import java.util.ArrayDeque;
import java.util.ArrayList;

public class Main {

    public static final int MOD998 = 998244353;
    public static final int MOD100 = 1000000007;

    static ArrayList<Integer> ope = new ArrayList<>();

    public static void main(String[] args) throws Exception {
        ContestScanner sc = new ContestScanner();
        ContestPrinter cp = new ContestPrinter();
        int T = sc.nextInt();
        for (int t = 0; t < T; t++) {
            solve(sc, cp);
        }
        cp.close();
    }

    static void solve(ContestScanner sc, ContestPrinter cp) {
        ope = new ArrayList<>();
        int N = sc.nextInt();
        int[][] A = sc.nextIntMatrix(N, N);
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                A[i][j]--;
            }
        }
        if (N % 2 == 1) {
            if (A[N / 2][0] != N / 2 * N) {
                reverseRow(A, N / 2);
            } else {
                reverseRow(A, 0);
            }
            if (A[0][N / 2] != N / 2) {
                reverseCol(A, N / 2);
            } else {
                reverseCol(A, 0);
            }
            for (int i = 0; i < N; i++) {
                if (A[N / 2][i] != N / 2 * N + i) {
                    cp.println(-1);
                    return;
                }
                if (A[i][N / 2] != i * N + N / 2) {
                    cp.println(-1);
                    return;
                }
            }
        }
        ArrayDeque<Integer> revrow = new ArrayDeque<>();
        for (int i = 0; i < N / 2; i++) {
            int[] mem = new int[4];
            mem[0] = A[i][0];
            mem[1] = A[i][N - 1];
            mem[2] = A[N - i - 1][0];
            mem[3] = A[N - i - 1][N - 1];
            int swap = 0;
            for (int p = 2; p >= 0; p--) {
                for (int q = p; q < 3; q++) {
                    if (mem[q] > mem[q + 1]) {
                        int tem = mem[q];
                        mem[q] = mem[q + 1];
                        mem[q + 1] = tem;
                        swap++;
                    }
                }
            }
            if (swap % 2 == 1) {
                revrow.add(i);
            }
        }
        ArrayDeque<Integer> revcol = new ArrayDeque<>();
        for (int i = 1; i < N / 2; i++) {
            int[] mem = new int[4];
            mem[0] = A[0][i];
            mem[1] = A[0][N - i - 1];
            mem[2] = A[N - 1][i];
            mem[3] = A[N - 1][N - i - 1];
            int swap = 0;
            for (int p = 2; p >= 0; p--) {
                for (int q = p; q < 3; q++) {
                    if (mem[q] > mem[q + 1]) {
                        int tem = mem[q];
                        mem[q] = mem[q + 1];
                        mem[q + 1] = tem;
                        swap++;
                    }
                }
            }
            if ((revrow.peek() == 0) == (swap % 2 == 0)) {
                revcol.add(i);
            }
        }
        boolean rv = false;
        while (!revrow.isEmpty() || !revcol.isEmpty()) {
            if (revrow.isEmpty()) {
                reverseRow(A, 0);
                rv = !rv;
                reverseCol(A, revcol.poll());
                if (revcol.isEmpty() && rv) {
                    reverseRow(A, 0);
                    rv = !rv;
                }
            } else if (revcol.isEmpty()) {
                reverseRow(A, revrow.poll());
                if (!revrow.isEmpty() || rv) {
                    reverseCol(A, 0);
                    rv = !rv;
                }
            } else {
                reverseRow(A, revrow.poll());
                reverseCol(A, revcol.poll());
            }
        }
        if (ope.size() % 2 == 1) {
            int[][] copy = new int[N][N];
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    int v = A[i][j];
                    int r = v / N;
                    int c = v % N;
                    copy[j][i] = c * N + r;
                }
            }
            A = copy;
        }

        for (int i = 0; i < N / 2; i++) {
            for (int j = 0; j < N / 2; j++) {
                int[] mem = new int[4];
                int[] memcopy = new int[4];
                mem[0] = A[i][j];
                mem[1] = A[i][N - j - 1];
                mem[2] = A[N - i - 1][j];
                mem[3] = A[N - i - 1][N - j - 1];
                System.arraycopy(mem, 0, memcopy, 0, 4);
                int swap = 0;
                for (int p = 2; p >= 0; p--) {
                    for (int q = p; q < 3; q++) {
                        if (mem[q] > mem[q + 1]) {
                            int tem = mem[q];
                            mem[q] = mem[q + 1];
                            mem[q + 1] = tem;
                            swap++;
                        }
                    }
                }
                if (swap % 2 == 1 || mem[0] != i * N + j || mem[1] != i * N + (N - j - 1)
                        || mem[2] != (N - i - 1) * N + j || mem[3] != (N - i - 1) * N + (N - j - 1)) {
                    cp.println(-1);
                    return;
                }
                for (int p = 0; p < 4; p++) {
                    for (int q = 0; q < 4; q++) {
                        if (memcopy[q] == mem[p]) {
                            memcopy[q] = p;
                            break;
                        }
                    }
                }
                int[][] pats = new int[][] { { i, j, i, j }, { i, N - j - 1, i, N - j - 1 },
                        { N - i - 1, j, N - i - 1, j }, { N - i - 1, N - j - 1, N - i - 1, N - j - 1 } };
                while (memcopy[0] != 0 || memcopy[1] != 1 || memcopy[2] != 2 || memcopy[3] != 3) {
                    int op = -1;
                    if (memcopy[0] == 0) {
                        op = 3;
                    } else if (memcopy[0] == 1) {
                        op = 1;
                    } else if (memcopy[0] == 2) {
                        op = 0;
                    } else {
                        op = 2;
                    }
                    for (int p = 0; p < 4; p++) {
                        if (p % 2 == 0) {
                            reverseRow(A, pats[op][p]);
                        } else {
                            reverseCol(A, pats[op][p]);
                        }
                    }
                    if (op == 0) {
                        int tem = memcopy[0];
                        memcopy[0] = memcopy[1];
                        memcopy[1] = memcopy[2];
                        memcopy[2] = tem;
                    } else if (op == 1) {
                        int tem = memcopy[1];
                        memcopy[1] = memcopy[0];
                        memcopy[0] = memcopy[3];
                        memcopy[3] = tem;
                    } else if (op == 2) {
                        int tem = memcopy[2];
                        memcopy[2] = memcopy[3];
                        memcopy[3] = memcopy[0];
                        memcopy[0] = tem;
                    } else {
                        int tem = memcopy[3];
                        memcopy[3] = memcopy[2];
                        memcopy[2] = memcopy[1];
                        memcopy[1] = tem;
                    }
                }
            }
        }
        cp.println(ope.size());
        for (int i = 0; i < ope.size(); i++) {
            cp.print(ope.get(i) + (i == ope.size() - 1 ? "\n" : " "));
        }
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                System.err.print(A[i][j] + " ");
            }
            System.err.println();
        }
    }

    static void reverseRow(int[][] mat, int row) {
        ope.add(row + 1);
        int i = 0;
        int j = mat[row].length - 1;
        while (i < j) {
            int tem = mat[row][i];
            mat[row][i] = mat[row][j];
            mat[row][j] = tem;
            i++;
            j--;
        }
    }

    static void reverseCol(int[][] mat, int col) {
        ope.add(col + 1);
        int i = 0;
        int j = mat.length - 1;
        while (i < j) {
            int tem = mat[i][col];
            mat[i][col] = mat[j][col];
            mat[j][col] = tem;
            i++;
            j--;
        }
    }

    static class ContestScanner {
        private final java.io.InputStream in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private static final long LONG_MAX_TENTHS = 922337203685477580L;
        private static final int LONG_MAX_LAST_DIGIT = 7;
        private static final int LONG_MIN_LAST_DIGIT = 8;

        public ContestScanner(java.io.InputStream in) {
            this.in = in;
        }

        public ContestScanner() {
            this(System.in);
        }

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (java.io.IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private static boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new java.util.NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new java.util.NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    int digit = b - '0';
                    if (n >= LONG_MAX_TENTHS) {
                        if (n == LONG_MAX_TENTHS) {
                            if (minus) {
                                if (digit <= LONG_MIN_LAST_DIGIT) {
                                    n = -n * 10 - digit;
                                    b = readByte();
                                    if (!isPrintableChar(b)) {
                                        return n;
                                    } else if (b < '0' || '9' < b) {
                                        throw new NumberFormatException(
                                                String.format("%d%s... is not number", n, Character.toString(b)));
                                    }
                                }
                            } else {
                                if (digit <= LONG_MAX_LAST_DIGIT) {
                                    n = n * 10 + digit;
                                    b = readByte();
                                    if (!isPrintableChar(b)) {
                                        return n;
                                    } else if (b < '0' || '9' < b) {
                                        throw new NumberFormatException(
                                                String.format("%d%s... is not number", n, Character.toString(b)));
                                    }
                                }
                            }
                        }
                        throw new ArithmeticException(
                                String.format("%s%d%d... overflows long.", minus ? "-" : "", n, digit));
                    }
                    n = n * 10 + digit;
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public long[] nextLongArray(int length) {
            long[] array = new long[length];
            for (int i = 0; i < length; i++)
                array[i] = this.nextLong();
            return array;
        }

        public long[] nextLongArray(int length, java.util.function.LongUnaryOperator map) {
            long[] array = new long[length];
            for (int i = 0; i < length; i++)
                array[i] = map.applyAsLong(this.nextLong());
            return array;
        }

        public int[] nextIntArray(int length) {
            int[] array = new int[length];
            for (int i = 0; i < length; i++)
                array[i] = this.nextInt();
            return array;
        }

        public int[][] nextIntArrayMulti(int length, int width) {
            int[][] arrays = new int[width][length];
            for (int i = 0; i < length; i++) {
                for (int j = 0; j < width; j++)
                    arrays[j][i] = this.nextInt();
            }
            return arrays;
        }

        public int[] nextIntArray(int length, java.util.function.IntUnaryOperator map) {
            int[] array = new int[length];
            for (int i = 0; i < length; i++)
                array[i] = map.applyAsInt(this.nextInt());
            return array;
        }

        public double[] nextDoubleArray(int length) {
            double[] array = new double[length];
            for (int i = 0; i < length; i++)
                array[i] = this.nextDouble();
            return array;
        }

        public double[] nextDoubleArray(int length, java.util.function.DoubleUnaryOperator map) {
            double[] array = new double[length];
            for (int i = 0; i < length; i++)
                array[i] = map.applyAsDouble(this.nextDouble());
            return array;
        }

        public long[][] nextLongMatrix(int height, int width) {
            long[][] mat = new long[height][width];
            for (int h = 0; h < height; h++)
                for (int w = 0; w < width; w++) {
                    mat[h][w] = this.nextLong();
                }
            return mat;
        }

        public int[][] nextIntMatrix(int height, int width) {
            int[][] mat = new int[height][width];
            for (int h = 0; h < height; h++)
                for (int w = 0; w < width; w++) {
                    mat[h][w] = this.nextInt();
                }
            return mat;
        }

        public double[][] nextDoubleMatrix(int height, int width) {
            double[][] mat = new double[height][width];
            for (int h = 0; h < height; h++)
                for (int w = 0; w < width; w++) {
                    mat[h][w] = this.nextDouble();
                }
            return mat;
        }

        public char[][] nextCharMatrix(int height, int width) {
            char[][] mat = new char[height][width];
            for (int h = 0; h < height; h++) {
                String s = this.next();
                for (int w = 0; w < width; w++) {
                    mat[h][w] = s.charAt(w);
                }
            }
            return mat;
        }
    }

    static class ContestPrinter extends java.io.PrintWriter {
        public ContestPrinter(java.io.PrintStream stream) {
            super(stream);
        }

        public ContestPrinter() {
            super(System.out);
        }

        private static String dtos(double x, int n) {
            StringBuilder sb = new StringBuilder();
            if (x < 0) {
                sb.append('-');
                x = -x;
            }
            x += Math.pow(10, -n) / 2;
            sb.append((long) x);
            sb.append(".");
            x -= (long) x;
            for (int i = 0; i < n; i++) {
                x *= 10;
                sb.append((int) x);
                x -= (int) x;
            }
            return sb.toString();
        }

        @Override
        public void print(float f) {
            super.print(dtos(f, 20));
        }

        @Override
        public void println(float f) {
            super.println(dtos(f, 20));
        }

        @Override
        public void print(double d) {
            super.print(dtos(d, 20));
        }

        @Override
        public void println(double d) {
            super.println(dtos(d, 20));
        }

        public void printArray(int[] array, String separator) {
            int n = array.length;
            for (int i = 0; i < n - 1; i++) {
                super.print(array[i]);
                super.print(separator);
            }
            super.println(array[n - 1]);
        }

        public void printArray(int[] array) {
            this.printArray(array, " ");
        }

        public void printArray(int[] array, String separator, java.util.function.IntUnaryOperator map) {
            int n = array.length;
            for (int i = 0; i < n - 1; i++) {
                super.print(map.applyAsInt(array[i]));
                super.print(separator);
            }
            super.println(map.applyAsInt(array[n - 1]));
        }

        public void printArray(int[] array, java.util.function.IntUnaryOperator map) {
            this.printArray(array, " ", map);
        }

        public void printArray(long[] array, String separator) {
            int n = array.length;
            for (int i = 0; i < n - 1; i++) {
                super.print(array[i]);
                super.print(separator);
            }
            super.println(array[n - 1]);
        }

        public void printArray(long[] array) {
            this.printArray(array, " ");
        }

        public void printArray(long[] array, String separator, java.util.function.LongUnaryOperator map) {
            int n = array.length;
            for (int i = 0; i < n - 1; i++) {
                super.print(map.applyAsLong(array[i]));
                super.print(separator);
            }
            super.println(map.applyAsLong(array[n - 1]));
        }

        public void printArray(long[] array, java.util.function.LongUnaryOperator map) {
            this.printArray(array, " ", map);
        }

    }
}