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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer; 
						  
						
						public class temp4 {
							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 class Reader 
						    { 
						        final private int BUFFER_SIZE = 1 << 16; 
						        private DataInputStream din; 
						        private byte[] buffer; 
						        private int bufferPointer, bytesRead; 
						  
						        public Reader() 
						        { 
						            din = new DataInputStream(System.in); 
						            buffer = new byte[BUFFER_SIZE]; 
						            bufferPointer = bytesRead = 0; 
						        } 
						  
						        public Reader(String file_name) throws IOException 
						        { 
						            din = new DataInputStream(new FileInputStream(file_name)); 
						            buffer = new byte[BUFFER_SIZE]; 
						            bufferPointer = bytesRead = 0; 
						        } 
						  
						        public String readLine() throws IOException 
						        { 
						            byte[] buf = new byte[64]; // line length 
						            int cnt = 0, c; 
						            while ((c = read()) != -1) 
						            { 
						                if (c == '\n') 
						                    break; 
						                buf[cnt++] = (byte) c; 
						            } 
						            return new String(buf, 0, cnt); 
						        } 
						  
						        public int nextInt() throws IOException 
						        { 
						            int ret = 0; 
						            byte c = read(); 
						            while (c <= ' ') 
						                c = read(); 
						            boolean neg = (c == '-'); 
						            if (neg) 
						                c = read(); 
						            do
						            { 
						                ret = ret * 10 + c - '0'; 
						            }  while ((c = read()) >= '0' && c <= '9'); 
						  
						            if (neg) 
						                return -ret; 
						            return ret; 
						        } 
						  
						        public long nextLong() throws IOException 
						        { 
						            long ret = 0; 
						            byte c = read(); 
						            while (c <= ' ') 
						                c = read(); 
						            boolean neg = (c == '-'); 
						            if (neg) 
						                c = read(); 
						            do { 
						                ret = ret * 10 + c - '0'; 
						            } 
						            while ((c = read()) >= '0' && c <= '9'); 
						            if (neg) 
						                return -ret; 
						            return ret; 
						        } 
						  
						        public double nextDouble() throws IOException 
						        { 
						            double ret = 0, div = 1; 
						            byte c = read(); 
						            while (c <= ' ') 
						                c = read(); 
						            boolean neg = (c == '-'); 
						            if (neg) 
						                c = read(); 
						  
						            do { 
						                ret = ret * 10 + c - '0'; 
						            } 
						            while ((c = read()) >= '0' && c <= '9'); 
						  
						            if (c == '.') 
						            { 
						                while ((c = read()) >= '0' && c <= '9') 
						                { 
						                    ret += (c - '0') / (div *= 10); 
						                } 
						            } 
						  
						            if (neg) 
						                return -ret; 
						            return ret; 
						        } 
						  
						        private void fillBuffer() throws IOException 
						        { 
						            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
						            if (bytesRead == -1) 
						                buffer[0] = -1; 
						        } 
						  
						        private byte read() throws IOException 
						        { 
						            if (bufferPointer == bytesRead) 
						                fillBuffer(); 
						            return buffer[bufferPointer++]; 
						        } 
						  
						        public void close() throws IOException 
						        { 
						            if (din == null) 
						                return; 
						            din.close(); 
						        } 
						    } */
							static class Print
						{
							    private final BufferedWriter bw;
							    public Print()
							    {
							        bw=new BufferedWriter(new OutputStreamWriter(System.out));
							    }
						    public void print(String str)throws IOException
							    {
							        bw.append(str);
							    }
							    public void println(String str)throws IOException
							    {
							        print(str);
							        bw.append("\n");
							    }
							    public void close()throws IOException
							    {
							        bw.close();
							    }} 
								
								
								
								public static void main(String[] args) throws IOException {			
									FastReader scn=new FastReader();
									Print pr=new Print();
									int n=scn.nextInt(),max=0;
									int[] arr=new int[n];
									for(int i=0;i<n;i++){
										arr[i]=scn.nextInt();
										if(arr[i]>=0){
											arr[i]=-1*arr[i]-1;
										}
										if(arr[i]<arr[max])max=i;
									}
									
									if((n&1)>0){
										arr[max]=-1*arr[max]-1;
									}
									for(int i=0;i<n;i++){
										pr.print(arr[i]+" ");
									}
									pr.println("");
									
									pr.close();
								}
								public static class node{
									int a;
									int b;
									public node(int a,int b){
										this.a=a;this.b=b;
									}
								}
								
						}
							