You have 2n integers 1, 2, ..., 2n. You have to redistribute these 2n elements into n pairs. After that, you choose x pairs and take minimum elements from them, and from the other n - x pairs, you take maximum elements.

Your goal is to obtain the set of numbers \\{b_1, b_2, ..., b_n\} as the result of taking elements from the pairs.

What is the number of different x-s (0 ≤ x ≤ n) such that it's possible to obtain the set b if for each x you can choose how to distribute numbers into pairs and from which x pairs choose minimum elements?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains the integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line of each test case contains n integers b_1, b_2, ..., b_n (1 ≤ b_1 < b_2 < ... < b_n ≤ 2n) — the set you'd like to get.

It's guaranteed that the sum of n over test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print one number — the number of different x-s such that it's possible to obtain the set b.

Example

Input


3
1
1
5
1 4 5 9 10
2
3 4


Output


1
3
1

Note

In the first test case, x = 1 is the only option: you have one pair (1, 2) and choose the minimum from this pair.

In the second test case, there are three possible x-s. If x = 1, then you can form the following pairs: (1, 6), (2, 4), (3, 5), (7, 9), (8, 10). You can take minimum from (1, 6) (equal to 1) and the maximum elements from all other pairs to get set b.

If x = 2, you can form pairs (1, 2), (3, 4), (5, 6), (7, 9), (8, 10) and take the minimum elements from (1, 2), (5, 6) and the maximum elements from the other pairs.

If x = 3, you can form pairs (1, 3), (4, 6), (5, 7), (2, 9), (8, 10) and take the minimum elements from (1, 3), (4, 6), (5, 7).

In the third test case, x = 0 is the only option: you can form pairs (1, 3), (2, 4) and take the maximum elements from both of them.
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.stream.Stream;
import java.util.Iterator;
import java.util.List;
import java.util.Map;


public class Main {
	

public static void main(String[] args){
 
   new Thread(null, null, "Anshum Gupta", 99999999) {
        public void run() {
            try {
                solve();
            } catch(Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }.start();
}
 

static final long INF_LONG = (long)(1e18 + 5), MOD = (long)1e9 + 7;//998244353; 
static final int MXN = (int)(1001), MXV = (int)(2e5 + 5), log = 18, INF = (int)1e9 + 500;
static boolean[] vis;
static ArrayList<ArrayList<Integer>> adj;
static int n, m, q, k, h, w;
static char[] str;
static int[] b, nb;



public static void solve() throws Exception {
	   // solve the problem here
		s = new MyScanner();
   		out = new MyWriter(new BufferedOutputStream(System.out));
   		
        int tc = s.nextInt();   
    	for(int i=1; i<=tc; i++) {
    		testcase();
    	}
          
        out.flush();
        out.close();
}



static void testcase() {
	
	n = s.nextInt();
	b = s.nextIntArray(n);
	
	nb = new int[n];
	boolean[] there = new boolean[2 * n + 1];
	for(int i = 0; i < n; i++) {
		there[b[i]] = true;
	}
	
	int ind = 0;
	for(int i = 1; i <= 2 * n; i++) {
		if(!there[i]) {
			nb[ind++] = i;
		}
	}
	
	
	// 1,2,3,4...,2*n
	// for n = 5
	// 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
	// b -> 1, 4, 5, 9, 10
	// x = 0 -> poss ? NO
	// x = 1 -> poss ?
	// min -> {1, 8}
	// max -> {4, 2}, {5, 3}, {9, 6}, {10, 7}
	// poss -> YES
	
	int last = getLastWhereWorks();
	
	int first = getFirstWhereWorks(last);
	
//	out.println("first = " + first + " last = " + last);
	
	int ans = Math.max(0, last - first + 1);
	out.println(ans);
	
}


private static int getFirstWhereWorks(int last) {
	
	int lo = 0, hi = last, ans = n + 1;
	while(lo <= hi) {
		
		int mid = (lo + hi) >> 1;
	
		if(worksRight(mid)) {
			hi = mid - 1;
			ans = mid;
			
		}
		
		else lo = mid + 1;
		
	}
	
	return ans;
	
}



private static int getLastWhereWorks() {
	
	int lo = 0, hi = n, ans = -1;
	
	while(lo <= hi) {
		
		int mid = (lo + hi) >> 1;
		if(worksLeft(mid)) {
			ans = mid;
			lo = mid + 1;
		}
		
		else hi = mid - 1;
		
	}
	
	return ans;
	
}




private static boolean worksLeft(int x) {
	
	for(int i = 0; i < x; i++) {
		if(nb[i + n - x] <= b[i]) return false;
	}
	
	return true;
}

private static boolean worksRight(int x) {
	
	for(int i = x; i < n; i++) {
		if(nb[i - x] >= b[i]) return false;
	}
	
	return true;
}



public static MyWriter out;
public static MyScanner s;
static void shuffleArray(int[] a) {
	Random random = new Random();
	for (int i = a.length-1; i > 0; i--) {
		int index = random.nextInt(i + 1);
		int tmp = a[index];
		a[index] = a[i];
		a[i] = tmp;
	}
}
static void shuffleSort(int[] a) {
	shuffleArray(a);
	Arrays.parallelSort(a);
}
static class MyScanner {
 
    BufferedReader br;
    StringTokenizer st;
 
    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public MyScanner(String fileName) {
    	try {
			br = new BufferedReader(new FileReader(fileName));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    int[] nextIntArray(int n){
    	int[]a = new int[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    long[] nextlongArray(int n) {
    	long[]a = new long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    Integer[] nextIntegerArray(int n){
    	Integer[]a = new Integer[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    Long[] nextLongArray(int n) {
    	Long[]a = new Long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    char[][] next2DCharArray(int n, int m){
    	char[][]arr = new char[n][m];
    	for(int i=0; i<n; i++) {
    		arr[i] = this.next().toCharArray();
    	}
    	return arr;
    }
    ArrayList<ArrayList<Integer>> readUndirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    		adj.get(v).add(u);
    	}
    	return adj;
    }
    ArrayList<ArrayList<Integer>> readDirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    	}
    	return adj;
    }
    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
 
static class MyWriter extends PrintWriter {
    MyWriter(OutputStream out) {
        super(out);
    }
    void println(int[] x) {
        println(x, " ");
    }
    void println(int[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(long[] x) {
        println(x, " ");
    }
    void println(long[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(Iterable<?> iterable) {
        println(iterable, " ");
    }
    void println(Iterable<?> iterable, String delimiter) {
        Iterator<?> i = iterable.iterator();
        if (i.hasNext()) {
            print(i.next());
            while (i.hasNext()) {
                print(delimiter);
                print(i.next());
            }
        }
        println();
    }
    void printLines(int[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(long[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(Iterable<?> iterable) {
        println(iterable, System.lineSeparator());
    }
}
 
}