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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }

            if (false) {
                slow(a.clone(), out);
            }

            double[] stackAm = new double[n];
            double[] stackVal = new double[n];
            int sp = 0;
            for (int i = 0; i < n; i++) {
                stackAm[sp] = 1;
                stackVal[sp] = a[i];
                ++sp;
                while (sp >= 2) {
                    double a1 = stackAm[sp - 1];
                    double a2 = stackAm[sp - 2];
                    double v1 = stackVal[sp - 1];
                    double v2 = stackVal[sp - 2];
                    if (v1 >= v2) {
                        break;
                    }
                    --sp;
                    stackAm[sp - 1] = a1 + a2;
                    stackVal[sp - 1] = (a1 * v1 + a2 * v2) / (a1 + a2);
                    if (stackVal[sp - 1] < 1e-20) {
                        stackVal[sp - 1] = 0.0;
                    }
                }
            }

            for (int i = 0; i < sp; i++) {
                for (int j = 0; j < stackAm[i]; j++) {
                    out.printf("%.9f\n", stackVal[i]);
                }
            }
        }

        private void slow(double[] a, PrintWriter out) {
            int n = a.length;
            Tree tree = new Tree(n);
            for (int i = 0; i < n; i++) {
                tree.set(i, i + 1, a[i]);
                int l = -1;
                int r = i;
                while (r - l > 1) {
                    int m = (l + r) / 2;
                    double sum = tree.sum(m, i + 1);
                    int am = (i + 1) - m;
                    double first = tree.get(m);
                    if (sum < am * first) {
                        r = m;
                    } else {
                        l = m;
                    }
                }

                int m = r;
                double sum = tree.sum(m, i + 1);
                int am = (i + 1) - m;
                tree.set(m, i + 1, sum / am);
            }

            for (int i = 0; i < n; i++) {
                out.printf("%.9f\n", tree.get(i));
            }
        }

        class Tree {
            int n;
            double[] set;
            double[] sum;

            Tree(int n) {
                this.n = n;
                set = new double[4 * n];
                sum = new double[4 * n];
                Arrays.fill(set, -1);
            }

            double get(int pos) {
                return get(0, 0, n, pos);
            }

            double sum(int l, int r) {
                return get(0, 0, n, l, r);
            }

            void set(int l, int r, double val) {
                set(0, 0, n, l, r, val);
            }

            double get(int root, int rl, int rr, int pos) {
                if (rl + 1 == rr) {
                    return sum[root];
                }
                push(root, rl, rr);
                int rm = (rl + rr) / 2;
                double res;
                if (pos < rm) {
                    res = get(2 * root + 1, rl, rm, pos);
                } else {
                    res = get(2 * root + 2, rm, rr, pos);
                }
                pull(root);
                return res;
            }

            double get(int root, int rl, int rr, int l, int r) {
                if (l < rl) {
                    l = rl;
                }
                if (r > rr) {
                    r = rr;
                }
                if (l >= r) {
                    return 0;
                }
                if (l == rl && r == rr) {
                    return sum[root];
                }
                push(root, rl, rr);
                int rm = (rl + rr) / 2;
                double res = 0;
                res += get(2 * root + 1, rl, rm, l, r);
                res += get(2 * root + 2, rm, rr, l, r);
                pull(root);
                return res;
            }

            void set(int root, int rl, int rr, int l, int r, double val) {
                if (l < rl) {
                    l = rl;
                }
                if (r > rr) {
                    r = rr;
                }
                if (l >= r) {
                    return;
                }
                if (l == rl && r == rr) {
                    apply(root, rl, rr, val);
                    return;
                }
                push(root, rl, rr);
                int rm = (rl + rr) / 2;
                set(2 * root + 1, rl, rm, l, r, val);
                set(2 * root + 2, rm, rr, l, r, val);
                pull(root);
            }

            void push(int root, int rl, int rr) {
                int rm = (rl + rr) / 2;
                if (set[root] > 0) {
                    apply(2 * root + 1, rl, rm, set[root]);
                    apply(2 * root + 2, rm, rr, set[root]);
                    set[root] = -1;
                }
            }

            void pull(int root) {
                sum[root] = sum[2 * root + 1] + sum[2 * root + 2];
            }

            private void apply(int root, int rl, int rr, double val) {
                set[root] = val;
                sum[root] = val * (rr - rl);
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

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

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

    }
}