You are given a binary matrix A of size n × n. Let's denote an x-compression of the given matrix as a matrix B of size n/x × n/x such that for every i ∈ [1, n], j ∈ [1, n] the condition A[i][j] = B[⌈ i/x ⌉][⌈ j/x ⌉] is met.

Obviously, x-compression is possible only if x divides n, but this condition is not enough. For example, the following matrix of size 2 × 2 does not have any 2-compression:

01  10 

For the given matrix A, find maximum x such that an x-compression of this matrix is possible.

Note that the input is given in compressed form. But even though it is compressed, you'd better use fast input.

Input

The first line contains one number n (4 ≤ n ≤ 5200) — the number of rows and columns in the matrix A. It is guaranteed that n is divisible by 4.

Then the representation of matrix follows. Each of n next lines contains n/4 one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from 0 to 9 or as uppercase Latin letters from A to F). Binary representation of each of these numbers denotes next 4 elements of the matrix in the corresponding row. For example, if the number B is given, then the corresponding elements are 1011, and if the number is 5, then the corresponding elements are 0101.

Elements are not separated by whitespaces.

Output

Print one number: maximum x such that an x-compression of the given matrix is possible.

Examples

Input


8
E7
E7
E7
00
00
E7
E7
E7


Output


1


Input


4
7
F
F
F


Output


1

Note

The first example corresponds to the matrix: 

11100111  11100111  11100111  00000000  00000000  11100111  11100111  11100111 

It is easy to see that the answer on this example is 1.
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {

    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;
    private static boolean DEBUG = false;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static int[][] n2dia(int r, int c) throws Exception {
        if (r < 0 || c < 0)
            throw new Exception("Array size should be non negative");
        int[][] array = new int[r][c];
        for (int i = 0; i < r; i++)
            array[i] = nia(c);
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T str) {
        try {
            printerBW.append(str.toString());
            if (DEBUG)
                flush();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    static void println() {
        print("\n");
    }

    static <T> void println(T str) {
        print(str + "\n");
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            flush();
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (args.length > 0 && args[0].equalsIgnoreCase("debug")
                || args.length > 1 && args[1].equalsIgnoreCase("debug"))
            DEBUG = true;

        main2();
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (args.length > 0 && args[0].equalsIgnoreCase("time") || args.length > 1 && args[1].equalsIgnoreCase("time"))
            print("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
        scannerIn.close();
    }

    static class Pair {
        long first;
        long second;

        Pair(long first, long second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object p2) {
            if (p2 instanceof Pair) {
                return ((Pair) p2).first == first && ((Pair) p2).second == second;
            }
            return false;
        }

        public String toString() {
            return "(first=" + first + ",second=" + second + ")";
        }
    }

    static class DisjointSet {
        int[] arr;
        int[] size;

        DisjointSet(int n) {
            arr = new int[n + 1];
            size = new int[n + 1];
            makeSet();
        }

        void makeSet() {
            for (int i = 1; i < arr.length; i++) {
                arr[i] = i;
                size[i] = 1;
            }
        }

        void union(int i, int j) {
            if (i == j)
                return;
            if (i > j) {
                i ^= j;
                j ^= i;
                i ^= j;
            }

            i = find(i);
            j = find(j);

            if (i == j)
                return;
            arr[j] = arr[i];
            size[i] += size[j];
            size[j] = size[i];
        }

        int find(int i) {
            if (arr[i] != i) {
                arr[i] = find(arr[i]);
                size[i] = size[arr[i]];
            }
            return arr[i];
        }

        int getSize(int i) {
            i = find(i);
            return size[i];
        }

        public String toString() {
            return Arrays.toString(arr);
        }
    }

    static long MOD = 1_000_000_007L;

    static void main2() throws Exception {
        int n = ni();
        int[][] t = new int[n][n];
        for (int i = 0; i < n; i++) {
            int[] in = convert(line());
            for (int j = 0; j < n; j++) {
                t[i] = in;
            }
        }
        long x = n;
        int size = 1;
        a1: for (int i = 0; i < n; i++) {
            size = 1;
            for (int j = 0; j < n; j++) {
                if (j == 0)
                    continue;
                if (x == 1)
                    break a1;
                if (t[i][j] == t[i][j - 1]) {
                    size++;
                } else {
                    x = gcd(x, size);
                    size = 1;
                }
            }
            x = gcd(x, size);
        }
        a2: for (int j = 0; j < n; j++) {
            size = 1;
            for (int i = 0; i < n; i++) {
                if (i == 0)
                    continue;
                if (x == 1)
                    break a2;
                if (t[i][j] == t[i - 1][j]) {
                    size++;
                } else {
                    x = gcd(x, size);
                    size = 1;
                }
            }
            x = gcd(x, size);
        }
        println(x);
    }

    static int[] convert(String input) {
        int[] ans = new int[4 * input.length()];
        int k = 0;
        for (int i = 0; i < input.length(); i++) {
            int comp = getInt(input.charAt(i));
            ans[k] = comp & 0b1000; ans[k] >>= 3;
            ans[k + 1] = comp & 0b0100; ans[k+1] >>= 2;
            ans[k + 2] = comp & 0b0010; ans[k+2] >>= 1;
            ans[k + 3] = comp & 0b0001;
            k += 4;
        }
        return ans;
    }

    static int getInt(char c) {
        if (c >= '0' && c <= '9')
            return Integer.parseInt("" + c);
        return 15 - 'F' + c;
    }

    static boolean isSqrt(double a) {
        double sr = Math.sqrt(a);
        return ((sr - Math.floor(sr)) == 0);
    }

    static long abs(long a) {
        return Math.abs(a);
    }

    static int min(int... arr) {
        int min = Integer.MAX_VALUE;
        for (int var : arr)
            min = Math.min(min, var);
        return min;
    }

    static int max(int... arr) {
        int max = Integer.MIN_VALUE;
        for (int var : arr)
            max = Math.max(max, var);
        return max;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
}