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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.LinkedBlockingQueue;

public class Main {
    private static AWriter writer = new AWriter(System.out);
    private static AReader reader = new AReader(System.in);
    private static final int INF=0X3F3F3F3F;
    private static int MAXN=6000+5;
    private static int MAXM=4000+5;
    private static int N,s,t;
    private static int[] dis;
    private static int[] head;
    private static boolean[] vis;
    private static int[] lev;
    private static int tot;
    private static Edge[][] edges;
    static class Edge{
        int flow,cap;
        public Edge() {
            this.flow = 0;
            this.cap = 0;
        }
    }
    private static int dfs(int s,int t,int flow){
        if(s==t)
            return flow;
        int now=flow;
        for(int i=0;i<N;i++){
            if(lev[i]==lev[s]+1&&edges[s][i].cap>edges[s][i].flow){
                int min=Math.min(now,edges[s][i].cap-edges[s][i].flow);
                int nowFlow=dfs(i,t,min);
                edges[s][i].flow+=nowFlow;
                edges[i][s].flow-=nowFlow;
                now-=nowFlow;
            }
            if(now==0)
                break;
        }
        return flow-now;
    }
    private static boolean bfs(int s,int t){
        lev=new int[MAXN];
        Queue<Integer> queue=new LinkedBlockingQueue<>();
        queue.add(s);
        lev[s]=1;
        while(!queue.isEmpty()){
            int u=queue.poll();
            for(int i=0;i<N;i++){
                if(lev[i]==0&&edges[u][i].cap>edges[u][i].flow){
                    lev[i]=lev[u]+1;
                    queue.add(i);
                }
            }
        }
        return lev[t]!=0;
    }
    private static void dinic(int s,int t){
        int flow=0,tf=0;
        while(bfs(s,t)){
            while((tf=dfs(s,t,INF))!=0){
                flow+=tf;
            }
        }
    }
    private static boolean[] vi;
    private static List<Long> list,sum;
    private static final double eps=10e-8;
    private static int n,k,b;
    private static int[] a;
    public static void main(String[] args) throws IOException {
        n=reader.nextInt();
        a=new int[n];
        int cnt=0,max=-0x3f3f3f3f,index=0;
        for(int i=0;i<n;i++) {
            a[i] = reader.nextInt();
            if(a[i]>=0)
                a[i]=-a[i]-1;
            cnt++;
            if(max<Math.abs(a[i])) {
                max = Math.abs(a[i]);
                index=i;
            }
        }
        if(cnt%2==1){
           a[index]=-a[index]-1;
        }
        for(int i:a){
            writer.print(i+" ");
        }
        writer.close();
        reader.close();
    }
}

class AReader implements Closeable {
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    public AReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }
    private String innerNextLine() {
        try {
            return reader.readLine();
        } catch (IOException ex) {
            return null;
        }
    }
    public boolean hasNext() {
        while (!tokenizer.hasMoreTokens()) {
            String nextLine = innerNextLine();
            if (nextLine == null) {
                return false;
            }
            tokenizer = new StringTokenizer(nextLine);
        }
        return true;
    }
    public String nextLine() {
        tokenizer = new StringTokenizer("");
        return innerNextLine();
    }
    public String next() {
        hasNext();
        return tokenizer.nextToken();
    }
    public int nextInt() {
        return Integer.valueOf(next());
    }
    public long nextLong() {
        return Long.valueOf(next());
    }
    public double nextDouble() {
        return Double.valueOf(next());
    }
    public BigDecimal nextBigDecimal(){ return new BigDecimal(next()); }
    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
    @Override
    public void close() throws IOException {
        reader.close();
    }
}

// Fast writer for ACM By Azure99
class AWriter implements Closeable {
    private BufferedWriter writer;

    public AWriter(OutputStream outputStream) {
        writer = new BufferedWriter(new OutputStreamWriter(outputStream));
    }

    public void print(Object object) throws IOException {
        writer.write(object.toString());
    }

    public void println(Object object) throws IOException {
        writer.write(object.toString());
        writer.write("\n");
    }

    @Override
    public void close() throws IOException {
        writer.close();
    }
}