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 static java.lang.Math.*;
  import static java.util.Arrays.*;
   
  public class cf1608d_2 {
   
      public static void main(String[] args) throws IOException {
          int n = ri(), cntw = 0, cntb = 0, invalid = 1, cntqq = 0, allbw = 1, allwb = 1;
          int fact[] = new int[2 * n + 1];
          fact[0] = fact[1] = 1;
          for (int i = 2; i <= 2 * n; ++i) {
              fact[i] = mmul(i, fact[i - 1]);
          }
          for (int i = 0; i < n; ++i) {
              char d[] = rcha();
              if (d[0] == 'B') {
                  ++cntb;
                  allwb = 0;
              }
              if (d[0] == 'W') {
                  ++cntw;
                  allbw = 0;
              }
              if (d[1] == 'B') {
                  ++cntb;
                  allbw = 0;
              }
              if (d[1] == 'W') {
                  ++cntw;
                  allwb = 0;
              }
              if (d[0] == '?' && d[1] == '?') {
                  ++cntqq;
              } else if (d[0] == d[1]) {
                  invalid = 0;
              }
          }
          if (cntw > n || cntb > n) {
              prln(0);
          } else {
              prln(msub(mmul(fact[2 * n - cntw - cntb], minv(fact[n - cntw]), minv(fact[n - cntb])), invalid * msub(mpow(2, cntqq), madd(allbw, allwb))));
          }
          close();
      }
   
      static int mmod = 998244353;
   
      static int madd(int a, int b) {
          return (a + b) % mmod;
      }
   
      static int madd(int... a) {
          int ans = a[0];
          for (int i = 1; i < a.length; ++i) {
              ans = madd(ans, a[i]);
          }
          return ans;
      }
   
      static int msub(int a, int b) {
          return (a - b + mmod) % mmod;
      }
   
      static int mmul(int a, int b) {
          return (int) ((long) a * b % mmod);
      }
   
      static int mmul(int... a) {
          int ans = a[0];
          for (int i = 1; i < a.length; ++i) {
              ans = mmul(ans, a[i]);
          }
          return ans;
      }
   
      static int minv(int x) {
          // return mpow(x, mmod - 2);
          return (exgcd(x, mmod)[0] % mmod + mmod) % mmod;
      }
   
      static int mpow(int a, long b) {
          if (a == 0) {
              return 0;
          }
          int ans = 1;
          while (b > 0) {
              if ((b & 1) > 0) {
                  ans = mmul(ans, a);
              }
              a = mmul(a, a);
              b >>= 1;
          }
          return ans;
      }
   
      static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
      static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
      static StringTokenizer input;
      static Random __r = new Random();
   
      // references
      // IBIG = 1e9 + 7
      // IMAX ~= 2e9
      // LMAX ~= 9e18
   
      // constants
      static final int IBIG = 1000000007;
      static final int IMAX = 2147483647;
      static final long LMAX = 9223372036854775807L;
      // math util
      static int minof(int a, int b, int c) {return min(a, min(b, c));}
      static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static long minof(long a, long b, long c) {return min(a, min(b, c));}
      static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static int maxof(int a, int b, int c) {return max(a, max(b, c));}
      static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static long maxof(long a, long b, long c) {return max(a, max(b, c));}
      static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static int fli(double d) {return (int) d;}
      static int cei(double d) {return (int) ceil(d);}
      static long fll(double d) {return (long) d;}
      static long cel(double d) {return (long) ceil(d);}
      static int gcd(int a, int b) {return b == 0 ? a : gcd(b, a % b);}
      static long gcd(long a, long b) {return b == 0 ? a : gcd(b, a % b);}
      static int[] exgcd(int a, int b) {if (b == 0) return new int[] {1, 0}; int[] y = exgcd(b, a % b); return new int[] {y[1], y[0] - y[1] * (a / b)};}
      static long[] exgcd(long a, long b) {if (b == 0) return new long[] {1, 0}; long[] y = exgcd(b, a % b); return new long[] {y[1], y[0] - y[1] * (a / b)};}
      static int randInt(int min, int max) {return __r.nextInt(max - min + 1) + min;}
      static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
      // array util
      static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void rsort(int[] a) {shuffle(a); sort(a);}
      static void rsort(long[] a) {shuffle(a); sort(a);}
      static void rsort(double[] a) {shuffle(a); sort(a);}
      static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      // input
      static void r() throws IOException {input = new StringTokenizer(rline());}
      static int ri() throws IOException {return Integer.parseInt(rline());}
      static long rl() throws IOException {return Long.parseLong(rline());}
      static double rd() throws IOException {return Double.parseDouble(rline());}
      static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
      static void ria(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni();}
      static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
      static void riam1(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1;}
      static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
      static void rla(long[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nl();}
      static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
      static void rda(double[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nd();}
      static char[] rcha() throws IOException {return rline().toCharArray();}
      static void rcha(char[] a) throws IOException {int n = a.length, i = 0; for (char c : rline().toCharArray()) a[i++] = c;}
      static String rline() throws IOException {return __i.readLine();}
      static String n() {return input.nextToken();}
      static int rni() throws IOException {r(); return ni();}
      static int ni() {return Integer.parseInt(n());}
      static long rnl() throws IOException {r(); return nl();}
      static long nl() {return Long.parseLong(n());}
      static double rnd() throws IOException {r(); return nd();}
      static double nd() {return Double.parseDouble(n());}
      // output
      static void pr(int i) {__o.print(i);}
      static void prln(int i) {__o.println(i);}
      static void pr(long l) {__o.print(l);}
      static void prln(long l) {__o.println(l);}
      static void pr(double d) {__o.print(d);}
      static void prln(double d) {__o.println(d);}
      static void pr(char c) {__o.print(c);}
      static void prln(char c) {__o.println(c);}
      static void pr(char[] s) {__o.print(new String(s));}
      static void prln(char[] s) {__o.println(new String(s));}
      static void pr(String s) {__o.print(s);}
      static void prln(String s) {__o.println(s);}
      static void pr(Object o) {__o.print(o);}
      static void prln(Object o) {__o.println(o);}
      static void prln() {__o.println();}
      static void pryes() {prln("yes");}
      static void pry() {prln("Yes");}
      static void prY() {prln("YES");}
      static void prno() {prln("no");}
      static void prn() {prln("No");}
      static void prN() {prln("NO");}
      static boolean pryesno(boolean b) {prln(b ? "yes" : "no"); return b;};
      static boolean pryn(boolean b) {prln(b ? "Yes" : "No"); return b;}
      static boolean prYN(boolean b) {prln(b ? "YES" : "NO"); return b;}
      static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
      static void h() {prln("hlfd"); flush();}
      static void flush() {__o.flush();}
      static void close() {__o.close();}
  }