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.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.LinkedBlockingQueue;
import java.util.zip.Inflater;


public class Main {
    private static AWriter writer = new AWriter(System.out);
    private static AReader reader = new AReader(System.in);
    private static final int INF=0X3F3F3F3F;
    private static int n,x,y;
    private static int a[];
    public static void main(String[] args) throws IOException {
        int T=reader.nextInt();
        while(T--!=0) {
            int n = reader.nextInt();
            a = new int[n];
            int mx2=-0x3f3f3f3f;
            int mx=-0x3f3f3f3f;
            for (int i = 0; i < n; i++) {
                a[i] = reader.nextInt();
                if(mx<=a[i]){
                    mx2=mx;
                    mx=a[i];
                }else if(a[i]>=mx2){
                    mx2=a[i];
                }
            }
            int len = mx2-1;
            writer.println(Math.min(len, n - 2));
        }
        writer.close();
        reader.close();
    }
}

class AReader implements Closeable {
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    public AReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }
    private String innerNextLine() {
        try {
            return reader.readLine();
        } catch (IOException ex) {
            return null;
        }
    }
    public boolean hasNext() {
        while (!tokenizer.hasMoreTokens()) {
            String nextLine = innerNextLine();
            if (nextLine == null) {
                return false;
            }
            tokenizer = new StringTokenizer(nextLine);
        }
        return true;
    }
    public String nextLine() {
        tokenizer = new StringTokenizer("");
        return innerNextLine();
    }
    public String next() {
        hasNext();
        return tokenizer.nextToken();
    }
    public int nextInt() {
        return Integer.valueOf(next());
    }
    public long nextLong() {
        return Long.valueOf(next());
    }
    public double nextDouble() {
        return Double.valueOf(next());
    }
    public BigDecimal nextBigDecimal(){ return new BigDecimal(next()); }
    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
    @Override
    public void close() throws IOException {
        reader.close();
    }
}

// Fast writer for ACM By Azure99
class AWriter implements Closeable {
    private BufferedWriter writer;

    public AWriter(OutputStream outputStream) {
        writer = new BufferedWriter(new OutputStreamWriter(outputStream));
    }

    public void print(Object object) throws IOException {
        writer.write(object.toString());
    }

    public void println(Object object) throws IOException {
        writer.write(object.toString());
        writer.write("\n");
    }

    @Override
    public void close() throws IOException {
        writer.close();
    }
}
