description: You are given n dominoes. Each domino has a left and a right cell. Each cell can be colored either black or white. Some cells are already colored, while some aren't yet.
  
  The coloring is said to be valid if and only if it is possible to rearrange the dominoes in some order such that for each 1 ≤ i ≤ n the color of the right cell of the i-th domino is different from the color of the left cell of the ((i mod n)+1)-st domino. 
  
  Note that you can't rotate the dominoes, so the left cell always remains the left cell, and the right cell always remains the right cell.
  
  Count the number of valid ways to color the yet uncolored cells of dominoes. Two ways are considered different if there is a cell that is colored white in one way and black in the other. In particular, colorings BW WB and WB BW different (and both invalid).
  
  As this number can be very big, output it modulo 998 244 353.
  
  Input
  
  The first line of the input contains a single integer n (1 ≤ n ≤ 10^5) — the number of dominoes.
  
  The next n lines describe dominoes. Each line contains two characters which represent the left and the right cell. Character B means that the corresponding cell is black, character W means that the corresponding cell is white, and ? means that the cell is yet to be colored. 
  
  Output
  
  Print a single integer — the answer to the problem.
  
  Examples
  
  Input
  
  
  1
  ?W
  
  
  Output
  
  
  1
  
  
  Input
  
  
  2
  ??
  W?
  
  
  Output
  
  
  2
  
  
  Input
  
  
  4
  BB
  ??
  W?
  ??
  
  
  Output
  
  
  10
  
  Note
  
  In the first test case, there is only one domino, and we need the color of its right cell to be different from the color of its left cell. There is only one way to achieve this.
  
  In the second test case, there are only 2 such colorings:
  
  BB WW and WB WB.
solution: import java.io.*;
  import java.util.*;
  import java.util.concurrent.ThreadLocalRandom;
  import java.math.*;
  
  /**
   __                  __
   ( _)                ( _)
   / / \\              / /\_\_
   / /   \\            / / | \ \
   / /     \\          / /  |\ \ \
   /  /   ,  \ ,       / /   /|  \ \
   /  /    |\_ /|      / /   / \   \_\
   /  /  |\/ _ '_| \   / /   /   \    \\
   |  /   |/  0 \0\    / |    |    \    \\
   |    |\|      \_\_ /  /    |     \    \\
   |  | |/    \.\ o\o)  /      \     |    \\
   \    |     /\\`v-v  /        |    |     \\
   | \/    /_| \\_|  /         |    | \    \\
   | |    /__/_ `-` /   _____  |    |  \    \\
   \|    [__]  \_/  |_________  \   |   \    ()
   /    [___] (    \         \  |\ |   |   //
   |    [___]                  |\| \|   /  |/
   /|    [____]                  \  |/\ / / ||
   (  \   [____ /     ) _\      \  \    \| | ||
   \  \  [_____|    / /     __/    \   / / //
   |   \ [_____/   / /        \    |   \/ //
   |   /  '----|   /=\____   _/    |   / //
   __ /  /        |  /   ___/  _/\    \  | ||
   (/-(/-\)       /   \  (/\/\)/  |    /  | /
   (/\/\)           /   /   //
   _________/   /    /
   \____________/    (
  
  
   @author NTUDragons-Reborn
   */
  
  public class C{
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          Task solver = new Task();
          solver.solve(in, out);
          out.close();
      }
      // main solver
      static class Task{
  
          double eps= 0.00000001;
          static final int MAXN = 200015;
          static final int MOD= 998244353;
  
          // stores smallest prime factor for every number
          static int spf[] = new int[MAXN];
  
          static boolean[] prime;
  
          Map<Integer,Set<Integer>> dp= new HashMap<>();
  
          // Calculating SPF (Smallest Prime Factor) for every
          // number till MAXN.
          // Time Complexity : O(nloglogn)
          public void sieve()
          {
              spf[1] = 1;
              for (int i=2; i<MAXN; i++)
  
                  // marking smallest prime factor for every
                  // number to be itself.
                  spf[i] = i;
  
              // separately marking spf for every even
              // number as 2
              for (int i=4; i<MAXN; i+=2)
                  spf[i] = 2;
  
              for (int i=3; i*i<MAXN; i++)
              {
                  // checking if i is prime
                  if (spf[i] == i)
                  {
                      // marking SPF for all numbers divisible by i
                      for (int j=i*i; j<MAXN; j+=i)
  
                          // marking spf[j] if it is not
                          // previously marked
                          if (spf[j]==j)
                              spf[j] = i;
                  }
              }
          }
  
          void sieveOfEratosthenes(int n)
          {
              // Create a boolean array
              // "prime[0..n]" and
              // initialize all entries
              // it as true. A value in
              // prime[i] will finally be
              // false if i is Not a
              // prime, else true.
              prime= new boolean[n + 1];
              for (int i = 0; i <= n; i++)
                  prime[i] = true;
      
              for (int p = 2; p * p <= n; p++)
              {
                  // If prime[p] is not changed, then it is a
                  // prime
                  if (prime[p] == true)
                  {
                      // Update all multiples of p
                      for (int i = p * p; i <= n; i += p)
                          prime[i] = false;
                  }
              }
          }
  
          // A O(log n) function returning primefactorization
          // by dividing by smallest prime factor at every step
          public Set<Integer> getFactorization(int x)
          {
              if(dp.containsKey(x)) return dp.get(x);
              Set<Integer> ret = new HashSet<>();
              while (x != 1)
              {
                  if(spf[x]!=2) ret.add(spf[x]);
                  x = x / spf[x];
              }
              dp.put(x,ret);
              return ret;
          }
          // function to find first index >= x
          public int lowerIndex(List<Integer> arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
          public int lowerIndex(int[] arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
  
          // function to find last index <= y
          public int upperIndex(List<Integer> arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
          public int upperIndex(int[] arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
  
          // function to count elements within given range
          public int countInRange(List<Integer> arr, int n, int x, int y)
          {
              // initialize result
              int count = 0;
              count = upperIndex(arr, n, y) -
                      lowerIndex(arr, n, x) + 1;
              return count;
          }
  
          public int add(int a, int b){
              a+=b;
              while(a>=MOD) a-=MOD;
              while(a<0) a+=MOD;
              return a;
          }
  
          public int mul(int a, int b){
              long res= (long)a*(long)b;
              return (int)(res%MOD);
          }
  
          public int power(int a, int b) {
              int ans=1;
              while(b>0){
                  if((b&1)!=0) ans= mul(ans,a);
                  b>>=1;
                  a= mul(a,a);
              }
              return ans;
          }
  
          int[] fact= new int[MAXN];
          int[] inv= new int[MAXN];
  
          public int Ckn(int n, int k){
              if(k<0 || n<0) return 0;
              if(n<k) return 0;
              return mul(mul(fact[n],inv[k]),inv[n-k]);
          }
  
          public int inverse(int a){
              return power(a,MOD-2);
          }
  
          public void preprocess() {
              fact[0]=1;
              for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
              inv[MAXN-1]= inverse(fact[MAXN-1]);
              for(int i=MAXN-2;i>=0;i--){
                  inv[i]= mul(inv[i+1],i+1);
              }
          }
  
          /**
           * return VALUE of lower bound for unsorted array
           */
          public int lowerBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.lower(x);
          }
          /**
           * return VALUE of upper bound for unsorted array
           */
          public int upperBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.higher(x);
          }
  
          public void debugArr(int[] arr){
              for(int i: arr) out.print(i+" ");
              out.println();
          }
  
          public int rand(){
              int min=0, max= MAXN;
              int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
              return random_int;
          }
          
          public void suffleSort(int[] arr){
              shuffleArray(arr);
              Arrays.sort(arr);
          }
  
  
          public void shuffleArray(int[] ar)
          {
              // If running on Java 6 or older, use `new Random()` on RHS here
              Random rnd = ThreadLocalRandom.current();
              for (int i = ar.length - 1; i > 0; i--)
              {
              int index = rnd.nextInt(i + 1);
              // Simple swap
              int a = ar[index];
              ar[index] = ar[i];
              ar[i] = a;
              }
          }
          
          InputReader in; PrintWriter out;
          CustomFileReader cin;
          int[] xor= new int[3*100000+5];
          int[] pow2= new int[1000000+1];
          public void solve(InputReader in, PrintWriter out) {
              this.in=in; this.out=out;
              // sieve();
              // pow2[0]=1;
              // for(int i=1;i<pow2.length;i++){
              //     pow2[i]= mul(pow2[i-1],2);
              // }
              int t= 1;
              preprocess();
              // int t=in.nextInt();
              // int t= cin.nextIntArrLine()[0];
              for(int i=1;i<=t;i++) solveB(i);
          }
      
          final double pi= Math.acos(-1);
          static Point base;
  
          int[] par;
          int[] size;
  
          PriorityQueue<Pair> q= new PriorityQueue<>((a,b)->b.x-a.x);
  
          private int find(int u){
              if(par[u]==u) return u;
              par[u]= find(par[u]);
              return par[u];
          }
  
          private boolean union(int u, int v){
              u= find(u); v= find(v);
              if(u==v) return false;
              if(size[u]>size[v]){
                  int temp= u; u=v; v= temp;
              }
              par[u]=v;
              size[v]+= size[u];
              return true;
          }
          private boolean already(int u, int v){
              return find(u)==find(v);
          }
  
          public void solveB(int t){
              int n= in.nextInt();
              int wb=0, bw=0, _b=0, b_=0, _w=0, w_=0, __=0, bb=0, ww=0;
              for(int i=0;i<n;i++){
                  String temp= in.nextToken();
                  if(temp.equals("BB")) bb++;
                  if(temp.equals("BW")) bw++;
                  if(temp.equals("WB")) wb++;
                  if(temp.equals("WW")) ww++;
                  if(temp.equals("B?")) b_++;
                  if(temp.equals("?B")) _b++;
                  if(temp.equals("W?")) w_++;
                  if(temp.equals("?W")) _w++;
                  if(temp.equals("??")) __++;
              }
              int b= 2*bb+bw+wb+b_+_b, w= 2*ww+bw+wb+w_+_w, x= 2*__+b_+_b+_w+w_;
              if(b>n) {
                  out.println(0);
                  return;
              }
              int res= Ckn(x,Math.max(n-b,0)), ans=0;
              int WB= wb+w_+_b, BW= bw+b_+_w;
              if(WB!=0 && BW!=0) {
                  if(__!=0)ans= power(2,__);
              }
              else if((WB==0 && BW!=0) || (WB!=0 && BW==0)) {
                  if(__!=0) ans= add(power(2,__),-1);
              }
              else {
                  if(__!=0) ans= add(power(2,__),-2);
              }
              if(bb==0 && ww==0)res= add(res,-ans);
              out.println(res);
          }
          
          public void solveA(int t){
              int n= in.nextInt();
              char[][] a= new char[n][2];
              for(int i=0;i<n;i++){
                  String temp= in.nextToken();
                  a[i][0]= temp.charAt(0); a[i][1]= temp.charAt(1);
              }
              int res=0;
              String temp= ""+a[0][0]+a[0][1];
              
              if(temp.equals("WW") || temp.equals("?W") || temp.equals("W?") || temp.equals("??")) res= add(res, calc("WW",a));
              if(temp.equals("WB") || temp.equals("W?") || temp.equals("?B") || temp.equals("??")) res= add(res, calc("WB", a));
              if(temp.equals("BB") || temp.equals("?B") || temp.equals("B?") || temp.equals("??")) res= add(res, calc("BB", a));
              if(temp.equals("BW") || temp.equals("?W") || temp.equals("B?") || temp.equals("??")) res= add(res, calc("BW", a));
              out.println(res);
          }
  
  
          private int calc(String s, char[][] a){
              int n= a.length;
              int[][] dp= new int[n][4];
              //0: ww , 1: wb ,2: bb, 3: bw
              if(s.equals("WW")) dp[0][0]=1;
              else if(s.equals("WB")) dp[0][1]=1;
              else if(s.equals("BB")) dp[0][2]=1;
              else if(s.equals("Bw")) dp[0][3]=1;
  
              for(int i=1;i<n-1;i++){
                  String temp= ""+a[i][0]+a[i][1];
                  out.println(temp);
                  if(temp.equals("WW") || temp.equals("?W") || temp.equals("W?") || temp.equals("??"))dp[i][0] = add(dp[i-1][1],dp[i-1][2]);
                  if(temp.equals("WB") || temp.equals("W?") || temp.equals("?B") || temp.equals("??"))dp[i][1] = add(dp[i-1][1],dp[i-1][2]);
                  if(temp.equals("BB") || temp.equals("?B") || temp.equals("B?") || temp.equals("??"))dp[i][2] = add(dp[i-1][0],dp[i-1][3]);
                  if(temp.equals("BW") || temp.equals("?W") || temp.equals("B?") || temp.equals("??"))dp[i][3] = add(dp[i-1][0],dp[i-1][3]);
              }
  
              if(n==1) return add(dp[0][0],add(dp[0][1],add(dp[0][2],dp[0][3])));
  
              String temp= ""+a[n-1][0]+a[n-1][1];
  
              if(s.charAt(0)=='B'){
                  if(temp.equals("WW") || temp.equals("?W") || temp.equals("W?") || temp.equals("??"))dp[n-1][0] = add(dp[n-2][1],dp[n-2][2]);
                  if(temp.equals("BW") || temp.equals("?W") || temp.equals("B?") || temp.equals("??"))dp[n-1][3] = add(dp[n-2][0],dp[n-2][3]);
              }
              else {
                  if(temp.equals("WB") || temp.equals("W?") || temp.equals("?B") || temp.equals("??"))dp[n-1][1] = add(dp[n-2][1],dp[n-2][2]);
                  if(temp.equals("BB") || temp.equals("?B") || temp.equals("B?") || temp.equals("??"))dp[n-1][2] = add(dp[n-2][0],dp[n-2][3]);
              }
              for(int i=0;i<n;i++){
                  for(int j=0;j<4;j++) out.print(dp[i][j]+" ");
                  out.println();
              }
              return add(dp[n-1][0],add(dp[n-1][1],add(dp[n-1][2],dp[n-1][3])));
  
          }
  
          static class Node implements Comparable<Node>{
              char op;
              int s;
              public Node (char op, int s) {
                  this.op= op;
                  this.s= s;
              }
              @Override
              public int compareTo(Node o) {
                  if (this.s==o.s) return (int)(this.op-o.op);
                  return this.s-o.s;
              }
  
          }
  
          private long distance(Point p1, Point p2) {
              long x= p1.x-p2.x, y= p1.y-p2.y;
              return x*x+y*y;
          }
  
  
          private boolean eqPoint(Point p1, Point p2){
              return p1.x==p2.x && p1.y==p2.y;
          }
  
          private double polarAngle(Point p1, Point p2) {
              // p1 -> p2
              if (p1.x==p2.x) return pi/2;
              else if (p1.y==p2.y){
                  if(p1.x<p2.x) return 0;
                  else return pi;
              }
              else {
                  double y= (double)p2.y-(double)p1.y;
                  double x= (double)p2.x-(double)p1.x;
                  BigDecimal alpha1= new BigDecimal(y);
                  BigDecimal alpha2= new BigDecimal(x);
                  BigDecimal val= alpha1.divide(alpha2);
  
                  double angle= Math.atan(val.doubleValue());
                  if (angle<0) angle+= pi;
                  out.println("angle: "+angle);
                  return angle;
              }
          }
  
          private boolean isRightTurn(Point p1, Point p2, Point p3){
              Vector v1= new Vector(p1,p2), v2= new Vector(p1,p3);
              if(crossProd(v1,v2)<0) return true;
              else return false;
          }
  
          private long crossProd(Vector v1, Vector v2){
              //x1*y2-x2*y1
              return v1.x*v2.y - v2.x*v1.y;
          }
  
          static class PointAngle implements Comparable<PointAngle>{
              Point p;
              double angle;
              long dis;
              public PointAngle(Point p, double angle, long dis) {
                  this.p= p;
                  this.angle= angle;
                  this.dis= dis;
  
              }
  
              @Override
              public int compareTo(PointAngle o) {
                  double dif= this.angle-o.angle;
                  if (dif <0) return -1;
                  else if(dif >0) return 1;
                  else {
                      long dif2r= this.dis-o.dis;
                      long dif2l= o.dis-this.dis;
  
                      if (base.x < this.p.x) return intDif(dif2r);
                      else return intDif(dif2l); 
                      
                  }
              }
  
              private int intDif(long a){
                  if (a>0) return 1;
                  else if(a<0) return -1;
                  else return 0;
              }
          }
  
  
      
          
          public long _gcd(long a,  long b)
          {
  
              if(b == 0) {
                  return a;
              }
              else {
                  return _gcd(b, a % b);
              }
          }
          public long _lcm(long a, long b){
              return (a*b)/_gcd(a,b);
          }
  
      }
  
  
      // static class SEG {
  
      //     Pair[] segtree;
          
      //     public SEG(int n){
              
      //         segtree= new Pair[4*n];
      //         Arrays.fill(segtree, new Pair(-1,Long.MAX_VALUE));
      //     }
      //     // void buildTree(int l, int r, int index) {
      //     //     if (l == r) {
      //     //         segtree[index].y = a[l];
      //     //         return;
      //     //     }
      //     //     int mid = (l + r) / 2;
      //     //     buildTree(l, mid, 2 * index + 1);
      //     //     buildTree(mid + 1, r, 2 * index + 2);
      //     //     segtree[index].y = Math.min(segtree[2 * index + 1].y, segtree[2 * index + 2].y);
      //     // }
          
      //     void update(int l, int r, int index, int pos, Pair val) {
      //         if (l == r) {
      //             segtree[index] = val;
      //             return;
      //         }
      //         int mid = (l + r) / 2;
      //         if (pos <= mid) update(l, mid, 2 * index + 1, pos, val);
      //         else update(mid + 1, r, 2 * index + 2, pos, val);
      //         if(segtree[2 * index + 1].y < segtree[2 * index + 2].y){
      //             segtree[index]= segtree[2 * index + 1];
      //         }
      //         else {
      //             segtree[index]= segtree[2 * index + 2];
      //         }
      //     }
          
      //     // Pair query(int l, int r, int from, int to, int index) {
      //     //     if (from <= l && r <= to)
      //     //         return segtree[index];
      //     //     if (r < from | to < l)
      //     //         return 0;
      //     //     int mid = (l + r) / 2;
      //     //     Pair left= query(l, mid, from, to, 2 * index + 1);
      //     //     Pair right= query(mid + 1, r, from, to, 2 * index + 2);
      //     //     if(left.y < right.y) return left;
      //     //     else return right;
              
      //     // }
          
          
      // }
  
      static class Venice{
          public Map<Long,Long> m= new HashMap<>();
          public long base=0;
          public long totalValue=0;
          private int M= 1000000007;
  
          private long addMod(long a, long b){
              a+=b;
              if(a>=M) a-=M;
              return a;
          }
  
          public void reset(){
              m= new HashMap<>();
              base=0;
              totalValue=0;
          }
          public void update(long add){
              base= base+ add;
          }
          public void add(long key, long val){
              long newKey= key-base;
              m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
          }
      }
  
  
  
      static class Tuple implements Comparable<Tuple>{
          int x, y, z;
          public Tuple(int x, int y, int z){
              this.x= x;
              this.y= y;
              this.z=z;
          }
          @Override
          public int compareTo(Tuple o){
              return this.z-o.z;
          }
      }
  
      static class Point implements Comparable<Point>{
          public long x;
          public long y;
          public Point(long x, long y){
              this.x= x;
              this.y= y;
          }
  
          @Override
          public int compareTo(Point o) {
              if(this.y!=o.y) return (int)(this.y-o.y);
              return (int)(this.x-o.x);
          }
      }
  
      static class Vector {
          public long x;
          public long y;
  
          // p1 -> p2
          public Vector(Point p1, Point p2){
              this.x= p2.x-p1.x;
              this.y= p2.y-p1.y;
          }
      }
  
      static class Pair implements Comparable<Pair>{
          public int x;
          public int y;
          public Pair(int x, int y){
              this.x= x;
              this.y= y;
          }
  
          @Override
          public int compareTo(Pair o) {
              if(this.x!=o.x) return this.x-o.x;
              return (int)(this.y-o.y);
          }
      }
  
      // public static class compareL implements Comparator<Tuple>{
      //     @Override
      //     public int compare(Tuple t1, Tuple t2) {
      //         return t2.l - t1.l;
      //     }
      // }
  
      // fast input reader class;
      static class InputReader {
          BufferedReader br;
          StringTokenizer st;
  
          public InputReader(InputStream stream) {
              br = new BufferedReader(new InputStreamReader(stream));
          }
  
          public String nextToken() {
              while (st == null || !st.hasMoreTokens()) {
                  String line = null;
                  try {
                      line = br.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
                  if (line == null) {
                      return null;
                  }
                  st = new StringTokenizer(line);
              }
              return st.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(nextToken());
          }
          public double nextDouble(){
              return Double.parseDouble(nextToken());
          }
          public long nextLong(){
              return Long.parseLong(nextToken());
          }
          public int[] nextIntArr(int n){
              int[] arr= new int[n];
              for(int i=0;i<n;i++) arr[i]= nextInt();
              return arr;
          }
          public long[] nextLongArr(int n){
              long[] arr= new long[n];
              for(int i=0;i<n;i++) arr[i]= nextLong();
              return arr;
          }
          public List<Integer> nextIntList(int n){
              List<Integer> arr= new ArrayList<>();
              for(int i=0;i<n;i++) arr.add(nextInt());
              return arr;
          }
          public int[][] nextIntMatArr(int n, int m){
              int[][] mat= new int[n][m];
              for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
              return mat;
          }
          public List<List<Integer>> nextIntMatList(int n, int m){
              List<List<Integer>> mat= new ArrayList<>();
              for(int i=0;i<n;i++){
                  List<Integer> temp= new ArrayList<>();
                  for(int j=0;j<m;j++) temp.add(nextInt());
                  mat.add(temp);
              }
              return mat;
          }
          public char[] nextStringCharArr(){
              return nextToken().toCharArray();
          }
      }
  
      static class CustomFileReader{
          String path="";
          Scanner sc;
          public CustomFileReader(String path){
              this.path=path;
              try{
                  sc= new Scanner(new File(path));
              }
              catch(Exception e){}
          }
          public String nextLine(){
              return sc.nextLine();
          }
          public int[] nextIntArrLine(){
              String line= sc.nextLine();
              String[] part= line.split("[\\s+]");
              int[] res= new int[part.length];
              for(int i=0;i<res.length;i++) res[i]= Integer.parseInt(part[i]);
              return res;
          }
      }
  }