Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn't like the number 0, he threw away all numbers equal to 0 from the array. As a result, he got an array a of length n.

Pupsen, on the contrary, likes the number 0 and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array b of length n such that ∑_{i=1}^{n}a_i ⋅ b_i=0. Since Vupsen doesn't like number 0, the array b must not contain numbers equal to 0. Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed 10^9. Please help Vupsen to find any such array b!

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The next 2 ⋅ t lines contain the description of test cases. The description of each test case consists of two lines.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5) — the length of the array.

The second line contains n integers a_1, a_2, …, a_n (-10^4 ≤ a_i ≤ 10^4, a_i ≠ 0) — the elements of the array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print n integers b_1, b_2, …, b_n — elements of the array b (|b_1|+|b_2|+… +|b_n| ≤ 10^9, b_i ≠ 0, ∑_{i=1}^{n}a_i ⋅ b_i=0).

It can be shown that the answer always exists.

Example

Input


3
2
5 5
5
5 -2 10 -9 4
7
1 2 3 4 5 6 7


Output


1 -1
-1 5 1 -1 -1
-10 2 2 -3 5 -1 -1

Note

In the first test case, 5 ⋅ 1 + 5 ⋅ (-1)=5-5=0. You could also print 3 -3, for example, since 5 ⋅ 3 + 5 ⋅ (-3)=15-15=0

In the second test case, 5 ⋅ (-1) + (-2) ⋅ 5 + 10 ⋅ 1 + (-9) ⋅ (-1) + 4 ⋅ (-1)=-5-10+10+9-4=0.
//package com.company;

import java.io.*;
import java.lang.reflect.Array;
import java.text.DecimalFormat;
import java.util.*;

public class Main {

    static boolean[] primecheck = new boolean[1000002];

    public static void main(String[] args) throws IOException {
        OutputStream outputStream = System.out;
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        PROBLEM solver = new PROBLEM();
        int t = 1;
        t = in.nextInt();
        for (int i = 0; i < t; i++) {
            solver.solve(in, out);
        }
        out.close();
    }

    static class PROBLEM {

        public void solve(FastReader in, PrintWriter out) {

            int n = in.nextInt(), a[] = in.readArray(n);
            int[] b = new int[n];

            if((n&1) == 0){
                for (int i = 0; i < n-1; i+=2) {
                    b[i] = a[i+1];
                    b[i+1] = a[i];

                    if(a[i] < 0 && a[i+1] < 0) b[i]*=-1;
                    else if(a[i] < 0) b[i+1] *= -1;
                    else if(a[i+1] < 0) b[i] *= -1;
                    else b[i] *= -1;
                }
            }else{
                for (int i = 0; i < n-3; i+=2) {
                    b[i] = a[i+1];
                    b[i+1] = a[i];

                    if(a[i] < 0 && a[i+1] < 0) b[i]*=-1;
                    else if(a[i] < 0) b[i+1] *= -1;
                    else if(a[i+1] < 0) b[i] *= -1;
                    else b[i] *= -1;
                }

                b[n-3] = a[n-2]*a[n-1];
                b[n-2] = a[n-1]*a[n-3];
                b[n-1] = a[n-2]*a[n-3]*2*-1;
            }

            for (int i = 0; i < n; i++) {
                out.print(b[i] + " ");
            }
            out.println();



//            int a = in.nextInt(), b = in.nextInt(), c = in.nextInt();
//
//            long x = 0, y = 0;
//
//            x = (c/2)*3 + (b/2)*2 + (a/2);
//            y = (c/2)*3 + (b/2)*2 + (a/2);
//
//            a &= 1;
//            b &= 1;
//            c &= 1;
//
//            if(c==1){
//                x+=3;
//                if(b == 1){
//                    y+=2 + a;
//                }else y+=a;
//            }else{
//                if(b == 1) {
//                    x += 2;
//                }
//                y+=a;
//            }
//
//            out.println(Math.abs(x-y));
        }
    }

    static ArrayList<ArrayList<Integer>> createAdj(int n, int e){

        FastReader in = new FastReader();
        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();

        for (int i = 0; i < n + 1; i++) {
            adj.add(new ArrayList<>());
        }

        for (int i = 0; i < e; i++) {

            int a = in.nextInt(), b = in.nextInt();
            System.out.println(a);

            adj.get(a).add(b);
            adj.get(b).add(a);
        }


        return adj;
    }

    static int binarySearch(int[] a, int l, int r, int x){
        if(r>=l){
            int mid = l + (r-l)/2;

            if(a[mid] == x) return mid;

            if(a[mid] > x) return binarySearch(a, l, mid-1, x);
            else return binarySearch(a,mid+1, r, x);
        }
        return -1;
    }

    static boolean isPalindromeI(int n){

        int d = 0;
        int y = n;
        while(y>0){
            d++;
            y/=10;
        }

        int[] a = new int[d];
        for (int i = 0; i < d; i++) {
            a[i] = n%10;
            n/=10;
        }

        System.out.println(Arrays.toString(a));
        for (int i = 0; i < d / 2; i++) {
            if(a[i] != a[d-i-1]) return false;
        }
        return true;
    }

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

    static boolean isSquare(double a) {
        boolean isSq = false;
        double b = Math.sqrt(a);
        double c = Math.sqrt(a) - Math.floor(b);

        if (c == 0) isSq = true;

        return isSq;
    }

    static int exponentMod(int A, int B, int C) {

        // Base cases
        if (A == 0)
            return 0;
        if (B == 0)
            return 1;

        // If B is even
        long y;
        if (B % 2 == 0) {
            y = exponentMod(A, B / 2, C);
            y = (y * y) % C;
        }

        // If B is odd
        else {
            y = A % C;
            y = (y * exponentMod(A, B - 1, C) % C) % C;
        }

        return (int) ((y + C) % C);
    }


    static class Pair implements Comparable<Pair>{

        int x, y;

        Pair(int x, int y){
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair o){
            int ans = Integer.compare(x, o.x);
            //if(o.y == y) ans = Integer.compare(x, o.x);

            return ans;
        }
    }

    static class Tuple implements Comparable<Tuple>{

        int x, y, id;

        Tuple(int x, int y, int id){
            this.x = x;
            this.y = y;
            this.id = id;
        }

        public int compareTo(Tuple o){
            int ans = Integer.compare(x, o.x);
            if(o.x == x) ans = Integer.compare(y, o.y);

            return ans;
        }
    }

//    public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
//        public U x;
//        public V y;
//
//        public Pair(U x, V y) {
//            this.x = x;
//            this.y = y;
//        }
//
//        public int hashCode() {
//            return (x == null ? 0 : x.hashCode() * 31) + (y == null ? 0 : y.hashCode());
//        }
//
//        public boolean equals(Object o) {
//            if (this == o)
//                return true;
//            if (o == null || getClass() != o.getClass())
//                return false;
//            Pair<U, V> p = (Pair<U, V>) o;
//            return (x == null ? p.x == null : x.equals(p.x)) && (y == null ? p.y == null : y.equals(p.y));
//        }
//
//        public int compareTo(Pair<U, V> b) {
//            int cmpU = x.compareTo(b.x);
//            return cmpU != 0 ? cmpU : y.compareTo(b.y);
//        }
//
//        public String toString() {
//            return String.format("(%s, %s)", x.toString(), y.toString());
//        }
//
//    }

    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());
        }

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

        boolean nextBoolean() {
            return !(nextInt() == 0);
        }
        // boolean nextBoolean(){return Boolean.parseBoolean(next());}

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int[] readArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) array[i] = nextInt();
            return array;
        }

    }

    private static int[] mergeSort(int[] array) {

        //array.length replaced with ctr
        int ctr = array.length;
        if (ctr <= 1) {
            return array;
        }

        int midpoint = ctr / 2;

        int[] left = new int[midpoint];
        int[] right;

        if (ctr % 2 == 0) {
            right = new int[midpoint];
        } else {
            right = new int[midpoint + 1];
        }

        for (int i = 0; i < left.length; i++) {
            left[i] = array[i];
        }

        for (int i = 0; i < right.length; i++) {
            right[i] = array[i + midpoint];
        }

        int[] result = new int[array.length];

        left = mergeSort(left);
        right = mergeSort(right);

        result = merge(left, right);

        return result;
    }

    private static int[] merge(int[] left, int[] right) {

        int[] result = new int[left.length + right.length];
        int leftPointer = 0, rightPointer = 0, resultPointer = 0;

        while (leftPointer < left.length || rightPointer < right.length) {

            if (leftPointer < left.length && rightPointer < right.length) {

                if (left[leftPointer] < right[rightPointer]) {
                    result[resultPointer++] = left[leftPointer++];
                } else {
                    result[resultPointer++] = right[rightPointer++];
                }
            } else if (leftPointer < left.length) {
                result[resultPointer++] = left[leftPointer++];
            } else {
                result[resultPointer++] = right[rightPointer++];
            }
        }
        return result;
    }

    public static void Sieve(int n) {

        Arrays.fill(primecheck, true);
        primecheck[0] = false;
        primecheck[1] = false;

        for (int i = 2; i * i < n + 1; i++) {
            if (primecheck[i]) {
                for (int j = i * 2; j < n + 1; j += i) {
                    primecheck[j] = false;
                }
            }
        }
    }
}


