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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ADIYWoodenLadder solver = new ADIYWoodenLadder();
        int testCount = in.scanInt();
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class ADIYWoodenLadder {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) ar[i] = in.scanInt();
            CodeHash.radixSort(ar);
            out.println(Math.min(n - 2, ar[n - 2] - 1));
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }

    static class CodeHash {
        public static int[] radixSort(int[] f) {
            int[] to = new int[f.length];
            {
                int[] b = new int[65537];
                for (int i = 0; i < f.length; i++) b[1 + (f[i] & 0xffff)]++;
                for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
                for (int i = 0; i < f.length; i++) to[b[f[i] & 0xffff]++] = f[i];
                int[] d = f;
                f = to;
                to = d;
            }
            {
                int[] b = new int[65537];
                for (int i = 0; i < f.length; i++) b[1 + (f[i] >>> 16)]++;
                for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
                for (int i = 0; i < f.length; i++) to[b[f[i] >>> 16]++] = f[i];
                int[] d = f;
                f = to;
                to = d;
            }
            return f;
        }

    }
}

