There are 2N squares arranged from left to right. You are given a string of length 2N representing the color of each of the squares.

The color of the i-th square from the left is black if the i-th character of S is `B`, and white if that character is `W`.

You will perform the following operation exactly N times: choose two distinct squares, then invert the colors of these squares and the squares between them. Here, to invert the color of a square is to make it white if it is black, and vice versa.

Throughout this process, you cannot choose the same square twice or more. That is, each square has to be chosen exactly once.

Find the number of ways to make all the squares white at the end of the process, modulo 10^9+7.

Two ways to make the squares white are considered different if and only if there exists i (1 \leq i \leq N) such that the pair of the squares chosen in the i-th operation is different.

Constraints

* 1 \leq N \leq 10^5
* |S| = 2N
* Each character of S is `B` or `W`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the number of ways to make all the squares white at the end of the process, modulo 10^9+7. If there are no such ways, print 0.

Examples

Input

2
BWWB


Output

4


Input

4
BWBBWWWB


Output

288


Input

5
WWWWWWWWWW


Output

0
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/B2";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        int n = in.nextInt();
        String s = in.next();
        ModLib mod = new ModLib(1000000007);

        int cur = 0;
        long res = 1;
        for (int i = 0; i < s.length(); i++) {
            if ((cur % 2 == 0 && s.charAt(i) == 'B') || (cur % 2 == 1 && s.charAt(i) == 'W')) {
                cur++;
            } else {
                if (cur == 0) {
                    System.out.println("0");
                    return;
                }
                res = mod.mult(res, cur);
                cur--;
            }
        }
        long fact = 1;
        for (int i = 0; i < n; i++) {
            fact = mod.mult(i + 1, fact);
        }
        if (cur == 0) {
            System.out.println(mod.mult(fact, res));
        } else {
            System.out.println(0);
        }
    }

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                // TODO 自動生成された catch ブロック
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }
}


class FastScanner {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
        // stream = new FileInputStream(new File("dec.in"));
    }

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

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

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = nextInt();

        return array;
    }

    public int[][] nextIntMap(int n, int m) {
        int[][] map = new int[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextIntArray(m);
        }
        return map;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nextLong();

        return array;
    }

    public long[][] nextLongMap(int n, int m) {
        long[][] map = new long[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextLongArray(m);
        }
        return map;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) {
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nextDouble();

        return array;
    }

    public double[][] nextDoubleMap(int n, int m) {
        double[][] map = new double[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextDoubleArray(m);
        }
        return map;
    }

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

    public String[] nextStringArray(int n) {
        String[] array = new String[n];
        for (int i = 0; i < n; i++)
            array[i] = next();

        return array;
    }

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

    public int[][] nextPackedIntArrays(int packN, int size) {
        int[][] res = new int[packN][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < packN; j++) {
                res[j][i] = nextInt();
            }
        }
        return res;
    }
}

class ModLib {
    final long mod;

    public ModLib(long mod) {
        this.mod = mod;
    }

    public long add(long a, long b) {
        return (a + b) % mod;
    }

    public long sub(long a, long b) {
        return (a - b + mod) % mod;
    }

    public long mult(long a, long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    public long pow(long a, long x) {
        long res = 1;
        for ( ; x > 0; x >>= 1) {
            if (x % 2 == 1) res = mult(res, a);
            a = mult(a, a);
        }

        return res;
    }

    public long div(long a, long b) {
        return mult(a, pow(b, mod - 2));
    }
}
