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 javafx.scene.layout.Priority;

import java.io.*;
import java.lang.reflect.Array;
import java.net.Inet4Address;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
import java.util.PriorityQueue;
public class templ implements Runnable {
    static class pair implements Comparable
    {
        int f,s;
        pair(int fi,int se)
        {
            f=fi;
            s=se;
        }
        public int compareTo(Object o)
        {
            pair pr=(pair)o;
            if(f>pr.f)
                return 1;
            else
                return -1;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            int ff;
            int ss;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                if((ff==this.f)&&(ss==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }
    }
    public class triplet implements Comparable
    {
        int f,s;
        int t;
        triplet(int f,int s,int t)
        {
            this.f=f;
            this.s=s;
            this.t=t;
        }
        public boolean equals(Object o)
        {
            triplet ob=(triplet)o;
            int ff,ss;
            int tt;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                tt=ob.t;
                if((ff==this.f)&&(ss==this.s)&&(tt==this.t))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s+" "+this.t).hashCode();
        }
        public int compareTo(Object o)
        {
            triplet tr=(triplet)o;
            if(f>tr.f)
                return 1;
            else if(f==tr.f)
            {
                if(s>tr.s)
                    return -1;
                else
                    return 1;
            }
            else
                return -1;
        }
    }
    String get(char n)
    {
        if(n=='0')
            return "0000";
        if(n=='1')
            return "0001";
        if(n=='2')
            return "0010";
        if(n=='3')
            return "0011";
        if(n=='4')
            return "0100";
        if(n=='5')
            return "0101";
        if(n=='6')
            return "0110";
        if(n=='7')
            return "0111";
        if(n=='8')
            return "1000";
        if(n=='9')
            return "1001";
        if(n=='A')
            return "1010";
        if(n=='B')
            return "1011";
        if(n=='C')
            return "1100";
        if(n=='D')
            return "1101";
        if(n=='E')
            return "1110";
        if(n=='F')
            return "1111";
        return "";
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new templ(),"templ",1<<27).start();
    }
    public void run()
    {
        try
        {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n=in.ni();
            int m[][]=new int[n+1][n+1];
            int a[][]=new int[n+1][n+1];
            for(int i=1;i<=n;i++)
            {
                StringBuilder ss=new StringBuilder();
                String s=in.nextLine();
                int l=s.length();
                for(int j=0;j<l;j++)
                {
                    char c=s.charAt(j);
                    ss.append(get(c));
                }
                l=ss.length();
                for(int j=0;j<l;j++)
                {
                    char c=ss.charAt(j);
                    int d=(int)c-(int)'0';
                    m[i][j+1]=d;
                }
            }
            a[1][1]=m[1][1];
            for(int i=2;i<=n;i++)
            {
                a[1][i]=m[1][i]+a[1][i-1];
            }
            for(int j=2;j<=n;j++)
            {
                a[j][1]=m[j][1]+a[j-1][1];
            }
            for(int i=2;i<=n;i++)
            {
                for(int j=2;j<=n;j++)
                {
                    a[i][j]=m[i][j]+a[i][j-1]+a[i-1][j]-a[i-1][j-1];
                }
            }
            int ans=-1;
            for(int ii=n;ii>=1;ii--)
            {
                if(n%ii!=0)
                    continue;
                int k=0;
                for(int i=ii;i<=n;i+=ii)
                {
                    for(int j=ii;j<=n;j+=ii)
                    {
                        int sum=a[i][j]-a[i-ii][j]-a[i][j-ii]+a[i-ii][j-ii];
                        if(sum==0||sum==ii*ii)
                            continue;
                        k=1;
                        break;
                    }
                }
                if(k==0)
                {
                    ans=ii;
                    break;
                }
            }
            out.println(ans);
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

    }
}