Nick had received an awesome array of integers a=[a_1, a_2, ..., a_n] as a gift for his 5 birthday from his mother. He was already going to explore its various properties but after unpacking he was disappointed a lot because the product a_1 ⋅ a_2 ⋅ ... a_n of its elements seemed to him not large enough.

He was ready to throw out the array, but his mother reassured him. She told him, that array would not be spoiled after the following operation: choose any index i (1 ≤ i ≤ n) and do a_i := -a_i - 1.

For example, he can change array [3, -1, -4, 1] to an array [-4, -1, 3, 1] after applying this operation to elements with indices i=1 and i=3. 

Kolya had immediately understood that sometimes it's possible to increase the product of integers of the array a lot. Now he has decided that he wants to get an array with the maximal possible product of integers using only this operation with its elements (possibly zero, one or more times, as many as he wants), it is not forbidden to do this operation several times for the same index. 

Help Kolya and print the array with the maximal possible product of elements a_1 ⋅ a_2 ⋅ ... a_n which can be received using only this operation in some order.

If there are multiple answers, print any of them.

Input

The first line contains integer n (1 ≤ n ≤ 10^{5}) — number of integers in the array.

The second line contains n integers a_1, a_2, …, a_n (-10^{6} ≤ a_i ≤ 10^{6}) — elements of the array

Output

Print n numbers — elements of the array with the maximal possible product of elements which can be received using only this operation in some order from the given array.

If there are multiple answers, print any of them.

Examples

Input


4
2 2 2 2


Output


-3 -3 -3 -3 

Input


1
0


Output


0 

Input


3
-3 -3 2


Output


-3 -3 2 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;

//import Number_theory.pair;

import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

//import graph_representation.edge;
public class hacker49 {
	public static int r1=0;
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
static 	ArrayList<Integer>[] f=new ArrayList[400001];
static int[] vis=new int[400001];
static 	int[] deg=new int[100001];
	static HashMap<Long,Integer> e=new HashMap<>();
	public static void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();

int n=s.nextInt();
//ArrayList<pair> e1=new ArrayList<>();
//ArrayList<pair> e2=new ArrayList<>();
long[] a=new long[n+1];
for(int i=1;i<=n;i++) {
	a[i]=s.nextLong();
	
}
//ArrayList<>
if(n%2==0) {
	for(int i=1;i<=n;i++) {
		if(a[i]>=0) {
			a[i]=(-a[i]-1);
		}
	}
	for(int i=1;i<=n;i++) {
		out.print(a[i]+" ");
	}
}else {

	for (int i=1;i<=n;i++){
        if (a[i] >= 0) a[i] = -a[i]-1;
    }
    if (n%2!=0){
        long mx = -1; 
        		int ind = -1;
        for (int i=1;i <= n; i++){
            if (Math.abs(a[i]) > mx){
                mx = Math.abs(a[i]);
                ind = i;
            }
        }
//        if(ind!=-1) {
        a[ind] = -a[ind]-1;
//        else {
        	
//        }
    }
    for(int i=1;i<=n;i++) {
    out.print(a[i]+" " );
    }
}
		out.close();

	}
	static void dfs(int node) {
		vis[node]=1;
		for(int i=0;i<f[node].size();i++) {
			if(vis[f[node].get(i)]==0) {
				dfs(f[node].get(i));
			}
		}
	}
	static class pair implements Comparable<pair>{
		private long a;
		private int b;
		pair(long a,int b){
			this.a=a;
			this.b=b;
		}
		public int compareTo(pair o) {
			return Long.compare(this.a, o.a);
		}
	}
	public static long im(long a) {
		return binary_exponentiation_1(a,mod-2)%mod;
	}
	public static long binary_exponentiation_1(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=((res)%(1000000007) * (a)%(1000000007))%(1000000007);
				n--;
			}else {
				a=((a)%(1000000007) *(a)%(1000000007))%(1000000007);
				n/=2;
			}
		}
		return (res)%(1000000007);
		
	}

	public static long[] fac=new long[100001];
	public static void find_factorial() {
		fac[0]=1;
		fac[1]=1;
		for(int i=2;i<=100000;i++) {
			fac[i]=(fac[i-1]*i)%(mod);
		}
	}
	static long c1=0;
	static long c2=0;
	static boolean bs1(long pos,long n,long x) {
		long l=0;
		long r=n;
		
		out:while(l<r) {
		long mid=(l+r)/2;
			if(mid<pos) {
//				if(l!=pos) {
//				c1++;}
				c1++;
				l=mid+1;
				
			}else {
				r=mid;
				c2++;
			}
		}
		if(c1<=x && c2<=(n-x)) {
//			return true;
//			System.out.println(c1+" "+c2);
		return true;
		}else {
			return false;
		}
		
	}
	static long v1=0;
	static long v2=0;
	static void bs2(long pos,long n,long x) {
		long left = 0, right = n;
		 
	    while(left < right) {
	        long middle = (left + right) / 2;
	        if (pos >= middle) {
	            if (pos != middle) v1++;
	            left = middle + 1;
	        }
	        else if (pos < middle){
	            v2++;
	            right = middle;
	        }
	    }
//		retur true
	    System.out.println(v1+" "+v2);
	}
	
	static long mod=1000000007;
	public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
	static long c=0;
	public static long res=1;
	public static void prime_factorization(long n) {
		for(long i=2;(long)(i*i)<=n;i++) {
			if(n%i==0) {
				long count=0;
				while(n%i==0) {
					count++;
					n/=i;
				}
//			prime_pairs.add(new pair(i,count));
//			res*=(count+1);
				c+=(count);
			}
		}
		if(n>1) {
//			prime_pairs.add(new pair(n,1));
//		res*=2;
			c+=(1);
		}
		
	}
	
		
	
}