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 codeforces;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Arrays;
import java.util.Collections;

public class alina {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

        int t, n, k, count = 0;
        t = in.nextInt();
        for (int i = 1; i <=t; i++) {
              n = in.nextInt();
            ArrayList<Integer> plank = new ArrayList<Integer>(n);
          
            for (int j = 0; j < n; j++) {
                int temp = in.nextInt();
                plank.add(temp);
            }

            // Collections.sort(plank, Collections.reverseOrder());
            Collections.sort(plank);
            Collections.reverse(plank);
            for (int j = 2; j < n; j++) {
                if (plank.get(j) >= 1) {
                    count++;
                }
                if (plank.get(0) <(count + 1) || plank.get(1) <(count + 1)) {
                    count--;
                 //   System.out.println("flag");
                    break;
                }
            }
            System.out.println("" + count);
           // System.out.println(plank);
            count = 0;

            // Arrays.sort(plank,Collections.reverseOrder());
            // Arrays.sort(plank);
        }

    }

}
