Problem: Mr. Apple, a gourmet, works as editor-in-chief of a gastronomic periodical. He travels around the world, tasting new delights of famous chefs from the most fashionable restaurants. Mr. Apple has his own signature method of review — in each restaurant Mr. Apple orders two sets of dishes on two different days. All the dishes are different, because Mr. Apple doesn't like to eat the same food. For each pair of dishes from different days he remembers exactly which was better, or that they were of the same quality. After this the gourmet evaluates each dish with a positive integer.

Once, during a revision of a restaurant of Celtic medieval cuisine named «Poisson», that serves chestnut soup with fir, warm soda bread, spicy lemon pie and other folk food, Mr. Apple was very pleasantly surprised the gourmet with its variety of menu, and hence ordered too much. Now he's confused about evaluating dishes.

The gourmet tasted a set of n dishes on the first day and a set of m dishes on the second day. He made a table a of size n × m, in which he described his impressions. If, according to the expert, dish i from the first set was better than dish j from the second set, then a_{ij} is equal to ">", in the opposite case a_{ij} is equal to "<". Dishes also may be equally good, in this case a_{ij} is "=".

Now Mr. Apple wants you to help him to evaluate every dish. Since Mr. Apple is very strict, he will evaluate the dishes so that the maximal number used is as small as possible. But Mr. Apple also is very fair, so he never evaluates the dishes so that it goes against his feelings. In other words, if a_{ij} is "<", then the number assigned to dish i from the first set should be less than the number of dish j from the second set, if a_{ij} is ">", then it should be greater, and finally if a_{ij} is "=", then the numbers should be the same.

Help Mr. Apple to evaluate each dish from both sets so that it is consistent with his feelings, or determine that this is impossible.

Input

The first line contains integers n and m (1 ≤ n, m ≤ 1000) — the number of dishes in both days.

Each of the next n lines contains a string of m symbols. The j-th symbol on i-th line is a_{ij}. All strings consist only of "<", ">" and "=".

Output

The first line of output should contain "Yes", if it's possible to do a correct evaluation for all the dishes, or "No" otherwise.

If case an answer exist, on the second line print n integers — evaluations of dishes from the first set, and on the third line print m integers — evaluations of dishes from the second set.

Examples

Input


3 4
&gt;&gt;&gt;&gt;
&gt;&gt;&gt;&gt;
&gt;&gt;&gt;&gt;


Output


Yes
2 2 2 
1 1 1 1 


Input


3 3
&gt;&gt;&gt;
&lt;&lt;&lt;
&gt;&gt;&gt;


Output


Yes
3 1 3 
2 2 2 


Input


3 2
==
=&lt;
==


Output


No

Note

In the first sample, all dishes of the first day are better than dishes of the second day. So, the highest score will be 2, for all dishes of the first day.

In the third sample, the table is contradictory — there is no possible evaluation of the dishes that satisfies it.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.*;
import java.util.*;
import java.util.LinkedList;
import java.math.*;
import java.lang.*;
import java.util.PriorityQueue;
import static java.lang.Math.*;
@SuppressWarnings("unchecked")
public class Solution implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static long min(long a,long b)
    {
        if(a>b)
        {
            return b;
        }
        return a;
    }
    public static int min(int a,int b)
    {
        if(a>b)
        {
            return b;
        }
        return a;
    }
    public static long max(long a,long b)
    {
        if(a>b)
        {
            return a;
        }
        return b;
    }
    public static int max(int a,int b)
    {
        if(a>b)
        {
            return a;
        }
        return b;
    }
    static class pair
    {
      long x;
      long y;
      pair(long x,long y)
      {
        this.x = x;
        this.y = y;
      }
    }
    public static int gcd(int a,int b)
    {
        if(a==0)
        return b;
        if(b==0)
        return a;
        while((a%=b)!=0&&(b%=a)!=0);
        return a^b;
    }
    public static long mod(long x)
    {
      if(x>0)
      {
        return x;
      }
      return -x;
    }
    static int mod = (int)1e9+7;
    public static long[][] mult(long[][] a,long[][] b)
    {
      int n = a.length;
      int m = b[0].length;
      long[][] res = new long[n][m];
      for(int i=0;i<n;i++)
      {
        for(int j=0;j<m;j++)
        {
          for(int k=0;k<a[0].length;k++)
          {
            res[i][j]  = (res[i][j]+a[i][k]*b[k][j])%mod;
          }
        }
      }
      return res;
    }
    static int[] height;
    static int[] parent;
    public static int parent(int u)
    {
      if(u==parent[u])
      {
        return u;
      }
      return parent[u] = parent(parent[u]);
    }
    public static void join(int u,int v)
    {
      int pu = parent(u);
      int pv = parent(v);
      if(pu==pv){
        return;
      }
      if(height[pu]>height[pv])
      {
        parent[pv] = pu;
      }
      else if(height[pu]<height[pv])
      {
        parent[pu] = pv;
      }
      else
      {
        parent[pu] = pv;
        height[pu]++;
      }
    }
    public static boolean cycle1(int u,boolean[] visit,boolean[] stck)
    {
      visit[u] = true;
      stck[u] = true;
      for(Integer v:list[u])
      {
        if(visit[v]&&stck[v])
        {
          return true;
        }
        if(!visit[v])
        {
          if(cycle1(v,visit,stck)){
            return true;
          }
        }
      }
      stck[u] = false;
      return false;
    }
    public static boolean cycle(boolean[] visit,boolean[] stck)
    {
      for(int i=0;i<visit.length;i++)
      {
        if(!visit[i]&&cycle1(i,visit,stck))
        {
          return true;
        }
      }
      return false;
    }
    public static void dfs(int u,boolean[] visit,int[] ans)
    {
      visit[u] = true;
      int max = 0;
      for(Integer v:list[u])
      {
        if(!visit[v])
        {
          dfs(v,visit,ans);
        }
        max = max(max,ans[v]);
      }
      ans[u] = max+1;
    }
    static ArrayList<Integer>[] list;
    public static int random(int min,int max)
    {
      return min+(int)((max-min)*Math.random());
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Solution(),"Main",1<<26).start();
    }    public void run() {
      InputReader sc  = new InputReader(System.in);
      PrintWriter out = new PrintWriter(System.out);
      int t1 = 1;
      while(t1-->0)
      {
        int n = sc.nextInt();
        int m = sc.nextInt();
        char[][] c = new char[n][];
        for(int i=0;i<n;i++)
        {
          c[i] = sc.readString().toCharArray();
        }
        height = new int[n+m];
        parent = new int[n+m];
        for(int i=0;i<n+m;i++)
        {
          parent[i] = i;
        }
        for(int i=0;i<n;i++)
        {
          for(int j=0;j<m;j++)
          {
            if(c[i][j]=='=')
            {
              join(i,n+j);
            }
          }
        }
        int[] hash = new int[n+m];
        int ind = 0;
        for(int i=0;i<n+m;i++)
        {
          if(parent[i]==i)
          {
            hash[i] = ind++;
          }
        }
        list = new ArrayList[ind];
        for(int i=0;i<ind;i++)
        {
          list[i] = new ArrayList<>();
        }
        for(int i=0;i<n;i++)
        {
          for(int j=0;j<m;j++)
          {
            int pi = parent(i);
            int pj = parent(n+j);
            if(c[i][j]=='>')
            {
              list[hash[pi]].add(hash[pj]);
            }
            else if(c[i][j]=='<')
            {
              list[hash[pj]].add(hash[pi]);
            }
          }
        }
        boolean[] visit = new boolean[ind];
        boolean[] stack1 = new boolean[ind];
        if(cycle(visit,stack1))
        {
          out.println("NO");
        }
        else
        {
            out.println("YES");
            Arrays.fill(visit,false);
            int[] ans = new int[ind];
            for(int i=0;i<ind;i++)
            {
              if(!visit[i])
              {
                dfs(i,visit,ans);
              }
            }
            for(int i=0;i<n;i++)
            {
              out.print(ans[hash[parent(i)]]+" ");
            }
            out.println();
            for(int j=0;j<m;j++)
            {
              out.print(ans[hash[parent(n+j)]]+" ");
            }
            out.println();
        }
      }
      out.close();
  }
}