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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class P3 {

	public static void main(String args[])
	{
		try
		{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		for(int i=0;i<t;i++)
		{
			int n=Integer.parseInt(br.readLine());
			int arr[]=new int[n];
			String a[]=br.readLine().split(" ");
			SortedSet<Integer> set=new TreeSet<>();
			for(int j=0;j<a.length;j++){
				arr[j]=Integer.parseInt(a[j]);
				set.add(arr[j]);
			}
			int first=set.last(),second;
			int count=0;
			for(int j=0;j<arr.length;j++)
				if(arr[j]==first)
					count++;
			if(count>=2)
				second=first;
			else
			{

				set.remove(first);
				second=set.last();
			}

        /* There should be atleast two elements */

		boolean flag=false;
		for(int j=n-2;j>=0;j--){
			if(first>=j+1 && second>=j+1)
			{
			flag=true;
			System.out.println(j);
			break;
			
			}
		}
		if(!flag)
		System.out.println(0);
		}	
		}
		catch(Exception e)
	{
	e.printStackTrace();	
	}
	}

}
