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>
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
import java.lang.*;
public class pillars
{
	public static void main (String[] args)throws IOException
	{
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    int t=Integer.parseInt(br.readLine());
	    while(t-->0)
	    {
	    int n=Integer.parseInt(br.readLine());
	    StringTokenizer tk=new StringTokenizer(br.readLine());
	    Vector<Integer> a=new Vector<Integer>(n);int i,max,max1,j;
	    for(i=0;i<n;i++)
	    {
	        j=Integer.parseInt(tk.nextToken());
	        a.add(j);
	    }
	    max=0;max1=-1;j=0;
	        for(i=0;i<n;i++)
	        {
	            j=a.get(i);
	            if(j>max)
	            {
	                max1=max;
	                max=j;
	            }
	            else if(j>max1 && j<=max)
	            {
	                max1=j;
	            }
	        }
	        a.removeElement(max);
	        a.removeElement(max1);
	        if(max1>1)
	        {
	            if(a.size()>=(max1-1))
	            {
	                System.out.println(max1-1);
	            }
	            else if(a.size()<(max1-1))
	            {
	                System.out.println(a.size());
	            }
	            
	        }
	        else
	   	    System.out.println("0");
	    }
	}
}