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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
import java.util.function.IntPredicate;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DPairs solver = new DPairs();
            int testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(i, in, out);
            out.close();
        }
    }

    static class DPairs {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.ri();
            int[] b = new int[n];
            boolean[] occupy = new boolean[2 * n];
            for (int i = 0; i < n; i++) {
                b[i] = in.ri() - 1;
                occupy[b[i]] = true;
            }
            Randomized.shuffle(b);
            Arrays.sort(b);
            int[] a = IntStream.range(0, 2 * n).filter(i -> !occupy[i]).toArray();
            int k = BinarySearch.lastFalse((int mid) -> {
                boolean ans = true;
                for (int i = 0; i < mid; i++) {
                    if (b[i] >= a[n - mid + i]) {
                        ans = false;
                    }
                }
                return !ans;
            }, 0, n);
            int k2 = BinarySearch.lastFalse((int mid) -> {
                boolean ans = true;
                for (int i = 0; i < mid; i++) {
                    if (b[n - 1 - i] <= a[mid - 1 - i]) {
                        ans = false;
                    }
                }
                return !ans;
            }, 0, n);

            int l = 0;
            int r = k;
            int ll = n - k2;
            int rr = k;
            l = Math.max(l, ll);
            r = Math.min(r, rr);
            int ans = Math.max(0, r - l + 1);
            out.println(ans);
        }

    }

    static class Randomized {
        public static void shuffle(int[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static int ceilAverage(int x, int y) {
            return (x | y) - ((x ^ y) >> 1);
        }

    }

    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public String next() {
            return readString();
        }

        public int ri() {
            return readInt();
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

    }

    static class BinarySearch {
        private BinarySearch() {
        }

        public static int lastFalse(IntPredicate predicate, int l, int r) {
            assert l <= r;
            while (l != r) {
                int mid = DigitUtils.ceilAverage(l, r);
                if (predicate.test(mid)) {
                    r = mid - 1;
                } else {
                    l = mid;
                }
            }
            return l;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 1 << 13;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }
}

