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.
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class JavaApplication1 {

    static int num = 0;
    static long mod = (long) 1e9 + 7;

    public static void main(String[] args) throws IOException {
        BufferedWriter print = new BufferedWriter(new OutputStreamWriter(System.out));
        fast in = new fast();
        int t = in.nextInt();
        while(t--!=0){
            int n=in.nextInt();
            int[]arrA=new int[n];
            for (int i = 0; i < n; i++) {
                arrA[i]=in.nextInt();
            }
            int[]arrB=new int[n];
            if(n%2==0){
                for (int i = 0; i < n; i+=2) {
                    arrB[i]=arrA[i+1];
                    arrB[i+1]=-arrA[i];
                }
            }else{
                if(arrA[0]!=arrA[2]){
                    arrB[0]=-arrA[1];
                    arrB[1]=arrA[0]-arrA[2];
                    arrB[2]=arrA[1];
                }else{
                    arrB[0]=-arrA[1];
                    arrB[1]=arrA[0]+arrA[2];
                    arrB[2]=-arrA[1];
                }
                for (int i = 3; i < n; i+=2) {
                    arrB[i]=arrA[i+1];
                    arrB[i+1]=-arrA[i];
                }
            }
            for (int i = 0; i < n; i++) {
                System.out.print(arrB[i]+" ");
            }
            System.out.println("");
        }
    }

    public static long binpow(long a, long b) {
        a %= mod;
        long out = 1;
        while (b > 0) {
            if ((b & 1) != 1) {
            } else {
                out = (out * a % mod);
            }
            a = (a * a % mod);
            b >>= 1;
        }
        return out;
    }

    static long LowerBound(long a[], long x) {
        long l = -1, r = a.length;
        while (l + 1 < r) {
            long m = (l + r) >>> 1;
            if (a[(int) m] >= x) {
                r = m;
            } else {
                l = m;
            }
        }
        return r;
    }

    public static boolean isPrime(long num) {
        if (num <= 1) {
            return false;
        } else {
            long sq = (long) Math.sqrt(num) + 1;
            for (long i = 2; i < sq; i++) {
                if (num % i == 0) {
                    return false;
                }
            }
            return true;
        }
    }

    public static boolean checkPalindrome(String x) {
        String temp = "";
        if (x.length() % 2 == 0) {
            for (int i = x.subSequence(x.length() / 2, x.length()).length() - 1; i >= 0; i--) {
                temp += x.subSequence(x.length() / 2, x.length()).charAt(i);
            }
            return x.substring(0, x.length() / 2).equals(temp);
        } else {
            for (int i = x.subSequence(x.length() / 2, x.length()).length() - 1; i > 0; i--) {
                temp += x.subSequence(x.length() / 2, x.length()).charAt(i);
            }
            return x.substring(0, x.length() / 2).equals(temp);
        }
    }

    public static boolean isVowel(char c) {
        if (c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u') {
            return true;
        } else {
            return false;
        }
    }

//    public static void sub(String s, String ans) {
//        if (s.length() == 0) {
//            arr.add(ans);
//            return;
//        }
//        sub(s.substring(1), ans + s.charAt(0));
//        sub(s.substring(1), ans);
//    }
    public static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    public static long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }

    static class fast {

        BufferedReader br;
        StringTokenizer st;

        public fast() {
            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());
        }

        double nextFloat() {
            return Float.parseFloat(next());
        }

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