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.BigInteger;
import java.util.*;

/**
 *
 * @author Saju
 *
 */

public class Main {

	static int[] dx = { 0, 1, 0, -1 };
	static int[] dy = { -1, 0, 1, 0 };

	static int[] ddx = { 0, 1, 0, -1, -1, 1, 1, -1 };
	static int[] ddy = { -1, 0, 1, 0, -1, -1, 1, 1 };

	static int[] kx = { 2, 1, -1, -2, -2, -1, 1, 2 };
	static int[] ky = { 1, 2, 2, 1, -1, -2, -2, -1 };

	static long MOD = Long.MAX_VALUE;

	static final int MAX = 50000;
	static long INF = Long.MAX_VALUE;

	static double PI = 3.1415926535;

	public static void main(String[] args) {

		InputReader in = new InputReader(System.in);
	
/*
	
		
*/

		int n = in.nextInt();
		int arr[] = new int[n];
		int minVal = -1;
		int minIndex = 0;
		for(int i = 0; i < n; i++){
			arr[i] = in.nextInt();
			if(arr[i] >= 0){
				arr[i] = (-arr[i]) - 1;
			}
			if(arr[i] < minVal){
				minVal = arr[i];
				minIndex = i;
			}
		}
		if(n % 2 != 0){
			arr[minIndex] = (-arr[minIndex]) - 1;
		}
		
		for(int i = 0; i < n; i++){
			System.out.print(arr[i] + " ");
		}
		
		
		
		System.exit(0);
	}

	// nCk
	// private static long binomialCoeff(int n, int k){
	// long[] arr = new long[k + 1];
	// arr[0] = 1;
	// for(int i = 1; i <= n; i++){
	// for(int j = Math.min(i, k); j > 0; j--){
	// arr[j] = (arr[j] + arr[j - 1]) % MOD;
	// }
	// }
	// return arr[k];
	// }

	// BIT =>
	// https://www.hackerearth.com/practice/notes/binary-indexed-tree-or-fenwick-tree/
	// static int BIT[] = new int[MAX + 5];
	//
	// private static int query(int index) {
	// int sum = 0;
	// for (; index > 0; index -= (index & (-index))) {
	// sum += BIT[index];
	// }
	// return sum;
	// }
	//
	// private static void update(int size, int index, int val) {
	// for (; index <= size; index += (index & (-index))) {
	// BIT[index] += val;
	// }
	// }

	/*
	 * 
	 * tutorial :
	 * https://helloacm.com/algorithms-series-0-1-backpack-dynamic-programming-
	 * and-backtracking/
	 * 
	 */

	// here arr and prob zero based index
	// static int backPack(int n, int m, int[] arr, double[] prob, double p) {
	// double dp[][] = new double[n + 1][m + 1];
	// for (int i = 0; i <= n; ++i) {
	// dp[i][0] = 1.0;
	// }
	// for (int i = 1; i <= n; i++) {
	// for (int j = 1; j <= m; j++) {
	//
	// if (j < arr[i - 1]) { // insufficient capacity
	// dp[i][j] = dp[i - 1][j];
	// } else {
	// dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - arr[i - 1]] * (1.0 -
	// prob[i - 1]));
	// }
	//
	// }
	// }
	// for (int i = m; i >= 0; i--) { // reverse checking the maximum weight
	// if ((1.0 - dp[n][i]) <= p) {
	// return i;
	// }
	// }
	// return 0;
	// }

	// here arr and prob one based index
	// static int backPack1(int n, int m, int[] arr, double[] prob, double p) {
	//
	// double dp[] = new double[m + 1];
	//
	// dp[0] = 1.0;
	// for (int i = 1; i <= n; i++) {
	// for (int j = m; j >= arr[i]; --j) {
	// // dp[j] = dp[j] || dp[j - A[i - 1]];
	// dp[j] = Math.max(dp[j], dp[j - arr[i]] * (1.0 - prob[i]));
	// }
	// }
	// for (int i = m; i >= 0; i--) {
	// if (1.0 - dp[i] <= p) {
	// return i;
	// }
	// }
	// return 0;
	// }

	/*
	 *
	 * tutorial :
	 * https://www.hackerearth.com/practice/algorithms/searching/ternary-search/
	 * tutorial/
	 *
	 */

	// lightoj -> 1146
	// static double ternary(Point a, Point b, Point c, Point d) {
	//
	// double l = 0;
	// double r = 1;
	//
	// for (int i = 0; i < 200; i++) {
	// double mid1 = l + ((r - l) / 3);
	// double mid2 = r - ((r - l) / 3);
	//
	// double dis1 = func(a, b, c, d, mid1);
	// double dis2 = func(a, b, c, d, mid2);
	//
	// if(dis1 > dis2){
	// l = mid1;
	//
	// }
	// else{
	// r = mid2;
	// }
	// }
	//
	// return l;
	//
	// }
	//
	// static double func(Point a, Point b, Point c, Point d, double multiple) {
	//
	// double xDifAB = b.x - a.x;
	// double yDifAB = b.y - a.y;
	// double xDifCD = d.x - c.x;
	// double yDifCD = d.y - c.y;
	//
	// double x1 = a.x + xDifAB * multiple;
	// double y1 = a.y + yDifAB * multiple;
	// double x2 = c.x + xDifCD * multiple;
	// double y2 = c.y + yDifCD * multiple;
	//
	// double distance = Math.sqrt(((x1 - x2) * (x1 - x2)) +
	// ((y1 - y2) * (y1 - y2)));
	//
	// return distance;
	// }
	//
	// static class Point{
	// double x;
	// double y;
	//
	// Point(double x, double y){
	// this.x = x;
	// this.y = y;
	// }
	// }

	// static void primeFactorization(int n) {
	// int temp = n;
	// Map<Integer, Integer> map = new HashMap<Integer, Integer>();
	// for (int i = 2; i <= Math.sqrt(n); i++) {
	// if (n % i == 0) {
	// int count = 0;
	// while (n % i == 0) {
	// count++;
	// n = n / i;
	// }
	// System.out.println("i: " + i + ", count: " + count);
	// map.put(i, count);
	// }
	//
	// }
	// if (n != 1) {
	// System.out.println(n);
	// map.put(n, 1);
	// }
	//
	//// calculateSumOfDivisor(map, temp);
	// }

	// static int counter[] = new int[MAX];
	//
	// private static void calculateSumOfDivisor(Map<Integer, Integer> map, int
	// n) {
	// int sum = 1;
	// for(Integer key : map.keySet()){
	// int count = map.get(key);
	// sum *= ((Math.pow(key, count + 1) - 1) / (key - 1));
	// }
	// if(sum < MAX){
	// if(counter[sum] < n){
	//// System.out.println("H");
	// counter[sum] = n;
	// }
	//
	// }
	//
	//// System.out.println(sum);
	// }

	// static int phi[] = new int[MAX];
	// static int phiStepCount[] = new int[MAX];
	// static void computeTotient() {
	//
	// // Create and initialize an array to store
	// // phi or totient values
	// for (int i = 1; i < MAX; i++) {
	// phi[i] = i; // indicates not evaluated yet
	// // and initializes for product
	// // formula.
	// }
	//
	// // Compute other Phi values
	// for (int p = 2; p < MAX; p++) {
	//
	// // If phi[p] is not computed already,
	// // then number p is prime
	// if (phi[p] == p) {
	//
	// // Phi of a prime number p is
	// // always equal to p-1.
	// phi[p] = p - 1;
	//
	// // Update phi values of all
	// // multiples of p
	// for (int i = 2 * p; i < MAX; i += p) {
	//
	// // Add contribution of p to its
	// // multiple i by multiplying with
	// // (1 - 1/p)
	// phi[i] = (phi[i] / p) * (p - 1);
	// }
	//
	// // for (int i = p; i < MAX; i += p) {
	// //
	// // phi[i] -= (phi[i] / p);
	// // }
	//
	// }
	// phiStepCount[p] = phiStepCount[phi[p]] + 1;
	// }
	//
	// for(int i = 1; i < MAX; i++){
	// phiStepCount[i] += phiStepCount[i - 1];
	// }
	// }

	// public static BigInteger floorOfNthRoot(BigInteger x, int n) {
	// int sign = x.signum();
	// if (n <= 0 || (sign < 0))
	// throw new IllegalArgumentException();
	// if (sign == 0)
	// return BigInteger.ZERO;
	// if (n == 1)
	// return x;
	// BigInteger a;
	// BigInteger bigN = BigInteger.valueOf(n);
	// BigInteger bigNMinusOne = BigInteger.valueOf(n - 1);
	// BigInteger b = BigInteger.ZERO.setBit(1 + x.bitLength() / n);
	// do {
	// a = b;
	// b = a.multiply(bigNMinusOne).add(x.divide(a.pow(n - 1))).divide(bigN);
	// } while (b.compareTo(a) == -1);
	// return a;
	// }

	// O(log(max(A, B))).
	// static long gcd(long a, long b) {
	// if (b == 0)
	// return a;
	// return gcd(b, a % b);
	// }

	private static double getDistance(double x1, double y1, double x2, double y2) {

		return Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
	}

	// private static int getDecimal(String str) {
	// int val = 0;
	//
	// for (int i = str.length() - 1, j = 0; i >= 0; i--, j++) {
	// if (str.charAt(i) == '1') {
	// val += Math.pow(2, j);
	// }
	// }
	// return val;
	// }

	// private static int call(int i, int j, int[][] colors) {
	//
	// if (i >= colors.length) {
	// return 0;
	// }
	//
	// if (dp[i][j] != -1) {
	// return dp[i][j];
	//
	// }
	//
	// int result = Integer.MAX_VALUE;
	//
	// for (int k = 0; k < 3; k++) {
	// if (k == j) {
	// continue;
	// } else {
	// result = Math.min(result, call(i + 1, k, colors) + colors[i][j]);
	// }
	// }
	//
	// return dp[i][j] = result;
	// }

	static int dp[][];

	// private static BigInteger fac(int n, int mod) {
	//
	// if (n <= 0) {
	// return BigInteger.ONE;
	// }
	// return BigInteger.valueOf(n).multiply(fac(n - 1, mod));
	// }

	// private static long modInverse(long n, long m){
	// return bigMod(n, m - 2, m);
	// }

	// private static long bigMod(long n, long k, long m) {
	//
	// long ans = 1;
	// while (k > 0) {
	// if ((k & 1) == 1) {
	// ans = (ans * n) % m;
	// }
	// n = (n * n) % m;
	// k >>= 1;
	// }
	// return ans;
	// }

	// Returns an iterator pointing to the first element
	// in the range [first, last] which does not compare less than val.
	// private static int lowerBoundNew(long[] arr, long num){
	// int start = 0;
	// int end = arr.length - 1;
	// int index = 0;
	// int len = arr.length;
	// int mid = 0;
	// while(true){
	// if(start > end){
	// break;
	// }
	// mid = (start + end) / 2;
	// if(arr[mid] > num){
	// end = mid - 1;
	// }
	// else if(arr[mid] < num){
	// start = mid + 1;
	// }
	// else{
	// while(mid >= 0 && arr[mid] == num){
	// mid--;
	// }
	// return mid + 1;
	// }
	// }
	// if(arr[mid] < num){
	// return mid + 1;
	// }
	// return mid;
	// }

	// upper_bound() is a standard library function
	// in C++ defined in the header .
	// It returns an iterator pointing to
	// the first element in the range [first, last)
	// that is greater than value, or last if no such element is found
	// private static int upperBoundNew(long[] arr, long num){
	//
	// int start = 0;
	// int end = arr.length - 1;
	// int index = 0;
	// int len = arr.length;
	// int mid = 0;
	// while(true){
	// if(start > end){
	// break;
	// }
	// mid = (start + end) / 2;
	// if(arr[mid] > num){
	// end = mid - 1;
	// }
	// else if(arr[mid] < num){
	// start = mid + 1;
	// }
	// else{
	// while(mid < len && arr[mid] == num){
	// mid++;
	// }
	// if(mid == len - 1 && arr[mid] == num){
	// return mid + 1;
	// }
	// else{
	// return mid;
	// }
	// }
	// }
	// if(arr[mid] < num){
	// return mid + 1;
	// }
	// return mid;
	// }

	// private static int upperBound(long[] arr, long num) {
	//
	// int start = 0;
	// int end = arr.length;
	//
	// int mid = 0;
	// int index = 0;
	// while (true) {
	//
	//// System.out.println(start + " " + end);
	// if (start > end) {
	// break;
	// }
	// mid = (start + end) / 2;
	// if (arr[mid] > num) {
	// end = mid - 1;
	//
	// } else if (arr[mid] < num) {
	// start = mid + 1;
	// } else {
	// return mid;
	// }
	//
	//// System.out.println("a: " + start + " " + end);
	// }
	//
	// // System.out.println(mid);
	// if (arr[mid] < num) {
	// index = mid + 1;
	// } else {
	// index = mid;
	// }
	// return index;
	// }

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public String next() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());

				}
			} catch (IOException e) {
				return null;
			}
			return tokenizer.nextToken();
		}

		public String nextLine() {
			String line = null;
			try {
				tokenizer = null;
				line = reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return line;
		}

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

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

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

		public boolean hasNext() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());
				}
			} catch (Exception e) {
				return false;
			}
			return true;
		}
	}
}

	 			 						 		 	 	 	   			 	 	