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.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.time.Duration;
import java.time.Instant;
import java.util.ArrayList;
import java.util.StringTokenizer;
import static java.lang.Math.min;
import static java.lang.Math.max;
import static java.lang.Math.abs;

@SuppressWarnings("unused")
public class Main {
	static boolean DEBUG = false;

	public static void main(String[] args) throws IOException {
		Instant start = Instant.now();
		if (args.length == 2) {
			System.setIn(new FileInputStream(new File("D://program//javaCPEclipse//MyJava//src//MyJava//input.txt")));
			// System.setOut(new PrintStream(new File("output.txt")));
			System.setErr(new PrintStream(new File("D://program//javaCPEclipse//MyJava//src//MyJava//error.txt")));
			DEBUG = true;
		}
		Reader fs = new Reader();
		PrintWriter pw = new PrintWriter(System.out);
		int t = fs.nextInt();
		while (t-- > 0) {
			int n = fs.nextInt();
			int a[] = fs.readArray(n);
			if(n % 2 == 1) {
				if(-a[1]-a[2] != 0) {
					pw.print(-a[1]-a[2] + " " + a[0] + " " + a[0] + " ");
				}
				else {
					pw.print(-a[1]+a[2] + " " + a[0] + " " + -a[0] + " ");
				}
				for(int i = 3 ; i < n ; i+=2	) {
					pw.print(a[i + 1] + " " + -a[i] + " ");
				}
			}
			else {
				for(int i = 0 ; i < n ; i+=2) {
					pw.print(a[i + 1] + " " + -a[i] + " ");
				}
			}
			pw.println();
		}
		Instant end = Instant.now();
		if (DEBUG) {
			pw.println(Duration.between(start, end));
		}
		pw.close();
	}

	public static void print(long a, long b, long c, PrintWriter pw) {
		pw.println(a + " " + b + " " + c);
		return;
	}

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		public Reader() {
			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());
		}

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

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

		int[][] read2Array(int n, int m) {
			int a[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					a[i][j] = nextInt();
				}
			}
			return a;
		}
	}
}