Let's denote a k-step ladder as the following structure: exactly k + 2 wooden planks, of which

  * two planks of length at least k+1 — the base of the ladder; 
  * k planks of length at least 1 — the steps of the ladder; 



Note that neither the base planks, nor the steps planks are required to be equal.

For example, ladders 1 and 3 are correct 2-step ladders and ladder 2 is a correct 1-step ladder. On the first picture the lengths of planks are [3, 3] for the base and [1] for the step. On the second picture lengths are [3, 3] for the base and [2] for the step. On the third picture lengths are [3, 4] for the base and [2, 3] for the steps. 

<image>

You have n planks. The length of the i-th planks is a_i. You don't have a saw, so you can't cut the planks you have. Though you have a hammer and nails, so you can assemble the improvised "ladder" from the planks.

The question is: what is the maximum number k such that you can choose some subset of the given planks and assemble a k-step ladder using them?

Input

The first line contains a single integer T (1 ≤ T ≤ 100) — the number of queries. The queries are independent.

Each query consists of two lines. The first line contains a single integer n (2 ≤ n ≤ 10^5) — the number of planks you have.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^5) — the lengths of the corresponding planks.

It's guaranteed that the total number of planks from all queries doesn't exceed 10^5.

Output

Print T integers — one per query. The i-th integer is the maximum number k, such that you can choose some subset of the planks given in the i-th query and assemble a k-step ladder using them.

Print 0 if you can't make even 1-step ladder from the given set of planks.

Example

Input


4
4
1 3 1 3
3
3 3 2
5
2 3 3 4 2
3
1 1 2


Output


2
1
2
0

Note

Examples for the queries 1-3 are shown at the image in the legend section.

The Russian meme to express the quality of the ladders:

<image>
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

public class Practice {
	
	
	static class length implements Comparator<String>
	{
		public int compare(String a,String b)
		{
			return(a.length()-b.length());
		}
	}
	
	
	
	
	   static class FastReader
	   {
		   BufferedReader br;
		   StringTokenizer st;
		   public FastReader()
		   {
			   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; 
	        } 
	   }

		public static void main(String []args) throws Exception
		{
			//Scanner sc=new Scanner(System.in);
			FastReader in =new FastReader();
			PrintWriter pw = new PrintWriter(System.out);
			//System.out.println
			int t=in.nextInt();
			
			//in.nextLine();
			//int t=in.nextInt();
			//int k=in.nextInt();
		     
			
			for(int i=0;i<t;i++)
			{
				int n=in.nextInt();
				int a[]=new int[n];
				for(int j=0;j<n;j++)
				{
					a[j]=in.nextInt();
				}
				
				int max=0,m1=0;
				for(int j=0;j<n;j++)
				{
					if(a[j]>max)
					{
						max=a[j];
						m1=j;
					}
				}
				int t1=max;
				max=0;
				for(int j=0;j<n;j++)
				{
					if(a[j]>max && j!=m1)
					{
						max=a[j];
						
					}
				}
				
				
				
				int t2=max;
				int min=Math.min(t1,t2);
				pw.println(Math.min(min-1,n-2));
			}
			
			
			
			
			
            pw.flush();
			pw.close();
			
	}
		
}		
		
		
		
		
		