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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.security.AccessControlException;
import java.util.Arrays;
import java.util.Collection;
import java.util.List;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.LongStream;
import java.util.stream.Stream;
public class _p001197A {
    static public void main(final String[] args) throws IOException {
        p001197A._main(args);
    }
//begin p001197A.java
static private class p001197A extends Solver{public p001197A(){nameIn="in/900/p001197A.in"
;}int n;int[]a;@Override protected void solve(){PriorityQueue<Integer>pq=new PriorityQueue<>
((x,y)->y-x);pq.addAll(toList(a));int a0=pq.poll();int a1=pq.poll();int k=Math.min
(a1-1,n-2);pw.println(k);}@Override public void readInput()throws IOException{n=
sc.nextInt();if(sc.hasNextLine()){sc.nextLine();}a=Arrays.stream(sc.nextLine().trim
().split("\\s+")).mapToInt(Integer::valueOf).toArray();}static public void _main
(String[]args)throws IOException{new p001197A().run();}}
//end p001197A.java
//begin net/leksi/contest/Solver.java
static private abstract class Solver{protected String nameIn=null;protected String
nameOut=null;protected boolean singleTest=false;protected boolean preprocessDebug
=false;protected boolean doNotPreprocess=false;protected PrintStream debugPrintStream
=null;protected Scanner sc=null;protected PrintWriter pw=null;final String SPACE
=" ";final String SPACES="\\s+";private void process()throws IOException{if(!singleTest
){int t=lineToIntArray()[0];while(t-->0){readInput();solve();}}else{readInput();
solve();}}abstract protected void readInput()throws IOException;abstract protected
void solve()throws IOException;protected int[]lineToIntArray()throws IOException
{return Arrays.stream(sc.nextLine().trim().split(SPACES)).mapToInt(Integer::valueOf
).toArray();}protected long[]lineToLongArray()throws IOException{return Arrays.stream
(sc.nextLine().trim().split(SPACES)).mapToLong(Long::valueOf).toArray();}protected
String joinToString(final int[]a){return Arrays.stream(a).mapToObj(Integer::toString
).collect(Collectors.joining(SPACE));}protected String joinToString(final long[]
a){return Arrays.stream(a).mapToObj(Long::toString).collect(Collectors.joining(SPACE
));}protected<T>String joinToString(final T[]a){return Arrays.stream(a).map(v->Objects
.toString(v)).collect(Collectors.joining(SPACE));}protected<T>String joinToString
(final T[]a,final Function<T,String>toString){return Arrays.stream(a).map(v->toString
.apply(v)).collect(Collectors.joining(SPACE));}protected<T>String joinToString(final
Collection<T>a){return a.stream().map(v->Objects.toString(v)).collect(Collectors
.joining(SPACE));}protected<T>String joinToString(final Collection<T>a,final Function<T
,String>toString){return a.stream().map(v->toString.apply(v)).collect(Collectors
.joining(SPACE));}protected<T>String joinToString(final Stream<T>a){return a.map
(v->Objects.toString(v)).collect(Collectors.joining(SPACE));}protected<T>String joinToString
(final Stream<T>a,final Function<T,String>toString){return a.map(v->toString.apply
(v)).collect(Collectors.joining(SPACE));}protected<T>String joinToString(final IntStream
a){return a.mapToObj(Integer::toString).collect(Collectors.joining(SPACE));}protected
<T>String joinToString(final LongStream a){return a.mapToObj(Long::toString).collect
(Collectors.joining(SPACE));}protected List<Long>intArrayToLongList(final int[]a
){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors.toList());}
protected List<Integer>toList(final int[]a){return Arrays.stream(a).mapToObj(Integer
::valueOf).collect(Collectors.toList());}protected List<Integer>toList(final IntStream
a){return a.mapToObj(Integer::valueOf).collect(Collectors.toList());}protected List<Long>
toList(final long[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors
.toList());}protected List<Long>toList(final LongStream a){return a.mapToObj(Long
::valueOf).collect(Collectors.toList());}protected<T>List<T>toList(final Stream<T>
a){return a.collect(Collectors.toList());}protected<T>List<T>toList(final T[]a){
return Arrays.stream(a).collect(Collectors.toList());}protected void run()throws
IOException{boolean done=false;try{if(nameIn !=null&&new File(nameIn).exists()){
try(FileInputStream fis=new FileInputStream(nameIn);PrintWriter pw0=select_output
();){done=true;sc=new Scanner(fis);pw=pw0;process();}}}catch(IOException ex){}catch
(AccessControlException ex){}if(!done){try(PrintWriter pw0=select_output();){sc=
new Scanner(System.in);pw=pw0;process();}}}private PrintWriter select_output()throws
FileNotFoundException{if(nameOut !=null){return new PrintWriter(nameOut);}return
new PrintWriter(System.out);}}
//end net/leksi/contest/Solver.java
}
