The flag of Berland is such rectangular field n × m that satisfies following conditions:

  * Flag consists of three colors which correspond to letters 'R', 'G' and 'B'. 
  * Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color. 
  * Each color should be used in exactly one stripe. 



You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).

Input

The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.

Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.

Output

Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).

Examples

Input

6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG


Output

YES


Input

4 3
BRG
BRG
BRG
BRG


Output

YES


Input

6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB


Output

NO


Input

4 4
RRRR
RRRR
BBBB
GGGG


Output

NO

Note

The field in the third example doesn't have three parralel stripes.

Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
        import java.util.*; 
                                        import java.math.*;
                                        import java.io.*;
                                        import java.text.DecimalFormat;
                                        import java.math.BigInteger;
                                        public class Main{
                                            //static int d=20;
                                            static long mod=1000000007 ;
                                            
                                            static ArrayList<ArrayList<Integer>> arr;
                                           // static long[] dp1,dp2;
                                            static int[] a;
                                            static int[] vis,num;
                                            static long max;
                                            static HashSet<String> hs;
                                            //static int flag,ans;
                                            static long max1,max2,ans1;
                                            
                                            static int flag=0;
                                            static int[] tin,tout,parent,level;
                                            static HashMap<Long,Integer> hm;
                                            static long[] dp1,dp2,dp3,dp4;
                                            static int ct=0;
                                               
                                            public static void main(String[] args)  throws IOException {
                                                ///long start=System.currentTimeMillis();
                                                boolean online =false;
                                                String fileName = "B-small-attempt0";
                                                PrintWriter out; 
                                                if (online) {
                                                    s.init(new FileInputStream(new File("Downloads/"+fileName + ".in")));
                                                     out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                                }
                                                 else {
                                                    s.init(System.in);   
                                                
                                                    out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
                                                    //out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                                }//r,b,y,g
                                                int n=s.ni();
                                                int m=s.ni();
                                                char[][] a=new char[n][m];
                                                for(int i=0;i<n;i++){
                                                    String x=s.ns();
                                                    for(int j=0;j<m;j++)
                                                        a[i][j]=x.charAt(j);
                                                }
                                                int flag=0;
                                                int flag1,flag2;
                                                flag1=flag2=1;

                                                if(n%3==0){
                                                    flag1=0;
                                                    int w=n/3;
                                                    char check='0';
                                                    for(int i=0;i<m;i++){
                                                        for(int j=0;j<w;j++){
                                                            if(check=='0')
                                                                check=a[j][i];
                                                            else if(check!=a[j][i]){
                                                                flag1=1;
                                                                break;
                                                            }

                                                        }
                                                    }
                                                    char check2='0';
                                                    for(int i=0;i<m;i++){
                                                        for(int j=w;j<2*w;j++){
                                                            if(check2=='0'){
                                                                if(a[j][i]==check){
                                                                    flag1=1;
                                                                    break;
                                                                }
                                                                check2=a[j][i];
                                                            }
                                                            else if(check2!=a[j][i]){
                                                                flag1=1;
                                                                break;
                                                            }

                                                        }
                                                    }
                                                    char check3='0';
                                                    for(int i=0;i<m;i++){
                                                        for(int j=2*w;j<3*w;j++){
                                                            if(check3=='0'){
                                                                if(a[j][i]==check || a[j][i]==check2){
                                                                    flag1=1;
                                                                    break;
                                                                }
                                                                check3=a[j][i];
                                                            }
                                                            else if(check3!=a[j][i]){
                                                                flag1=1;
                                                                break;
                                                            }

                                                        }
                                                    }

                                                }
                                                if(flag1==1 && m%3==0){
                                                    flag2=0;
                                                    int w=m/3;
                                                    char check='0';
                                                    for(int i=0;i<w;i++){
                                                        for(int j=0;j<n;j++){
                                                            if(check=='0')
                                                                check=a[j][i];
                                                            else if(check!=a[j][i]){
                                                                flag2=1;
                                                                break;
                                                            }

                                                        }
                                                    }
                                                    char check2='0';
                                                    for(int i=w;i<2*w;i++){
                                                        for(int j=0;j<n;j++){
                                                            if(check2=='0'){
                                                                if(a[j][i]==check){
                                                                    flag2=1;
                                                                    break;
                                                                }
                                                                check2=a[j][i];
                                                            }
                                                            else if(check2!=a[j][i]){
                                                                flag2=1;
                                                                break;
                                                            }

                                                        }
                                                    }
                                                    char check3='0';
                                                    for(int i=2*w;i<3*w;i++){
                                                        for(int j=0;j<n;j++){
                                                            if(check3=='0'){
                                                                if(a[j][i]==check || a[j][i]==check2){
                                                                    flag2=1;
                                                                    break;
                                                                }
                                                                check3=a[j][i];
                                                            }
                                                            else if(check3!=a[j][i]){
                                                                flag2=1;
                                                                break;
                                                            }

                                                        }
                                                    }

                                                }
                                                if(flag1==0 || flag2==0)
                                                    out.println("YES");
                                                else
                                                    out.println("NO");
                                                out.close();
                                                    
                                                  
                                                        
                                        
                                            } 
                                            

                                            public static void union(int[] a,int x,int y){
                                                int u=find(a,x);
                                                int v=find(a,y);
                                                a[v]=u;

                                            }
                                            public static int find(int[] a,int x){
                                                if(a[x]!=x){
                                                    a[x]=find(a,a[x]);
                                                }
                                                return a[x];
                                            }
                                            public static int gcd(int a, int b){
                                                    if (a == 0) return b;
                                                    return gcd(b % a, a);
                                            }
                                                
                                            public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
                                                vis[c]=1;
                                                if(g!=-1){
                                                    if(!arr.get(c).contains(g)){
                                                        flag=1;
                                                        return;
                                                    }
                                                }
                                                for(int x:arr.get(c)){
                                                    if(x!=p && x!=g && vis[x]==0 ){
                                                        cfs(arr,x,c,p,vis);
                                                    }
                                                }
     
                                            }
                                                                  //   public static void dfs(int u,int p){
             //                            //       if(p>=0)
             //                            //           tin[u]=tout[u]=tt++;
             //                            //       if(p>=0)
             //                            //           level[u]=level[p]+1;
             //                            //       parent[u]=p;
             //                            //       for(int x:arr.get(u)){
             //                            //           if(x!=p){
             //                            //               dfs(x,u);
             //                            //               tout[u]=Math.max(tout[u],tout[x]);
             //                            //           }
             //                            //       }
             //                            //       
             //
             //
                                         //   }
                                            public static int lca(int[][] p,int a,int b){
                                                if(level[a]<level[b]){
                                                    int x=a;
                                                    a=b;
                                                    b=x;
                                                }
                                                int log=p[0].length;
                                                for(int i=log-1;i>=0;i--){
                                                    if(1<<i<=level[a]-level[b]){
                                                        a=p[a][i];
                                                    }
                                                }
                                                if(a==b)
                                                    return a;
                                                for(int i=log-1;i>=0;i--){
                                                    if(p[a][i]!=p[b][i]){
                                                        a=p[a][i];
                                                        b=p[b][i];
                                                    }
                                                }
                                                return p[a][0];
             
                                            }
                                            public static int[][] par(int[] parent){
                                                int n=arr.size();
                                                int[][] p=new int[n][17];
                                                for(int i=0;i<n;i++)
                                                    p[i][0]=parent[i];
                                                for(int k=1;k<17;k++){
                                                    for(int i=0;i<n;i++){
                                                        if(p[i][k-1]>-1)
                                                            p[i][k]=p[p[i][k-1]][k-1];
                                                        else
                                                            p[i][k]=-1;
                                                    }
                                                }
                                                return p;
                                            }
                                            static class Edge implements Comparable<Edge>{
                                                   int from;
                                                    int to;
                                                    long cost;
                                            
                                                   public Edge(int from, int to, long weight) {
                                                       this.from = from;
                                                       this.to = to;
                                                       this.cost= weight;
                                                   }
                                                   public int compareTo(Edge o){
                                                        return (int)Math.signum(cost-o.cost); 
                                                   }

                                            }                               
                                            static class Node {
                                                int start;
                                                int end;
                            
                                                int cost;
                                                int updated;
                            
                                                Node[] nodes;
                            
                                                public Node(int start, int end) {
                                                    this.start = start;
                                                    this.end = end;
                            
                                                    if (start < end) {
                                                        int[] pos = {start, (start + end) / 2, end};
                                                        nodes = new Node[2];
                                                        for (int i = 0; i < 2; i++) {
                                                            nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                                                        }
                                                    }
                                                }
                            
                                                public void update(int queryStart, int queryEnd, int value) {
                                                    if (queryEnd < start || end < queryStart) {
                                                        return;
                                                    }
                            
                                                    if (queryStart <= start && end <= queryEnd) {
                                                        cost += value;
                                                        updated += value;
                                                        return;
                                                    }
                            
                                                    propagate();
                                                    for (Node node: nodes) {
                                                        node.update(queryStart, queryEnd, value);
                                                    }
                                                }
                            
                                                public int query(int pos) {
                                                    if (pos < start || end < pos) {
                                                        return 0;
                                                    }
                            
                                                    if (start == end) {
                                                        return cost;
                                                    }
                            
                                                    propagate();
                                                    int ans = 0;
                                                    for (Node node: nodes) {
                                                        ans = Math.max(ans, node.query(pos));
                                                    }
                                                    return ans;
                                                }
                            
                                                public void propagate() {
                                                    if (updated != 0 && start < end) {
                                                        for (Node node: nodes) {
                                                            node.cost += updated;
                                                            node.updated += updated;
                                                        }
                                                        updated = 0;
                                                    }
                                                }
                                            }
                                            public static double nthroot(int n, double A) {
                                                return nthroot(n, A, 0.0000001);
                                            }
                                            public static double nthroot(int n, double A, double p) {
                                                if(A < 0) {
                                                    System.err.println("A < 0");// we handle only real positive numbers
                                                    return -1;
                                                } else if(A == 0) {
                                                    return 0;
                                                }
                                                double x_prev = A;
                                                double x = A / n;  // starting "guessed" value...
                                                while(Math.abs(x - x_prev) > p) {
                                                    x_prev = x;
                                                    x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
                                                }
                                                return x;
                                            }
                                            
                                            static class item implements Comparable<item> {
                                                int from,to,cost;
                                                public item(int x,int y){
                                                    from=x;
                                                    to=y;
                                                    
                                                }
                                                public int compareTo(item o){
                                                    
                                                    return  o.cost-cost;
                                                }
                                                
                                            }
                                           
                                            public static void dfs2(int c,int p,int[] a){
                                                //System.out.println(c+" "+p);
                                               
                                                
                                                
                     
                                            }
            //public static void dfs(int x,int[] vis,Stack<Integer> st){
                                            //    vis[x]=1;
                                            //    ArrayList<Integer> arr2=arr.get(x);
                                            //    Collections.sort(arr2);
                                            //    for(int i=arr2.size()-1;i>=0;i--){
                                            //        int z=arr2.get(i);
                                            //        if(vis[z]==0)
                                            //            dfs(z,vis,st);
                                            //    }
                                            //    st.push(x);
                     //
                                            //}
                                            public static long gcd(long a, long b){
                                                    if (a == 0) return b;
                                                    return gcd(b % a, a);
                                            }
                                                
                                            public static boolean check(long x){
                                                if(x%4==0 || x%7==0 || x%11==0)
                                                    return true;
                                                if(x<4 || x<7 || x<11)
                                                    return false;
                                                if(x%2==0){
                                                    return check(x/2);
                                                }
                                                else
                                                    return check(x/2) && check((x+1)/2);
                                            }
                                            public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
                                                long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
                                                if(val<0)
                                                    return 1;
                                                else if(val>0)
                                                    return -1;
                                                else
                                                    return 0;
                                            }
                                            
                                            static class BIT{
                                            
                                                int N;
                                                long tree[];
                                                
                                                BIT(int N){
                                                    this.N = N;
                                                    tree = new long[N + 1];
                                                }
                                                
                                                void update(int idx,long val){
                                                    while(idx <= N){
                                                        tree[idx]+=val;
                                                        idx += (idx & -idx);
                                                    }
                                                }
                                                
                                                long query(int l,int r){
                                                    if(l == 1)
                                                        return read(r);
                                                    else
                                                        return read(r) - read(l-1);
                                                }
                                                
                                                long read(int idx){
                                                    long sum = 0;
                                                    while(idx > 0){
                                                        sum += tree[idx];
                                                        idx -= (idx & -idx);
                                                    }
                                                    return sum;
                                                }
                                            }
                                            public static boolean pal(String a){
                                                int i=0;
                                                int j=a.length()-1;
                                                while(i<j){
                                                    if(a.charAt(i)!=a.charAt(j)){
                                                        return false;
                                                    }
                                                    i++;
                                                    j--;
                                                }
                                                return true;
                                                    
                                            }
                                            public static long find(long n,long k){
                                                if(n==2){
                                                    if(k==1 || k==3)
                                                        return 1;
                                                    else
                                                        return 2;
                                                }
                                                long t=pow2(2,n,mod)-1;
                                                long z=(t+1)/2;
                                                if(k==z)
                                                    return n;
                                                if(k<z)
                                                    return find(n-1,k);
                                                else
                                                    return find(n-1,k-z);
                                            }
                                            public static long pow2(long a,long b,long mod){
                                                    
                                                    long ans=1;
                                                   // long z=b;
                                                    while(b>0){
                                                       
                                                        if(b%2==1)
                                                            ans=(a*ans)%mod;
                                                        a=(a*a)%mod;
                                                        b/=2;
                                                    }
                                                  
                                                    return  ans;
                                            }
                                             public static long pow3(long a,long b){
                                                    
                                                    long ans=1;
                                                   // long z=b;
                                                    while(b>0){
                                                       
                                                        if(b%2==1)
                                                            ans=(a*ans);
                                                        a=(a*a);
                                                        b/=2;
                                                    }
                                                  
                                                    return  ans;
                                            }
                                            public static long fib(long n){
                                                long[][]    f=new long[][]{{1L,1L},{1L,0}};
                                                if(n==0)
                                                    return 0;
                                                f=arrpow(f,n-1);
                                                return f[0][0];
                                            }
                                            public static long[][] arrpow(long[][] a,long b){
                                               
                                                    int n=a.length;
                                                  //  long z=b;
                                                    long[][] ans=new long[n][n];
                                                    for(int i=0;i<n;i++)
                                                        ans[i][i]=1L;
                                                    while(b>0){
                                                        
                                                        if(b%2==1)
                                                            ans=mul(a,ans);
                                                        a=mul(a,a);
                                                        b/=2;
                                                    }
                                                    
                                                    return  ans;
                                            }
                                            public static long[][] mul(long[][] a,long[][] b){
                                                int n=a.length;
                                                int m=b[0].length;
                                                long[][] ans=new long[n][m];
                                                if(n==2 && m==2 && b.length==2){
                                                    ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
                                                    ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
                                                    ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
                                                    ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
                                                    return ans;
                 
                                                }
                                                for(int i=0;i<n;i++){
                                                    for(int j=0;j<m;j++){
                                                        for(int k=0;k<b.length;k++){
                                                            ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                                                        }
                                                    }
                                                }
                                                return ans; 
                                            }
                                             static class name implements Comparable<name> {
                                                long l,b,h;
                                                public name(long   x,long y,long z){
                                                    {
                                                        l=x;
                                                        b=y;        
                                                    }
                                                    
                                                    
                                                    h=z;
                                                }
                                                public int compareTo(name o){
                                                    return -(int)(l*b-o.l*o.b);
                                                }
                                                
                                            }
                                            public static class s {
                                                static BufferedReader reader;
                                                static StringTokenizer tokenizer;
                                            
                                                /** call this method to initialize reader for InputStream */
                                                static void init(InputStream input) {
                                                    reader = new BufferedReader(
                                                                new InputStreamReader(input) );
                                                    tokenizer = new StringTokenizer("");
                                                }   
                                            
                                                /** get next word */
                                                static String ns() throws IOException {
                                                    while ( ! tokenizer.hasMoreTokens() ) {
                                                        //TODO add check for eof if necessary
                                                        tokenizer = new StringTokenizer(
                                                            reader.readLine() );
                                                    }
                                                    return tokenizer.nextToken();
                                                }
                                            
                                                static int ni() throws IOException {
                                                    return Integer.parseInt( ns() );
                                                }
                                            
                                                static double nd() throws IOException {
                                                    return Double.parseDouble( ns() );
                                                }
                                                static long nl() throws IOException {
                                                    return Long.parseLong( ns() );
                                                }
                                            }
                                        }   