                }
            }

            q[++top] = i;
        }

        var ans = new double[n];
        for (var i = 1; i <= top; i++) {
            var j = q[i];
            var k = q[i - 1];
            double avg = (double) (sum[j] - sum[k]) / (j - k);
            for (var l = k + 1; l <= j; l++) {
                ans[l - 1] = avg;
            }
        }

        out.println(ans);
    }

    private static final double EPS = 1e-12;
    private static final Comparator<Double> EPS_COMPARATOR = (x, y) -> {
        if (x + EPS < y) {
            return -1;
        } else if (x - EPS > y) {
            return 1;
        } else {
            return 0;
        }
    };

    @SuppressWarnings("unused")
    private static int binarySearch(int left, int right, Predicate<Integer> leftShouldAdvance) {
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (leftShouldAdvance.test(mid)) {
                left = mid + 1;
            } else {
                right = mid;
            }
        }

        return left;
    }

    @SuppressWarnings("unused")
    private static class Pair<T, U> {

        T a;
        U b;

        Pair(T a, U b) {
            this.a = a;
            this.b = b;
        }

        static <T, U> Pair<T, U> of(T a, U b) {
            return new Pair<>(a, b);
        }

        T getA() {
            return a;
        }

        U getB() {
            return b;
        }

    }

    @SuppressWarnings("unused")
    private static class IntPair extends Pair<Integer, Integer> {

        IntPair(Integer a, Integer b) {
            super(a, b);
        }

        static IntPair of(int a, int b) {
            return new IntPair(a, b);
        }

    }

    @SuppressWarnings("unused")
    private static class Triple<T, U, V> {

        T a;
        U b;
        V c;

        Triple(T a, U b, V c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

        T getA() {
            return a;
        }

        U getB() {
            return b;
        }

        V getC() {
            return c;
        }

    }

    @SuppressWarnings("unused")
    private static class IntTriple extends Triple<Integer, Integer, Integer> {

        IntTriple(Integer a, Integer b, Integer c) {
            super(a, b, c);
        }

    }

    @SuppressWarnings("unused")
    private static class FastReader {

        private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private static StringTokenizer in;

        public String next() {
            while (in == null || !in.hasMoreTokens()) {
                try {
                    in = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    return null;
                }
            }
            return in.nextToken();
        }

        public BigDecimal nextBigDecimal() {
            return new BigDecimal(next());
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public boolean nextBoolean() {
            return Boolean.valueOf(next());
        }

        public byte nextByte() {
            return Byte.valueOf(next());
        }

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

        public double[] nextDoubleArray(int length) {
            var a = new double[length];
            for (var i = 0; i < length; i++) {
                a[i] = nextDouble();
            }
            return a;
        }

        public int nextInt() {
            return Integer.valueOf(next());
        }

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

        public long nextLong() {
            return Long.valueOf(next());
        }

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

    }

    @SuppressWarnings("unused")
    private static class FastWriter extends PrintWriter {

        public FastWriter() {
            super(System.out);
        }

        public void println(double[] a) {
            for (var i = 0; i < a.length; i++) {
                print(a[i]);
                print(i + 1 < a.length ? ' ' : '\n');
            }
        }

        public void println(int[] a) {
            for (var i = 0; i < a.length; i++) {
                print(a[i]);
                print(i + 1 < a.length ? ' ' : '\n');
            }
        }

        public void println(long[] a) {
            for (var i = 0; i < a.length; i++) {
                print(a[i]);
                print(i + 1 < a.length ? ' ' : '\n');
            }
        }

        public <T> void println(T[] a) {
            for (var i = 0; i < a.length; i++) {
                print(a[i]);
                print(i + 1 < a.length ? ' ' : '\n');
            }
        }

        public void debug(String name, Object o) {
            String value = Arrays.deepToString(new Object[] { o });
            value = value.substring(1, value.length() - 1);
            System.err.println(name + " => " + value);
        }

    }

}