You are given an array of integers a_1,a_2,…,a_n. Find the maximum possible value of a_ia_ja_ka_la_t among all five indices (i, j, k, l, t) (i<j<k<l<t).

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

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

The second line of each test case contains n integers a_1,a_2,…,a_n (-3× 10^3≤ a_i≤ 3× 10^3) — given array.

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

Output

For each test case, print one integer — the answer to the problem.

Example

Input


4
5
-1 -2 -3 -4 -5
6
-1 -2 -3 1 2 -1
6
-1 0 0 0 -1 -1
6
-9 -7 -5 -3 -2 1


Output


-120
12
0
945

Note

In the first test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ (-4)⋅ (-5)=-120.

In the second test case, choosing a_1,a_2,a_3,a_5,a_6 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ 2⋅ (-1)=12.

In the third test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ 0⋅ 0⋅ 0⋅ (-1)=0.

In the fourth test case, choosing a_1,a_2,a_3,a_4,a_6 is a best choice: (-9)⋅ (-7) ⋅ (-5)⋅ (-3)⋅ 1=945.
import java.io.*;
import java.util.*;

public class A {

	static PrintWriter out;
	
	static class FIO {
		BufferedReader in;
		StringTokenizer st = null;
		FIO() throws IOException{
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			st = null;
		}
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(in.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
	static class thing {
		int a, b;
		public thing(int a, int b) {
			this.a = a;
			this.b = b;
		}
	}
	static class cmp implements Comparator<thing> {
		@Override
		public int compare(thing o1, thing o2) {
			return o1.a - o2.a;
		}
	}
	static FIO in;
	public static void main(String[] args) throws IOException {
		in = new FIO();
		int tc = in.nextInt();
		while (tc-- > 0) {
			new solver();
		}
		out.close();
		
	}
	static class solver {
		solver() {
			int N = in.nextInt();
			long[] ar = new long[N];
			for (int i = 0; i < N; ++i)
				ar[i] = in.nextLong();
			long [] prod = new long[6];
			long[] minp = new long[6];
			boolean[] used = new boolean[6];
			for (int i = 0; i < 6; ++i) {
				prod[i] = (long) -1e18;
				minp[i] = (long) 1e18;
			}
			prod[0] = 1;
			minp[0] = 1;
			used[0] = true;
			for (int i = 0; i < N; ++i) {
				for (int j = 5; j >= 1; --j) {
					if (!used[j - 1]) continue;
					prod[j] = Math.max(prod[j], Math.max(ar[i] * prod[j-1], ar[i] * minp[j-1]));
					minp[j] = Math.min(minp[j], Math.min(ar[i] * prod[j-1], ar[i] * minp[j-1]));
					used[j] = true;
				}
			}
			out.println(prod[5]);
			
		}
	}

}
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 * */
