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.util.*;
import java.math.*;
import java.lang.reflect.Array;

public class A {
    static final int MOD = 1000000007; // 1e9 + 7
    static final boolean AUTO_FLUSH = false; // slow if true
    // int = num(); // long = ll();
    // string = next(); // a string line = line();
    // ---------------------------------- \
    
    void main() {
        int T = num();
        while (T-- > 0) {
            int n = num();
            List<Integer> list = new ArrayList<>();
            for (int i = 0; i < n; i++)
                list.add(num());
            Collections.sort(list, Collections.reverseOrder());
            int a = list.get(0)-1, b = list.get(1)-1;
            int max = Math.min(a, Math.min(b, list.size()-2));
            outln(max);
        }
    }
    
    // ---------------------------------- \
    //#region
    public static void main(String[] args) {
        if (!ONLINE_JUDGE)
            startTime();
        new A().main();
        boolean endsWithEnter = TO_BE_PRINTED.length() == 0 || TO_BE_PRINTED.charAt(TO_BE_PRINTED.length() - 1) == '\n';
        flush();
        if (ONLINE_JUDGE)
            return;
        if (!endsWithEnter)
            log('\n');
        logTime();
        logMem();
    }
    static Random RAND = new Random();
    static int random(int from, int to) {
        return RAND.nextInt(to-from+1)+from;
    }
    static void logTime() {
        log("Time: " + getTime() + "ms");
    }
    static void logMem() {
        log("Memory (End): " + (int) (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) / 1024 + " KB");
    }
    static long ll() {
        return Long.parseLong(next());
    }
    static int num() {
        return Integer.parseInt(next());
    }
    static void generateInputMode() throws Exception {
        System.setOut(new PrintStream(new FileOutputStream("F://PROGRAMMING/input.txt")));
    }
    static String line() {
        if (!tokenize())
            return null;
        INPUT_STREAM.setLength(0);
        if (STRING_TOKENIZER.hasMoreTokens())
            INPUT_STREAM.append(STRING_TOKENIZER.nextToken());
        while (STRING_TOKENIZER.hasMoreTokens())
            INPUT_STREAM.append(' ').append(STRING_TOKENIZER.nextToken());
        return INPUT_STREAM.length() == 0 ? null : INPUT_STREAM.toString();
    }
    static void startTime() {
        TIME_COMPLEXITY = System.currentTimeMillis();
    }
    static long getTime() {
        return System.currentTimeMillis() - TIME_COMPLEXITY;
    }
    static void flush() {
        System.out.print(TO_BE_PRINTED.toString());
        TO_BE_PRINTED.setLength(0);
    }
    static void out(Object o) {
        TO_BE_PRINTED.append(o);
        if (AUTO_FLUSH)
            flush();
    }
    static void _log(String s) {
        System.err.print(s);
    }
    static void _logln(String s) {
        System.err.println(s);
    }
    static void _logln() {
        System.err.println();
    }
    static void outln(Object o) {
        out(o);
        outln();
    }
    static void outln() {
        out("\n");
    }
    static class Pair implements Comparable<Pair> {
        public int a, b;
        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public static Pair of(int a, int b) {
            return new Pair(a, b);
        }
        public int compareTo(Pair p) {
            if (a == p.a)
                return Integer.compare(b, p.b);
            return Integer.compare(a, p.a);
        }
        public String toString() {
            return "[" + a + "," + b + "]";
        }
        public boolean equals(Pair p) {
            return p.a == a && p.b == b;
        }
    }
    static boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    static void logArr(Object val) {
        if (ONLINE_JUDGE)
            return;
        Class<?> valKlass = val.getClass();
        Object[] outputArray = null;
        for(Class<?> arrKlass : new Class<?>[] { int[].class, float[].class, double[].class, boolean[].class, 
            byte[].class, short[].class, long[].class, char[].class }) {
            if (valKlass.isAssignableFrom(arrKlass)) {
                int arrlength = Array.getLength(val);
                outputArray = new Object[arrlength];
                for(int i = 0; i < arrlength; ++i)
                    outputArray[i] = Array.get(val, i);
                break;
            }
        }
        if(outputArray == null)
            outputArray = (Object[])val;
        logArr0(outputArray);
    }
    static void logArr0(Object[] objs) {
        if (ONLINE_JUDGE)
            return;
        if (objs.length == 0) {
            _log("* \n");
            return;
        }
        _log("* " + objs[0]);
        for (int i = 1; i < objs.length; i++)
            _log(objs[i].toString().equals("\n") ? "\n>" : (" " + objs[i]));
        _logln();
    }
    static void log(Object... objs) {
        if (ONLINE_JUDGE)
            return;
        logArr0(objs);
    }
    static String next() {
        return tokenize() ? STRING_TOKENIZER.nextToken() : null;
    }
    static boolean tokenize() {
        if (STRING_TOKENIZER == null || !STRING_TOKENIZER.hasMoreTokens()) {
            try {
                STRING_TOKENIZER = new StringTokenizer(STREAM_READER.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }
    static long TIME_COMPLEXITY;
    static BufferedReader STREAM_READER = new BufferedReader(new InputStreamReader(System.in), 32768);
    static StringTokenizer STRING_TOKENIZER;
    static StringBuilder INPUT_STREAM = new StringBuilder(), TO_BE_PRINTED = new StringBuilder();
    //#endregion
}