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.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

public class Main2 {

    static int mod = 1000000007;
    static FastScanner scanner;

    static class Ans {
        long a, b;

        public Ans(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }

    public static void main(String[] args) {
        scanner = new FastScanner();
        int n = scanner.nextInt();
        long[] a = scanner.nextLongArray(n);
        long[] b = Arrays.copyOf(a, n);

        for (int i = 0; i < n; i++) {
            if (a[i] >= 0) b[i] = -a[i] - 1;
            else b[i] = a[i];
        }
        if (n % 2 == 0) {
            System.out.println(LongStream.of(b).mapToObj(ii -> "" + ii).collect(Collectors.joining(" ")));
        } else {
            int minNeg = -1;
            int maxPos = -1;
            for (int i = 0; i < n; i++) {
                if (a[i] < -1 && (minNeg == -1 || a[i] < a[minNeg])) minNeg = i;
                if (a[i] > 0 && (maxPos == -1 || a[i] > a[maxPos])) maxPos = i;
            }
            if (minNeg != -1 && maxPos != -1) {
                if (Math.abs(a[minNeg]) < Math.abs(-a[maxPos] - 1)) {
                    b[maxPos] = a[maxPos];
                } else {
                    b[minNeg] = -a[minNeg] - 1;
                }
            } else if (minNeg != -1) {
                b[minNeg] = -a[minNeg]-1;
            } else if (maxPos != -1) {
                b[maxPos] = a[maxPos];
            } else {
                if (b[0] == a[0]) {
                    b[0] = -a[0]-1;
                } else {
                    b[0] = a[0];
                }
            }
            System.out.println(LongStream.of(b).mapToObj(ii -> "" + ii).collect(Collectors.joining(" ")));
        }
    }


/*    public static void main(String[] args) {
        scanner = new FastScanner();
        int n = scanner.nextInt();
        int[] a = scanner.nextIntArray(n);
        if (n == 1) {
            if (a[0] < 0) {
                a[0] = -a[0] - 1;
            }
            System.out.println(a[0]);
            return;
        }
        Arrays.sort(a);




        int negs = 0;
        int zeros = 0;
        int minNeg = Integer.MIN_VALUE;
        int minPos = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            negs += a[i] < 0 ? 1 : 0;
            zeros += a[i] == 0 ? 1 : 0;
            if (a[i] < -1 && a[i] > a[minNeg]) minNeg = i;
            if (a[i] > 0 && a[i] < a[minPos]) minPos = i;
        }
        if (negs == n) {
            System.out.println(IntStream.of(a).mapToObj(i -> "" + i).collect(Collectors.joining(" ")));
            return;
        }
        if (zeros == n) {
            if (n % 2 == 0) {
                System.out.println(IntStream.range(0, n).mapToObj(ii -> "-1" ).collect(Collectors.joining(" ")));
            } else {
                System.out.println(IntStream.of(a).mapToObj(i -> "" + i).collect(Collectors.joining(" ")));
            }
        }

        if (negs + zeros == n) {
            if (zeros % 2 == 0) {
                for (int i = 0; i < n; i++) if (a[i] == 0) a[i] = -1;
                System.out.println(IntStream.of(a).mapToObj(i -> "" + i).collect(Collectors.joining(" ")));
                return;
            } else {
                if (a[0] == -1) {
                    System.out.println(IntStream.of(a).mapToObj(i -> "" + i).collect(Collectors.joining(" ")));
                    return;
                }
                for (int i = n - 1; i >= 0; i--) {
                    if (a[i] == 0) a[i] = -1;
                    if (a[i] == -1) continue;
                    a[i] = -a[i] - 1;
                    break;
                }
                System.out.println(IntStream.of(a).mapToObj(i -> "" + i).collect(Collectors.joining(" ")));
                return;
            }
        }
        int pos = n - zeros - negs;
        if (pos + zeros % 2 == 0) {
            if (negs % 2 == 0) {
                for (int i = 0; i < n; i++) if (a[i] >= 0) a[i] = -a[i] - 1;
            } else {

            }
        } else {
            if (negs % 2 != 0) {

            }
        }
    }*/

    static class WithIdx implements Comparable<WithIdx> {
        long val;
        int idx;

        public WithIdx(long val, int idx) {
            this.val = val;
            this.idx = idx;
        }

        @Override
        public int compareTo(WithIdx o) {
            if (val == o.val) {
                return Integer.compare(idx, o.idx);
            }
            return Long.compare(val, o.val);
        }

        public WithIdx change() {
            this.val = -this.val - 1;
            return this;
        }
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                throw new RuntimeException();
            }
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        int[] nextIntArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) res[i] = nextInt();
            return res;
        }

        long[] nextLongArray(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) res[i] = nextLong();
            return res;
        }

        String[] nextStringArray(int n) {
            String[] res = new String[n];
            for (int i = 0; i < n; i++) res[i] = nextToken();
            return res;
        }
    }

    static class PrefixSums {
        long[] sums;

        public PrefixSums(long[] sums) {
            this.sums = sums;
        }

        public long sum(int fromInclusive, int toExclusive) {
            if (fromInclusive > toExclusive) throw new IllegalArgumentException("Wrong value");
            return sums[toExclusive] - sums[fromInclusive];
        }

        public static PrefixSums of(int[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }

        public static PrefixSums of(long[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }
    }

    static class ADUtils {
        static void sort(int[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                int a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }

        static void reverse(int[] arr) {
            int last = arr.length / 2;
            for (int i = 0; i < last; i++) {
                int tmp = arr[i];
                arr[i] = arr[arr.length - 1 - i];
                arr[arr.length - 1 - i] = tmp;
            }
        }

        static void sort(long[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                long a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }
    }

    static class MathUtils {
        static long[] FIRST_PRIMES = {
                2,     3,      5,      7,     11,     13,     17,     19,     23,     29,
                31,     37,     41,     43,     47,     53,     59,     61,     67,     71,
                73,     79,     83,     89  ,   97 ,    101,    103,    107,    109,    113,
                127,    131,    137,    139,    149,    151,    157,    163,    167,    173,
                179,    181,    191,    193,    197,    199,    211,    223,    227,    229,
                233,    239,    241,    251,    257,    263,    269,    271,    277,    281,
                283,    293,    307,    311,    313,    317,    331,    337,    347,    349,
                353,    359,    367,    373,    379,    383,    389,    397,    401,    409,
                419,    421,    431,    433,    439,    443,    449,    457,    461,    463,
                467,    479,    487,    491,    499,    503,    509,    521,    523,    541,
                547,    557,    563,    569,    571,    577,    587,    593,    599,    601,
                607,    613,    617,    619,    631,    641,    643,    647,    653,    659,
                661,    673,    677,    683,    691,    701,    709,    719,    727,    733,
                739,    743,    751,    757,    761,    769,    773,    787,    797,    809,
                811,    821,    823,    827,    829,    839,    853,    857,    859,    863,
                877,    881,    883,    887,    907,    911,    919,    929,    937,    941,
                947,    953,    967,    971,    977,    983,    991,    997,   1009,   1013,
                1019,   1021,   1031,   1033,   1039,   1049,   1051};

        static long[] primes(int to) {
            long[] all = new long[to + 1];
            long[] primes = new long[to + 1];
            all[1] = 1;
            int primesLength = 0;
            for (int i = 2; i <= to; i ++) {
                if (all[i] == 0) {
                    primes[primesLength++] = i;
                    all[i] = i;
                }
                for (int j = 0; j < primesLength && i * primes[j] <= to && all[i] >= primes[j]; j++) {
                    all[(int) (i * primes[j])] = primes[j];
                }
            }
            return Arrays.copyOf(primes, primesLength);
        }

        static long modpow(long b, long e, long m) {
            long result = 1;

            while (e > 0) {
                if ((e & 1) == 1) {
                    /* multiply in this bit's contribution while using modulus to keep
                     * result small */
                    result = (result * b) % m;
                }
                b = (b * b) % m;
                e >>= 1;
            }

            return result;
        }

        static long submod(long x, long y, long m) {
            return (x - y + m) % m;
        }
    }
}
