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 Coding {

    static long MOD = 1000000007;
    static long[] fact = new long[100002];
    static long[] pow2 = new long[100002];
    static int MAXVAL = 10000000;

    public static void main(String[] args) {
        BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        //precompute();
        try {
            int t = Integer.valueOf(bi.readLine());
            while (t > 0) {
                int n = Integer.valueOf(bi.readLine());
                Long[] ar = new Long[n];
                String[] inputs = bi.readLine().split(" ");
                for(int i=0;i<n;++i) {
                    ar[i] = Long.parseLong(inputs[i]);
                }
                long[] maxm = new long[5];
                long[] minm = new long[5];
                for(int i=0;i<=4;++i) {
                    maxm[i] = Long.MIN_VALUE;
                    minm[i] = Long.MAX_VALUE;
                }
                maxm[0] = minm[0] = ar[0];
                for(int i=1;i<n;++i) {
                    for(int j=Math.min(i, 4);j>=0;--j) {
                        if (j==0) {
                            maxm[j] = Math.max(maxm[j], ar[i]);
                            minm[j] = Math.min(minm[j], ar[i]);
                        } else {
                            if (maxm[j-1]!=Long.MIN_VALUE) {
                                maxm[j] = Math.max(maxm[j], maxm[j-1]*ar[i]);
                                minm[j] = Math.min(minm[j], maxm[j-1]*ar[i]);
                            }
                            if (minm[j-1]!=Long.MAX_VALUE) {
                                maxm[j] = Math.max(maxm[j], minm[j-1]*ar[i]);
                                minm[j] = Math.min(minm[j], minm[j-1]*ar[i]);
                            }
                        }
                    }
                }

                writer.append(String.valueOf(maxm[4]));
                writer.append("\n");
                writer.flush();
                t--;
            }
            writer.flush();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static int gcd(int a, int b) {
        if (a<b) {
            return gcd(b, a);
        }
        if (a%b==0) {
            return b;
        }
        return gcd(b, a%b);
    }

    private static void dfs(int cur, List<Integer>[] adj, int[] nodeCount, int[] maxChild,  int parent, int[] par) {
        par[cur] = parent;
        for(int i=0;i<adj[cur].size();++i) {
            int nxt = adj[cur].get(i);
            if (nxt!=parent) {
                dfs(nxt, adj, nodeCount, maxChild, cur, par);
                nodeCount[cur]+=nodeCount[nxt];
                maxChild[cur] = Math.max(maxChild[cur], nodeCount[nxt]);
            }
        }
    }

    private static int dfs2(int cur, List<Integer>[] adj, int parent) {
        for(int i=0;i<adj[cur].size();++i) {
            int nxt = adj[cur].get(i);
            if (nxt!=parent) {
                return dfs2(nxt, adj, cur);
            }
        }
        return cur;
    }

    private static int findDist(int a, int b, int[] par) {
        Map<Integer, Integer> dist = new HashMap<>();
        int count = 0;
        dist.put(a, 0);
        while (par[a]!=-1) {
            a = par[a];
            count++;
            dist.put(a, count);
        }
        count=0;
        while(!dist.containsKey(b)) {
            b = par[b];
            count++;
        }
        return count+dist.get(b);
    }

    private static int findLongestPath(int cur, int prev, List<Integer>[] adj, int[] dep) {
        int diameter = 0;
        int highest = -1, second=-1;
        for(int i=0;i<adj[cur].size();++i) {
            int nxt = adj[cur].get(i);
            if (nxt!=prev) {
                diameter = Math.max(diameter, findLongestPath(nxt, cur, adj, dep));
                if (dep[nxt]>highest) {
                    second = highest;
                    highest = dep[nxt];
                } else if (dep[nxt]>second) {
                    second = dep[nxt];
                }
            }
        }
        diameter = Math.max(diameter, highest + second + 2);
        return diameter;
    }

    static long ncr(int n, int r) {
        long num = fact[n];
        long denom = (modExp(fact[r], MOD-2)*modExp(fact[n-r], MOD-2))%MOD;
        //System.out.println("num is " + num + " denom is" + denom);
        return (num*denom)%MOD;
    }

    static long modExp(long a, long b) {
        //System.out.println("a is " + a + " and b is " + b);
        if (a==1) return 1;
        long ans = 1;
        while (b!=0) {
            if (b%2==1) {
                ans = (ans*a)%MOD;
            }
            a = (a*a)%MOD;
            b/=2;
        }
        return ans;
    }

    private static void precompute() {
        fact[0] = 1;
        pow2[0] = 1;
        for(int i=1;i<=100000;++i) {
            fact[i] = (fact[i-1]*i)%MOD;
            pow2[i] = (pow2[i-1]*2)%MOD;
        }
    }
}