Your favorite music streaming platform has formed a perfectly balanced playlist exclusively for you. The playlist consists of n tracks numbered from 1 to n. The playlist is automatic and cyclic: whenever track i finishes playing, track i+1 starts playing automatically; after track n goes track 1.

For each track i, you have estimated its coolness a_i. The higher a_i is, the cooler track i is.

Every morning, you choose a track. The playlist then starts playing from this track in its usual cyclic fashion. At any moment, you remember the maximum coolness x of already played tracks. Once you hear that a track with coolness strictly less than x/2 (no rounding) starts playing, you turn off the music immediately to keep yourself in a good mood.

For each track i, find out how many tracks you will listen to before turning off the music if you start your morning with track i, or determine that you will never turn the music off. Note that if you listen to the same track several times, every time must be counted.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5), denoting the number of tracks in the playlist.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9), denoting coolnesses of the tracks.

Output

Output n integers c_1, c_2, …, c_n, where c_i is either the number of tracks you will listen to if you start listening from track i or -1 if you will be listening to music indefinitely.

Examples

Input


4
11 5 2 7


Output


1 1 3 2


Input


4
3 2 5 3


Output


5 4 3 6


Input


3
4 3 6


Output


-1 -1 -1

Note

In the first example, here is what will happen if you start with... 

  * track 1: listen to track 1, stop as a_2 < (a_1)/(2). 
  * track 2: listen to track 2, stop as a_3 < (a_2)/(2). 
  * track 3: listen to track 3, listen to track 4, listen to track 1, stop as a_2 < (max(a_3, a_4, a_1))/(2). 
  * track 4: listen to track 4, listen to track 1, stop as a_2 < (max(a_4, a_1))/(2). 



In the second example, if you start with track 4, you will listen to track 4, listen to track 1, listen to track 2, listen to track 3, listen to track 4 again, listen to track 1 again, and stop as a_2 < (max(a_4, a_1, a_2, a_3, a_4, a_1))/(2). Note that both track 1 and track 4 are counted twice towards the result.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.function.LongBinaryOperator;
import java.util.TreeSet;
import java.util.OptionalLong;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.util.stream.LongStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.io.Writer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

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

    static class DBalancedPlaylist {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            int n = in.ints();
            long[] a = in.longs(n);
            int[] ans = new int[n];
            {
                long max = IntMath.max(a), min = IntMath.min(a);
                if (min > (max - 1) / 2) {
                    for (int i = 0; i < n; i++) out.ans(-1);
                    out.ln();
                    return;
                }
            }
            DBalancedPlaylist.IndexedValue[] values = new DBalancedPlaylist.IndexedValue[n];
            for (int i = 0; i < n; i++) values[i] = new DBalancedPlaylist.IndexedValue(i, a[i]);
            IntroSort.sort(values, Comparator.comparing(val -> val.value));
            ArrayUtil.reverse(values, 0, n);
            TreeSet<Integer> done = new TreeSet<>();

            IntSegmentTree st = new IntSegmentTree(a, Math::min, Integer.MAX_VALUE, Math::min);
            for (int index = 0; index < n; index++) {
                int i = values[index].index;
                long threshold = (a[i] - 1) / 2;


                long mintoLast = st.query(i + 1, n);
                Integer bound = done.higher(i);
                if (bound != null) {
                    if (st.query(i + 1, bound) > threshold) {
                        ans[i] = ans[bound] + bound - i;
                        done.add(i);
                        continue;
                    }
                } else if (!done.isEmpty()) {
                    bound = done.first();
                    if (Math.min(st.query(0, bound), mintoLast) > threshold) {
                        ans[i] = ans[bound] + bound + n - i;
                        done.add(i);
                        continue;
                    }
                }
                done.add(i);


                int min, max;
                if (mintoLast <= threshold) {
                    min = i + 1;
                    max = n;
                    while (max - min > 1) {
                        int mid = (min + max) / 2;
                        if (st.query(i + 1, mid) <= threshold) max = mid;
                        else min = mid;
                    }
                    ans[i] = min - i;
                } else {
                    min = 0;
                    max = i;
                    while (max - min > 1) {
                        int mid = (min + max) / 2;
                        if (st.query(0, mid) <= threshold) max = mid;
                        else min = mid;
                    }
                    ans[i] = n - i + min;
                }
            }
            out.ans(ans).ln();
        }

        private static class IndexedValue {
            int index;
            long value;

            public IndexedValue(int index, long value) {
                this.index = index;
                this.value = value;
            }

        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ans(int... n) {
            for (int n1 : n) {
                ans(n1);
            }
            return this;
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class IntroSort {
        private static int INSERTIONSORT_THRESHOLD = 16;

        private IntroSort() {
        }

        static <T> void sort(T[] a, int low, int high, int maxDepth, Comparator<T> comparator) {
            while (high - low > INSERTIONSORT_THRESHOLD) {
                if (maxDepth-- == 0) {
                    HeapSort.sort(a, low, high, comparator);
                    return;
                }
                int cut = QuickSort.step(a, low, high, comparator);
                sort(a, cut, high, maxDepth, comparator);
                high = cut;
            }
            InsertionSort.sort(a, low, high, comparator);
        }

        public static <T> void sort(T[] a, Comparator<T> comparator) {
            if (a.length <= INSERTIONSORT_THRESHOLD) {
                InsertionSort.sort(a, 0, a.length, comparator);
            } else {
                sort(a, 0, a.length, 2 * BitMath.msb(a.length), comparator);
            }
        }

    }

    static final class BitMath {
        private BitMath() {
        }

        public static int count(int v) {
            v = (v & 0x55555555) + ((v >> 1) & 0x55555555);
            v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
            v = (v & 0x0f0f0f0f) + ((v >> 4) & 0x0f0f0f0f);
            v = (v & 0x00ff00ff) + ((v >> 8) & 0x00ff00ff);
            v = (v & 0x0000ffff) + ((v >> 16) & 0x0000ffff);
            return v;
        }

        public static int msb(int v) {
            if (v == 0) {
                throw new IllegalArgumentException("Bit not found");
            }
            v |= (v >> 1);
            v |= (v >> 2);
            v |= (v >> 4);
            v |= (v >> 8);
            v |= (v >> 16);
            return count(v) - 1;
        }

        public static int extractMsb(int v) {
            v = (v & 0xFFFF0000) > 0 ? v & 0xFFFF0000 : v;
            v = (v & 0xFF00FF00) > 0 ? v & 0xFF00FF00 : v;
            v = (v & 0xF0F0F0F0) > 0 ? v & 0xF0F0F0F0 : v;
            v = (v & 0xCCCCCCCC) > 0 ? v & 0xCCCCCCCC : v;
            v = (v & 0xAAAAAAAA) > 0 ? v & 0xAAAAAAAA : v;
            return v;
        }

    }

    static class InsertionSort {
        private InsertionSort() {
        }

        static <T> void sort(T[] a, int low, int high, Comparator<? super T> comparator) {
            for (int i = low; i < high; i++) {
                for (int j = i; j > low && comparator.compare(a[j - 1], a[j]) > 0; j--) {
                    ArrayUtil.swap(a, j - 1, j);
                }
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public long longs() {
            return Long.parseLong(string());
        }

        public long[] longs(int length) {
            return IntStream.range(0, length).mapToLong(x -> longs()).toArray();
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static <T> void reverse(T[] a, int left, int right) {
            right--;
            while (left < right) {
                T temp = a[left];
                a[left++] = a[right];
                a[right--] = temp;
            }
        }

        public static <T> void swap(T[] a, int x, int y) {
            T t = a[x];
            a[x] = a[y];
            a[y] = t;
        }

    }

    static interface Verified {
    }

    static final class IntMath {
        private IntMath() {
        }

        public static long min(long... v) {
            return Arrays.stream(v).min().orElseThrow(NoSuchElementException::new);
        }

        public static long max(long... v) {
            return Arrays.stream(v).max().orElseThrow(NoSuchElementException::new);
        }

    }

    static class HeapSort {
        private HeapSort() {
        }

        private static <T> void heapfy(T[] a, int low, int high, int i, T val, Comparator<? super T> comparator) {
            int child = 2 * i - low + 1;
            while (child < high) {
                if (child + 1 < high && comparator.compare(a[child], a[child + 1]) < 0) {
                    child++;
                }
                if (comparator.compare(val, a[child]) >= 0) {
                    break;
                }
                a[i] = a[child];
                i = child;
                child = 2 * i - low + 1;
            }
            a[i] = val;
        }

        static <T> void sort(T[] a, int low, int high, Comparator<T> comparator) {
            for (int p = (high + low) / 2 - 1; p >= low; p--) {
                heapfy(a, low, high, p, a[p], comparator);
            }
            while (high > low) {
                high--;
                T pval = a[high];
                a[high] = a[low];
                heapfy(a, low, high, low, pval, comparator);
            }
        }

    }

    static class QuickSort {
        private QuickSort() {
        }

        private static <T> void med(T[] a, int low, int x, int y, int z, Comparator<? super T> comparator) {
            if (comparator.compare(a[z], a[x]) < 0) {
                ArrayUtil.swap(a, low, x);
            } else if (comparator.compare(a[y], a[z]) < 0) {
                ArrayUtil.swap(a, low, y);
            } else {
                ArrayUtil.swap(a, low, z);
            }
        }

        static <T> int step(T[] a, int low, int high, Comparator<? super T> comparator) {
            int x = low + 1, y = low + (high - low) / 2, z = high - 1;
            if (comparator.compare(a[x], a[y]) < 0) {
                med(a, low, x, y, z, comparator);
            } else {
                med(a, low, y, x, z, comparator);
            }

            int lb = low + 1, ub = high;
            while (true) {
                while (comparator.compare(a[lb], a[low]) < 0) {
                    lb++;
                }
                ub--;
                while (comparator.compare(a[low], a[ub]) < 0) {
                    ub--;
                }
                if (lb >= ub) {
                    return lb;
                }
                ArrayUtil.swap(a, lb, ub);
                lb++;
            }
        }

    }

    static class IntSegmentTree {
        private final int n;
        private final int m;
        private final long[] tree;
        private final LongBinaryOperator op;
        private final LongBinaryOperator up;
        private final long zero;

        public IntSegmentTree(long[] array, LongBinaryOperator op, long zero, LongBinaryOperator up) {
            this.n = array.length;
            int msb = BitMath.extractMsb(n);
            this.m = n == msb ? msb : (msb << 1);
            this.tree = new long[m * 2 - 1];
            this.op = op;
            this.up = up;
            this.zero = zero;
            Arrays.fill(tree, zero);
            System.arraycopy(array, 0, this.tree, m - 1, array.length);
            for (int i = m - 2; i >= 0; i--) {
                tree[i] = op.applyAsLong(tree[2 * i + 1], tree[2 * i + 2]);
            }
        }

        public long query(int l, int r) {
            long left = zero, right = zero;
            l += m - 1;
            r += m - 1;
            while (l < r) {
                if ((l & 1) == 0) {
                    left = op.applyAsLong(left, tree[l]);
                }
                if ((r & 1) == 0) {
                    right = op.applyAsLong(tree[r - 1], right);
                }
                l = l / 2;
                r = (r - 1) / 2;
            }
            return op.applyAsLong(left, right);
        }

    }
}

