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.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;
import static java.lang.Math.min;
import static java.lang.Math.max;


@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(), a[] = fs.readArray(n);
			int ans[] = new int[n];
			if (n % 2 == 0) {
				for (int i = 0; i < n; i += 2) {
					int temp = __lcm(a[i], a[i + 1]);
					if (temp < 0) {
						if (a[i] < 0) {
							ans[i] = -temp;
							ans[i + 1] = temp;
						} else {
							ans[i] = -temp;
							ans[i + 1] = temp;
						}
					} else {
						ans[i] = -temp;
						ans[i + 1] = temp;
					}
				}
				for(int i=0 ; i < n ; i++) {
					pw.print(ans[i]/a[i] + " ");
				}
				pw.println();
			} else {
				for (int i = 0; i < n - 3; i += 2) {
					int temp = __lcm(a[i], a[i + 1]);
					if (temp < 0) {
						if (a[i] < 0) {
							ans[i] = -temp;
							ans[i + 1] = temp;
						} else {
							ans[i] = temp;
							ans[i + 1] = -temp;
						}
					} else {
						ans[i] = temp;
						ans[i + 1] = -temp;
					}
				}
				// n - 1 , n - 2, n - 3;
				int x = Math.abs(a[n - 1]), y = Math.abs(a[n-2]), z = Math.abs(a[n - 3]);
				ans[n-2] = y*(Math.abs(x - z));
				ans[n-3] = z*y;
				ans[n-1] = y*x;
				int temp = max(ans[n-1], max(ans[n-2], ans[n-3]));
				if(temp != ans[n-1])
				{
					ans[n-1] *= -1;
				}
				if(temp != ans[n-2]) {
					ans[n-2] *= -1;
				}
				if(temp != ans[n-3]) {
					ans[n-3] *= -1;
				}
				debug(ans, "ans");
				for(int i=0 ; i<n ; i++) {
					ans[i] /= a[i];
				}
				debug(ans, "ans");
				int sum = 0;
				for(int pp : ans) {
					pw.print(pp + " ");
				}
				for(int i = 0 ; i < n ;i++)sum += ans[i]*a[i];
				pw.println();
			}
		}
		Instant end = Instant.now();
		if (DEBUG) {
			pw.println(Duration.between(start, end));
		}
		pw.close();
	}

	static void debug(int a[], String l) {
		if (DEBUG) {
			System.err.print(l + "-> [");
			for (int x : a)
				System.err.print(x + " ");
			System.err.println("]");
		}
	}

	static void debug(long a[], String l) {
		if (DEBUG) {
			System.err.print("l-> [");
			for (long x : a)
				System.err.print(x + " ");
			System.err.println("]");
		}
	}

	static <T> void debug(HashSet<Integer> a, String l) {
		if (DEBUG) {
			System.err.println(l + " -> ");
			System.err.println(a);
		}
	}

	static void debug(String a, String l) {
		if (DEBUG) {
			System.err.println(l + " -> " + a);
		}
	}

	static void debug(StringBuilder a, String l) {
		if (DEBUG) {
			System.err.println(l + " -> " + a);
		}
	}

	static <T extends Number, V extends T> void debug(HashMap<T, V> a, String l) {
		if (DEBUG) {
			System.err.println(l + " -> ");
			System.err.println(a);
		}
	}

	static <T extends Number> void debug(T a, String l) {
		if (DEBUG) {
			System.err.println(l + " -> " + a);
		}
	}

	static <T extends Number> void debug(T[] a, String l) {
		if (DEBUG) {
			System.err.print(l + " -> \n" + "[ ");
			for (int i = 0; i < a.length; i++) {
				System.err.print(a[i] + " ");
			}
			System.err.println("]");
		}
	}

	static <T> void debug(ArrayList<T> a, String l) {
		if (DEBUG) {
			System.err.print(l + " -> ");
			System.err.print("[ ");
			for (T q : a) {
				System.err.print(q + " ");
			}
			System.err.println("]");
		}
	}

	public static int __lcm(int a, int b) {
		return (a * b) / (__gcd(a, b));
	}

	public static int __gcd(int a, int b) {
		if (b != 0) {
			return __gcd(b, a % b);
		} else {
			return a;
		}
	}

	public static int lower_bound(ArrayList<Integer> ar, int k) {
		int s = 0;
		int e = ar.size();
		while (s != e) {
			int mid = s + e >> 1;
			if (ar.get(mid) < k) {
				s = mid + 1;
			} else {
				e = mid;
			}
		}
		if (s == ar.size()) {
			return -1;
		}
		return s;
	}

	public static int upper_bound(ArrayList<Integer> ar, int k) {
		int s = 0;
		int e = ar.size();
		while (s != e) {
			int mid = s + e >> 1;
			if (ar.get(mid) <= k) {
				s = mid + 1;
			} else {
				e = mid;
			}
		}
		if (s == ar.size()) {
			return -1;
		}
		return s;
	}

	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;
		}
	}
}