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.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.PI;
import static java.lang.System.in;
import static java.lang.System.out;
import static java.lang.System.err;
/*
-1 1 
11 19 11 19 11 
1 1 1 1 1 1 -3 
*/
public class D {    

    static long LCM(long a, long b) {
        long gcd = Foster.gcd(a, b);
        return (a*b)/gcd;
    }

    static long[] forOdd(long a[], int n) {
        long sumNeg = 0, sumPos = 0;
        boolean hasPos = false, hasNeg = false;
        for(long i : a) {
            if(i < 0) {
                sumNeg += Math.abs(i);
                hasNeg = true;
            }
            else {
                sumPos += i;
                hasPos = true;
            }
        }
        if(!hasNeg) {
            int idx = biggestIdx(a);
            sumNeg = Math.abs(a[idx]);
            sumPos -= Math.abs(a[idx]);
            long lcm = LCM(sumNeg, sumPos);
            long b[] = new long[n];
            for(int i = 0; i < n; i++) {
                if(i==idx) {
                    b[i] = - (lcm/sumNeg);
                } else {
                    b[i] = lcm/sumPos;
                }
            }
            return b;
        }
        if(!hasPos) {
            int idx = biggestIdx(a);
            sumPos = Math.abs(a[idx]);
            sumNeg -= Math.abs(a[idx]);
            long lcm = LCM(sumNeg, sumPos);
            long b[] = new long[n];
            for(int i = 0; i < n; i++) {
                if(i==idx) {
                    b[i] = -(lcm/sumPos);
                } else {
                    b[i] = lcm/sumNeg;
                }
            }
            return b;
        }
        
        long sum = 0;
        for(long i : a) sum += i;
        int idx = biggestIdx(a);
        sumNeg = Math.abs(a[idx]);
        sumPos = Math.abs(sum-a[idx]);
        if(sumPos==0) {
            idx = biggestIdx(a);
            sumNeg = Math.abs(a[idx]);
            sumPos = Math.abs(sum-a[idx]);
        }
            
        if(sumPos==0) {
            sumNeg = 0;
            sumPos = 0;
            for(long i : a) {
                if(i < 0)   sumNeg += Math.abs(i);
                else    sumPos += i;
            }
            long lcm = LCM(sumNeg, sumPos);
            long b[] = new long[n];
            for(int i = 0; i < n; i++) {
                if(a[i] < 0) {
                    b[i] = lcm/sumNeg;
                } else {
                    b[i] = lcm/sumPos;
                }
            }
            return b;

        } else {
            long b[] = solveForBoth(sumNeg, sumPos, a, n, idx, sum);
            return b;
        }         
    }
    static long[] solveForBoth(long sumNeg, long sumPos, long []a, int n, int idx, long sum) {
        
        long lcm = LCM(sumNeg, sumPos);
        long b[] = new long[n];
        for(int i = 0; i < n; i++) {
            if(i==idx) {
                if(a[idx] < 0 && sum-a[idx] < 0) {
                    b[i] = -(lcm/sumNeg);
                }
                else if(a[idx] > 0 && sum-a[idx] > 0) {
                    b[i] = -(lcm/sumNeg);
                } else {
                    b[i] = (lcm/sumNeg);
                }
            } else {
                b[i] = lcm/sumPos;
            }
        }
 
        return b;
    }

    public static void main(String[] args) throws Exception {   
        Foster sc = new Foster();
        PrintWriter p = new PrintWriter(out);

       /*
        * Is that extra condition needed
        * Check overflow in pow function or in general
        * Check indices of read array functions
        * Think of an easier solution because the problems you solve are always easy
        * Check the iterator of loop
        */   

        int t = sc.nextInt();
        while(t--!=0) {
            int n = sc.nextInt();
            long a[] = sc.longArray(n);
            long b[] = new long[n];
            if(n%2==0) {
                for(int i = 0; i < n; i++) {
                    if(i%2==0) {
                        b[i] = -a[i+1];
                    } else {
                        b[i] = a[i-1];
                    }
                }
            }
            else {
                long copyA[] = Arrays.copyOf(a, 3);
                long tempB[] = forOdd(copyA, 3);
                b[0] = tempB[0];    b[1] = tempB[1];    b[2] = tempB[2];
                for(int i = 3; i < n; i++) {
                    if(i%2!=0) {
                        b[i] = -a[i+1];
                    } else {
                        b[i] = a[i-1];
                    }
                }
            }

            // go(a, b);
            for(int i = 0; i < a.length; i++) {
                p.print(b[i] + " ");
            }
            p.println();
        }
        p.close();
    }
    

    static void go(long a[], long b[]) {
        long sum = 0;
        for(int i = 0; i < a.length; i++) {
            sum += (a[i] * b[i]);
        }
        out.println("final = " + sum);
    }

    static int biggestIdx(long a[]) {
        long min = Integer.MAX_VALUE;
        int idx = -1;
        for(int i = 0; i < a.length; i++) {
            if(Math.abs(a[i]) < min) {
                min = Math.abs(a[i]);
                idx = i;
            }
        }
        return idx;
    }

    static long[] sort(long a[]) {
        ArrayList<Long> arr = new ArrayList<>();
        for(long i : a) {
            arr.add(i);
        }
        Collections.sort(arr);
        for(int i = 0; i < arr.size(); i++) {
            a[i] = arr.get(i);
        }
        return a;
    }
    static int[] sort(int a[]) {
        ArrayList<Integer> arr = new ArrayList<>();
        for(int i : a){
            arr.add(i);
        }
        Collections.sort(arr);
        // Collections.reverse(arr);
        for(int i = 0; i < arr.size(); i++){
            a[i] = arr.get(i);
        }
        return a;
    }   

    static class Foster {
        BufferedReader br = new BufferedReader(new InputStreamReader(in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                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());
        }
        int[] intArray(int n) {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        long[] longArray(int n) {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        static long pow(long... a) {
            long mod = Long.MAX_VALUE;
            if(a.length == 3)   mod = a[2];
            long res = 1;
            while(a[1] > 0) {
                if((a[1] & 1) == 1)
                    res = (res * a[0]) % mod;
                a[1] /= 2;
                a[0] = (a[0] * a[0]) % mod;
            }
            return res;
        }
        static long gcd(long a, long b) {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }
    }
}