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.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.math.*;
 
public class Myclass{
	
	static  ArrayList a[]=new ArrayList[500001];
	
		
	 public void solve () {
	    	InputReader in =new InputReader(System.in);
	    	PrintWriter pw = new PrintWriter(System.out);
	    	int n = in.nextInt();
	    	long a[]=new long[3*n];
	    	for(int i = 0;i<n;i++)
	    	{ 
	    		long x=in.nextLong();
	    		a[n+i]=a[i]=x;
	    		a[2*n+i] = x;
	    		
	    	}
	    	Segment s = new Segment(3*n,a);
	    	s.build(0, 0, 3*n-1);
	    	Queue<Integer>q = new LinkedList<>();
	    	int idx = 1;
	    	q.add(0);
	    	long maxi = a[0];
	    	int cnt = 0;
	    	int ans []=new int [3*n+1];
	    	while(!q.isEmpty()) {
	    		while(idx<3*n && 2L*a[idx]>=maxi) {
	    			q.add(idx);
	    			maxi =Math.max(maxi, a[idx]);
	    			idx++;
	    		}
	    		boolean chk = false;
	    		int val = idx - 1;
	    		while(!q.isEmpty()) {
		    		if(!q.isEmpty() && q.peek()>=n) break;
	    			if(idx<3*n-1 && s.query(0, 0, 3*n-1, q.peek(), idx-1, 0)>2*a[idx])
	    			{
	    				ans [q.peek()] = (val - q.peek()+1);
	    				q.poll();
	    			}
	    			else if(idx == 3*n) {
	    				ans [q.peek()] = -1;
	    				q.poll();
	    			}
	    			else break;
	    		}
	    		if(idx<3*n) {
	    			q.add(idx);
	    			maxi = a[idx];
	    			if(!q.isEmpty())
	    				maxi =s.query(0, 0, 3*n-1, q.peek(), idx, 0);
	    		}
	    		if(!q.isEmpty() && q.peek()>=n) break;
	    		
	    	}
	    	for(int i = 0;i<n;i++) {
	    		pw.print(ans[i]+" ");
	    	}
	    	pw.flush();
	    	pw.close();
	    	
	 }
    public static void main(String[] args) throws Exception {
    	new Thread(null,new Runnable() {
            public void run() {
                new Myclass().solve();
            }
        },"1",1<<26).start();
    	
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static long d;
        public static long p;
        public static long q;
        public void extended(long a,long b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                long temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        
        static class pair implements Comparable<pair>
        {
          Integer x;
          Integer y;
          Long z;
            pair(int l,int m,long n)
            {
                this.x=l;
                this.y=m;
                this.z=n;
            }
 
           
 
			public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return (x)+" "+(y)+" "+z;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x.equals(x) && p.y.equals(y) ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Long(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
               
    
}
 
class dsu{
    int parent[];
    long sz[];
    dsu(int n){
        parent=new int[n+1];
        sz=new long[n+1];
        for(int i=0;i<=n;i++)
        {
            parent[i]=i;
            sz[i]=1;
        }
    }
    int root(int n) {
        while(parent[n]!=n)
        { 
            parent[n]=parent[parent[n]];
            n=parent[n];
        }
        return n;
    }
    void union(int _a,int _b) {
        int p_a=root(_a);
        int p_b=root(_b);
        
        parent[p_a]=p_b;
        sz[p_b]+=sz[p_a];
            
    }
    long find(int a,int b) {
    	int root_a=root(a);
    	int root_b=root(b);
        if(root_a==root_b)
            return 0;
        else
            return  sz[root_a]*sz[root_b];
    }
    
    
}
class Segment{ 
    long seg[];
    long lazy[];
    long a[];
    Segment (int n,long a2 []){
    	a = new long [n];
        seg=new long[4*n];
        lazy=new long[4*n];
        a = a2.clone();
    }
    public void build(int node,int start,int end) {
        if(start==end) {
            seg[node]=a[start];
            return ;
        }
        int mid=(start+end)/2;
        build(2*node+1,start,mid);
        build(2*node+2,mid+1,end);
        seg[node]=Math.max(seg[2*node+1], seg[2*node+2]);
    }
    
   
   /* public void update(int node,int start,int end,int fi,long val) {
        if(start==end) {
            seg[node]+=val;
            return;
        }
        int mid=(start+end)/2;
        if(fi>=start && fi<=mid) {
            update(2*node+1,start,mid,fi,val);
        }
        else
            update(2*node+2,mid+1,end,fi,val);
        seg[node]=Math.max(seg[2*node+1],seg[2*node+2]);
    }*/
    public long query(int node,int start,int end,int l,int r,int t) {
        if(l>end || r<start)
        {
        		return 0;
        }
        if(start>=l && end<=r)
        {
        	return seg[node];
        }
        
        int  mid=(start+end)/2;
         return Math.max(query(2*node+1,start,mid,l,r,t),query(2*node+2,mid+1,end,l,r,t));

    }
   /* public void updateRange(int node,int start,int end,int l,int r,long m) {
        if(lazy[node]!=0) {
            seg[node]=Math.max(lazy[node],seg[node]);
            if(start!=end) {
                lazy[2*node+1]=(Math.max(lazy[node],lazy[2*node+1]));
                lazy[2*node+2]=(Math.max(lazy[node],lazy[2*node+2]));
            }
            lazy[node]=0;
        }
        if(l>end || r<start)
            return ;
        if(start>=l && end<=r) {
            seg[node]=Math.max(m,seg[node]);
            if(start!=end) {
            	 lazy[2*node+1]=(Math.max(m,lazy[2*node+1]));
                 lazy[2*node+2]=(Math.max(m,lazy[2*node+2]));
            }
            return ;
        }
        int mid=(start+end)/2;
        updateRange(2*node+1,start,mid,l,r,m);
        updateRange(2*node+2,mid+1,end,l,r,m);
        seg[node]=Math.max(seg[2*node+1],seg[2*node+2]);
    }
    public long queryRange(int node,int start,int end,int l,int r) {
    	if(lazy[node]!=0) {
            seg[node]=Math.max(lazy[node],seg[node]);
            if(start!=end) {
                lazy[2*node+1]=(Math.max(lazy[node],lazy[2*node+1]));
                lazy[2*node+2]=(Math.max(lazy[node],lazy[2*node+2]));
            }
            lazy[node]=0;
        }
        if(l>end || r<start)
            return 0;
        if(start>=l && end<=r)
            return seg[node];
        
        int  mid=(start+end)/2;
        return Math.max(queryRange(2*node+1,start,mid,l,r),queryRange(2*node+2,mid+1,end,l,r));
    }*/
    
}
