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.util.*;
public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int inf = (int) 1e9;
	static int mod = (int) 1e9 + 7;
	static int[] si;
	static ArrayList<Integer> primes;
	static HashSet<Integer> pr;
	static int n;
	static boolean[] in;
	static HashMap<Integer, Integer> factors;
	static HashSet<Integer> f;
    static long []fac;
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n=sc.nextInt();
		pair1 []a=new pair1 [n];
		for(int i=0;i<n;i++)
			a[i]=new pair1(sc.nextInt(), i);
		if(n==1) {
			 if(a[0].a<0)
				   a[0].a=-a[0].a-1;
			out.println(a[0].a);
			
		}
		else if(n%2==0) {
			for(int i=0;i<n;i++)
			   if(a[i].a>=0)
				   a[i].a=-a[i].a-1;
			for(pair1 o:a)
				out.print(o.a+" ");
		}
		else {
			for(int i=0;i<n;i++)
				   if(a[i].a<0)
					   a[i].a=-a[i].a-1;
			Arrays.sort(a);
			int pos=n;
			for(int i=0;i<n;i++)
				if(a[i].a!=0)
					break;
				else {
					pos--;
					a[i].a=-1;
				}
			 pair2 []aa=new pair2[n];
			if(pos==0) {
				for(int i=0;i<n;i++)
					out.print(0+" ");
			}
			else	if( pos==1) {
				for(int i=0;i<n;i++)
					aa[i]=new pair2(a[i].a, a[i].idx);
				Arrays.sort(aa);
				for(pair2 o:aa)
					out.print(o.a+" ");
			}
			else {
				for(int i=n-1;i>=0;i--) {
					if(pos==1)
						break;
					a[i].a=-a[i].a-1;
					pos--;
				}
				for(int i=0;i<n;i++)
					aa[i]=new pair2(a[i].a, a[i].idx);
				Arrays.sort(aa);
				for(pair2 o:aa)
					out.print(o.a+" ");
			}
		  
		}
		out.flush();
	}
	public static class pair1 implements Comparable<pair1>{
		int a;
		int idx;
		pair1(int a,int i){
			this.a=a;
			idx=i;
		}
		public String toString() {
			return a+" "+idx;
		}
		@Override
		public int compareTo(pair1 o) {
			return o.a-a;
		}
	}
	public static class pair2 implements Comparable<pair2>{
		int a;
		int idx;
		pair2(int a,int i){
			this.a=a;
			idx=i;
		}
		public String toString() {
			return a+" "+idx;
		}
		@Override
		public int compareTo(pair2 o) {
			// TODO Auto-generated method stub
			return idx-o.idx;
		}
	}
	static int inver(long x) {
		int a = (int) x;
		int e = (mod - 2);
		int res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				// System.out.println(res*a);
				res = (int) ((1l * res * a) % mod);
			}
			a = (int) ((1l * a * a) % mod);
			e >>= 1;
		}
		// out.println(res+" "+x);
		return res % mod;
	}
	static int atMostSum(int arr[], int n, int k) 
	{ 
	    int sum = 0; 
	    int cnt = 0, maxcnt = 0; 
	  
	    for (int i = 0; i < n; i++) { 
	          
	        // If adding current element doesn't 
	        // cross limit add it to current window 
	        if ((sum + arr[i]) <= k) { 
	            sum += arr[i];  
	            cnt++; 
	        }  
	  
	        // Else, remove first element of current 
	        // window and add the current element 
	        else if(sum!=0) 
	        { 
	            sum = sum - arr[i - cnt] + arr[i]; 
	        } 
	  
	        // keep track of max length. 
	        maxcnt = Math.max(cnt, maxcnt);  
	    } 
	    return maxcnt; 
	}
	public static int[] longestSubarray(int[] inp) {
		// array containing prefix sums up to a certain index i
		int[] p = new int[inp.length];
		p[0] = inp[0];
		for (int i = 1; i < inp.length; i++) {
			p[i] = p[i - 1] + inp[i];
		}

		// array Q from the description below
		int[] q = new int[inp.length];
		q[inp.length - 1] = p[inp.length - 1];
		for (int i = inp.length - 2; i >= 0; i--) {
			q[i] = Math.max(q[i + 1], p[i]);
		}
		int a = 0;
		int b = 0;
		int maxLen = 0;
		int curr;
		int[] res = new int[] { -1, -1 };
		while (b < inp.length) {
			curr = a > 0 ? q[b] - p[a - 1] : q[b];
			if (curr >= 0) {
				if (b - a > maxLen) {
					maxLen = b - a;
					res = new int[] { a, b };
				}
				b++;
			} else {
				a++;
			}
		}
		return res;
	}

	static void factor(int n) {
		if (si[n] == n) {
			f.add(n);
			return;
		}
		f.add(si[n]);
		factor(n / si[n]);
	}

	static void seive() {
		si = new int[1000001];
		primes = new ArrayList<>();
		int N = 1000001;
		pr = new HashSet<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
				pr.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);

		}
	}

	static public class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array, sTree, lazy;

		SegmentTree(int[] in) {
			array = in;
			N = in.length - 1;
			sTree = new int[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N << 1];
			build(1, 1, N);
		}
         public String toString() {
        	 return Arrays.toString(sTree);
         }
		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = array[b];
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				sTree[node] = gcd(sTree[node << 1] , sTree[node << 1 | 1]);
			}
		}

		void update_point(int index, int val) // O(log n)
		{
			index += N - 1;
			sTree[index] += val;
			while (index > 1) {
				index >>= 1;
				sTree[index] = sTree[index << 1] + sTree[index << 1 | 1];
			}
		}

		void update_range(int i, int j, int val) // O(log n)
		{
			update_range(1, 1, N, i, j, val);
		}

		void update_range(int node, int b, int e, int i, int j, int val) {
			if (i > e || j < b)
				return;
			if (b >= i && e <= j) {
				sTree[node] += (e - b + 1) * val;
				lazy[node] += val;
			} else {
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node << 1, b, mid, i, j, val);
				update_range(node << 1 | 1, mid + 1, e, i, j, val);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}

		}

		void propagate(int node, int b, int mid, int e) {
			lazy[node << 1] += lazy[node];
			lazy[node << 1 | 1] += lazy[node];
			sTree[node << 1] += (mid - b + 1) * lazy[node];
			sTree[node << 1 | 1] += (e - mid) * lazy[node];
			lazy[node] = 0;
		}

		int query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		int query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			//propagate(node, b, mid, e);
			int q1 = query(node << 1, b, mid, i, j);
			int q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return gcd(q1 , q2);
		}
	}

	static int gcd(int a, int b) {

		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];

			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			Arrays.fill(size, 1);
		}

		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		void combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];

			} else {
				p[a] = b;
				size[b] += size[a];
			}
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}