1463_D. Pairs_10239
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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1463d {

    public static void main(String[] args) throws IOException {
        int t = ri();
        while (t --> 0) {
            int n = ri(), b[] = ria(n), mx = n, mn = 0, last = 0, unused = 0;
            for (int i = 0; i < n; ++i) {
                unused += b[i] - last - 1;
                if (unused > 0) {
                    --unused;
                } else {
                    ++mn;
                }
                last = b[i];
            }
            last = 2 * n + 1;
            unused = 0;
            for (int i = n - 1; i >= 0; --i) {
                unused += last - b[i] - 1;
                if (unused > 0) {
                    --unused;
                } else {
                    --mx;
                }
                last = b[i];
            }
            prln(mx - mn + 1);
        }
        close();
    }

    static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __r = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final long LMAX = 9223372036854775807L;

    // math util
    static int minof(int a, int b, int c) {
        return min(a, min(b, c));
    }

    static int minof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        int min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static long minof(long a, long b, long c) {
        return min(a, min(b, c));
    }

    static long minof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return min(x[0], x[1]);
        if (x.length == 3) return min(x[0], min(x[1], x[2]));
        long min = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
        return min;
    }

    static int maxof(int a, int b, int c) {
        return max(a, max(b, c));
    }

    static int maxof(int... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        int max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static long maxof(long a, long b, long c) {
        return max(a, max(b, c));
    }

    static long maxof(long... x) {
        if (x.length == 1) return x[0];
        if (x.length == 2) return max(x[0], x[1]);
        if (x.length == 3) return max(x[0], max(x[1], x[2]));
        long max = x[0];
        for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
        return max;
    }

    static int powi(int a, int b) {
        if (a == 0) return 0;
        int ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static long powl(long a, int b) {
        if (a == 0) return 0;
        long ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) ans *= a;
            a *= a;
            b >>= 1;
        }
        return ans;
    }

    static int fli(double d) {
        return (int) d;
    }

    static int cei(double d) {
        return (int) ceil(d);
    }

    static long fll(double d) {
        return (long) d;
    }

    static long cel(double d) {
        return (long) ceil(d);
    }

    static int gcf(int a, int b) {
        return b == 0 ? a : gcf(b, a % b);
    }

    static long gcf(long a, long b) {
        return b == 0 ? a : gcf(b, a % b);
    }

    static int[] exgcd(int a, int b) {
        if (b == 0) return new int[]{1, 0};
        int[] y = exgcd(b, a % b);
        return new int[]{y[1], y[0] - y[1] * (a / b)};
    }

    static long[] exgcd(long a, long b) {
        if (b == 0) return new long[]{1, 0};
        long[] y = exgcd(b, a % b);
        return new long[]{y[1], y[0] - y[1] * (a / b)};
    }

    static int randInt(int min, int max) {
        return __r.nextInt(max - min + 1) + min;
    }

    static long mix(long x) {
        x += 0x9e3779b97f4a7c15L;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
        x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
        return x ^ (x >> 31);
    }

    // array util
    static void reverse(int[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            int swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(long[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            long swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(double[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            double swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void reverse(char[] a) {
        for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
            char swap = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = swap;
        }
    }

    static void shuffle(int[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            int swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(long[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            long swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void shuffle(double[] a) {
        int n = a.length - 1;
        for (int i = 0; i < n; ++i) {
            int ind = randInt(i, n);
            double swap = a[i];
            a[i] = a[ind];
            a[ind] = swap;
        }
    }

    static void rsort(int[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(long[] a) {
        shuffle(a);
        sort(a);
    }

    static void rsort(double[] a) {
        shuffle(a);
        sort(a);
    }

    static int[] copy(int[] a) {
        int[] ans = new int[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static long[] copy(long[] a) {
        long[] ans = new long[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static double[] copy(double[] a) {
        double[] ans = new double[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    static char[] copy(char[] a) {
        char[] ans = new char[a.length];
        for (int i = 0; i < a.length; ++i) ans[i] = a[i];
        return ans;
    }

    // input
    static void r() throws IOException {
        input = new StringTokenizer(rline());
    }

    static int ri() throws IOException {
        return Integer.parseInt(rline());
    }

    static long rl() throws IOException {
        return Long.parseLong(rline());
    }

    static double rd() throws IOException {
        return Double.parseDouble(rline());
    }

    static int[] ria(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni();
        return a;
    }

    static int[] riam1(int n) throws IOException {
        int[] a = new int[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = ni() - 1;
        return a;
    }

    static long[] rla(int n) throws IOException {
        long[] a = new long[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nl();
        return a;
    }

    static double[] rda(int n) throws IOException {
        double[] a = new double[n];
        r();
        for (int i = 0; i < n; ++i) a[i] = nd();
        return a;
    }

    static char[] rcha() throws IOException {
        return rline().toCharArray();
    }

    static String rline() throws IOException {
        return __i.readLine();
    }

    static String n() {
        return input.nextToken();
    }

    static int rni() throws IOException {
        r();
        return ni();
    }

    static int ni() {
        return Integer.parseInt(n());
    }

    static long rnl() throws IOException {
        r();
        return nl();
    }

    static long nl() {
        return Long.parseLong(n());
    }

    static double rnd() throws IOException {
        r();
        return nd();
    }

    static double nd() {
        return Double.parseDouble(n());
    }

    // output
    static void pr(int i) {
        __o.print(i);
    }

    static void prln(int i) {
        __o.println(i);
    }

    static void pr(long l) {
        __o.print(l);
    }

    static void prln(long l) {
        __o.println(l);
    }

    static void pr(double d) {
        __o.print(d);
    }

    static void prln(double d) {
        __o.println(d);
    }

    static void pr(char c) {
        __o.print(c);
    }

    static void prln(char c) {
        __o.println(c);
    }

    static void pr(char[] s) {
        __o.print(new String(s));
    }

    static void prln(char[] s) {
        __o.println(new String(s));
    }

    static void pr(String s) {
        __o.print(s);
    }

    static void prln(String s) {
        __o.println(s);
    }

    static void pr(Object o) {
        __o.print(o);
    }

    static void prln(Object o) {
        __o.println(o);
    }

    static void prln() {
        __o.println();
    }

    static void pryes() {
        prln("yes");
    }

    static void pry() {
        prln("Yes");
    }

    static void prY() {
        prln("YES");
    }

    static void prno() {
        prln("no");
    }

    static void prn() {
        prln("No");
    }

    static void prN() {
        prln("NO");
    }

    static boolean pryesno(boolean b) {
        prln(b ? "yes" : "no");
        return b;
    }

    ;

    static boolean pryn(boolean b) {
        prln(b ? "Yes" : "No");
        return b;
    }

    static boolean prYN(boolean b) {
        prln(b ? "YES" : "NO");
        return b;
    }

    static void prln(int... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(long... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static void prln(double... a) {
        for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
        if (a.length > 0) prln(a[a.length - 1]);
        else prln();
    }

    static <T> void prln(Collection<T> c) {
        int n = c.size() - 1;
        Iterator<T> iter = c.iterator();
        for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i) ;
        if (n >= 0) prln(iter.next());
        else prln();
    }

    static void h() {
        prln("hlfd");
        flush();
    }

    static void flush() {
        __o.flush();
    }

    static void close() {
        __o.close();
    }
}
3
1
1
5
1 4 5 9 10
2
3 4
 3
1
1
5
1 4 5 9 10
2
1 4
 3
1
1
5
1 4 5 9 10
2
2 4
 3
1
1
5
1 4 5 7 10
2
1 4
 3
1
1
5
1 4 5 8 10
2
2 4
 3
1
1
5
1 2 5 9 10
2
2 4
 3
1
1
5
1 2 5 9 10
2
1 2
 3
1
1
5
1 4 6 9 10
2
1 4
 3
1
1
5
1 4 5 6 10
2
2 4
 3
1
1
5
1 3 5 9 10
2
1 4
 3
1
1
5
2 4 5 6 10
2
2 4
 3
1
1
5
2 3 5 9 10
2
1 4
 3
1
1
5
1 4 7 9 10
2
1 4
 3
1
1
5
1 4 5 9 10
2
1 2
 3
1
1
5
1 3 5 7 10
2
1 4
 3
1
1
5
2 4 5 6 10
2
3 4
 3
1
1
5
2 4 5 6 10
2
1 4
 3
1
1
5
1 3 5 9 10
2
2 4
 3
1
1
5
1 2 5 7 10
2
1 4
 3
1
2
5
1 3 5 7 10
2
1 4
 3
1
1
5
1 4 5 6 10
2
3 4
 3
1
1
5
1 4 5 6 10
2
1 4
 3
1
1
5
1 4 7 9 10
2
1 2
 3
1
1
5
2 4 5 7 10
2
1 4
 3
1
1
5
1 2 5 7 10
2
1 2
 3
1
1
5
1 4 5 8 10
2
1 4
 3
1
1
5
2 3 5 7 10
2
1 4
 3
1
1
5
1 4 5 7 10
2
1 2
 3
1
1
5
2 3 5 7 10
2
2 4
 3
1
2
5
2 3 5 7 10
2
2 4
 3
1
1
5
1 4 5 9 10
2
1 3
 3
1
1
5
1 4 6 9 10
2
1 2
 3
1
1
5
2 3 5 9 10
2
2 4
 3
1
2
5
1 4 5 7 10
2
1 4
 3
1
1
5
1 3 5 6 10
2
1 4
 3
1
2
5
1 4 5 6 10
2
1 4
 3
1
1
5
1 2 5 8 10
2
1 4
 3
1
2
5
2 4 5 7 10
2
1 4
 3
1
2
5
2 4 5 6 10
2
2 4
 3
1
1
5
2 3 5 7 8
2
2 4
 3
1
1
5
2 4 5 9 10
2
2 4
 3
1
1
5
2 4 5 7 10
2
1 2
 3
1
1
5
2 4 5 7 8
2
1 2
 3
1
1
5
1 3 4 9 10
2
2 4
 3
1
1
5
1 4 5 8 10
2
1 3
 3
1
1
5
1 4 5 8 10
2
2 3
 3
1
2
5
2 3 5 7 10
2
2 3
 3
1
1
5
1 4 7 9 10
2
1 3
 3
1
2
5
1 3 5 6 10
2
1 4
 3
1
2
5
2 3 5 7 10
2
1 3
 3
1
2
5
1 3 5 9 10
2
1 4
 3
1
1
5
2 3 5 7 10
2
1 3
 3
1
1
5
1 4 6 9 10
2
2 4
 3
1
1
5
3 4 5 6 10
2
2 4
 3
1
2
5
1 2 5 7 10
2
1 4
 3
1
2
5
2 4 5 7 10
2
2 4
 3
1
1
5
2 4 5 6 8
2
1 2
 3
1
2
5
1 2 5 7 10
2
2 4
 3
1
1
5
1 3 6 9 10
2
2 4
 3
1
1
5
1 2 5 8 10
2
1 2
 3
1
1
5
2 4 5 8 10
2
2 4
 3
1
1
5
1 3 5 9 10
2
2 3
 3
1
2
5
1 4 6 7 10
2
1 4
 3
1
2
5
2 3 5 9 10
2
1 4
 3
1
2
5
2 3 5 7 10
2
1 4
 3
1
1
5
1 2 5 8 10
2
2 4
 3
1
2
5
1 4 5 6 10
2
2 4
 3
1
1
5
2 3 4 9 10
2
2 4
 3
1
1
5
1 2 5 7 10
2
2 4
 3
1
1
5
1 3 5 7 10
2
2 3
 3
1
1
5
1 2 5 9 10
2
1 3
 3
1
1
5
3 4 5 7 10
2
1 4
 3
1
1
5
2 3 5 8 10
2
1 4
 3
1
1
5
2 3 5 6 10
2
1 4
 3
1
2
5
1 2 5 8 10
2
1 4
 3
1
1
5
2 4 7 9 10
2
1 3
 3
1
2
5
3 4 5 7 10
2
2 4
 3
1
1
5
2 4 5 8 10
2
3 4
 3
1
1
5
1 2 5 9 10
2
1 4
 3
1
2
5
2 3 5 8 10
2
1 4
 3
1
2
5
3 4 5 7 9
2
2 4
 3
1
1
5
2 4 5 7 9
2
1 4
 3
1
1
5
1 4 7 8 10
2
1 4
 3
1
1
5
1 2 5 9 10
2
2 3
 3
1
1
5
1 4 5 7 8
2
1 2
 3
1
1
5
1 3 5 7 10
2
1 3
 3
1
2
5
1 2 6 7 10
2
2 4
 3
1
1
5
1 3 5 8 10
2
1 2
 3
1
1
5
2 3 4 9 10
2
1 4
 3
1
1
5
2 3 7 8 10
2
1 4
 3
1
1
5
2 3 5 6 10
2
2 4
 3
1
1
5
2 3 5 8 10
2
1 2
 3
1
1
5
2 3 7 8 10
2
2 4
 3
1
2
5
1 4 5 9 10
2
2 4
 3
1
2
5
3 4 5 7 10
2
1 4
 3
1
2
5
2 4 5 9 10
2
2 4
 3
1
2
5
1 2 3 7 10
2
1 4
 3
1
1
5
1 3 8 9 10
2
2 4
 3
1
1
5
1 2 5 8 10
2
1 3
 3
1
1
5
2 4 7 9 10
2
2 3
 3
1
2
5
1 4 5 7 8
2
1 2
 3
1
1
5
1 3 8 9 10
2
2 3
 3
1
1
5
1 2 5 6 10
2
1 4
 3
1
2
5
1 3 5 9 10
2
2 4
 3
1
1
5
2 4 5 7 10
2
2 4
 3
1
2
5
1 4 5 8 10
2
1 4
 3
1
1
5
1 4 6 8 10
2
2 4
 3
1
2
5
1 2 5 9 10
2
2 4
 3
1
1
5
2 4 5 9 10
2
1 2
 3
1
2
5
2 4 5 7 10
2
3 4
 3
1
2
5
1 3 6 9 10
2
2 4
 3
1
1
5
1 2 6 8 10
2
1 2
 3
1
2
5
1 4 5 9 10
2
1 4
 3
1
2
5
2 3 5 6 10
2
1 4
 3
1
1
5
2 3 7 9 10
2
1 3
 3
1
1
5
1 4 5 7 9
2
1 4
 3
1
1
5
1 2 5 6 10
2
2 3
 3
1
2
5
1 3 6 9 10
2
1 4
 3
1
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