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.util.*;
import java.math.*;
public class work
{
    static FastReader s;;
    static int dp[];
    static PrintWriter out;
    static class pair
    {
        int a,b;
        pair(int x, int y)
        {
            a=x;
            b=y;
        }
    }
    public static void main(String[] args) throws IOException
    {
        
        s = new FastReader();
        out=new PrintWriter(System.out);
    int t = s.ni();
    while(t-->0)
    {
        int n = s.ni();
        Integer arr[] = iarr(n);
        Arrays.sort(arr);
        int val = arr[n-2];
        int ans = 0;
        
        ans = Math.min(val-1, (n-2));
        
        println(ans);
        
        out.flush();
    }
        out.close();

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

    static long lgcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return lgcd(b, a % b);  
    }*/

    

    static class FastReader
    {

        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public FastReader(String file_name) throws IOException
        {
            br = new BufferedReader(new FileReader(file_name));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int ni()
        {
            return Integer.parseInt(next());
        }

        long nl()
        {
            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;
        }
        
    }

    static void piarr(int arr[])
    {
        int n = arr.length;
        for (int i = 0; i < n; i++)
        {
            print(arr[i]+" ");
        }
        println("");
    }

    static void plarr(long arr[])
    {
        int n = arr.length;
        for (int i = 0; i < n; i++)
        {
            print(arr[i]+" ");
        }
        println("");
    }

    static void println(Object line) 
    {
        out.println(line);
    }
    static void print(Object line) 
    {
        out.print(line);
    }
    static Integer[] iarr(int n)
    {
        Integer arr[]=new Integer[n];
        for(int i = 0; i < n;i++)
            arr[i]=s.ni();
        return arr;
    }

    static Long[] larr(int n)
    {
        Long arr[]=new Long[n];
        for(int i = 0; i < n;i++)
            arr[i]=s.nl();
        return arr;
    }

    static Integer[][] i2arr(int n, int m)
    {
        Integer arr[][]=new Integer[n][m];
        for(int i = 0; i < n;i++)
            for(int j = 0; j < m;j++)
                arr[i][j]=s.ni();
        return arr;
    }

    static Long[][] l2arr(int n, int m)
    {
        Long arr[][]=new Long[n][m];
        for(int i = 0; i < n;i++)
            for(int j = 0; j < m;j++)
                arr[i][j]=s.nl();
        return arr;
    }

    static char [] nc()
    {
        String str = s.next();
        char c[] = str.toCharArray();
        return c;
    }
    static char [][] n2c(int n)
    {
        char c[][] = new char[n][];
        for (int i = 0; i < n; i++)
            c[i] = s.next().toCharArray();
        return c;
    }

}