Cirno gave AquaMoon a chessboard of size 1 × n. Its cells are numbered with integers from 1 to n from left to right. In the beginning, some of the cells are occupied with at most one pawn, and other cells are unoccupied.

In each operation, AquaMoon can choose a cell i with a pawn, and do either of the following (if possible): 

  * Move pawn from it to the (i+2)-th cell, if i+2 ≤ n and the (i+1)-th cell is occupied and the (i+2)-th cell is unoccupied. 
  * Move pawn from it to the (i-2)-th cell, if i-2 ≥ 1 and the (i-1)-th cell is occupied and the (i-2)-th cell is unoccupied. 



You are given an initial state of the chessboard. AquaMoon wants to count the number of states reachable from the initial state with some sequence of operations. But she is not good at programming. Can you help her? As the answer can be large find it modulo 998 244 353.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the size of the chessboard.

The second line contains a string of n characters, consists of characters "0" and "1". If the i-th character is "1", the i-th cell is initially occupied; otherwise, the i-th cell is initially unoccupied.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, print the number of states that reachable from the initial state with some sequence of operations modulo 998 244 353.

Example

Input


6
4
0110
6
011011
5
01010
20
10001111110110111000
20
00110110100110111101
20
11101111011000100010


Output


3
6
1
1287
1287
715

Note

In the first test case the strings "1100", "0110" and "0011" are reachable from the initial state with some sequence of operations.
import java.io.*;
public class AquaMoonAndChess{
    static class InputReader {
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16; // Change this to increase your input size //
        private static final InputStream DEFAULT_STREAM = System.in;private static final int MAX_DECIMAL_PRECISION = 21;private int c;private byte[] buf;private int bufferSize, bufIndex, numBytesRead;private InputStream stream;private static final byte EOF = -1;private static final byte NEW_LINE = 10;private static final byte CARRIAGE_RETURN = 13;private static final byte SPACE = 32;private static final byte DASH = 45;private static final byte DOT = 46;private char[] charBuffer;private static byte[] bytes = new byte[58];private static int[] ints = new int[58];private static char[] chars = new char[128];static { char ch = ' ';int value = 0;byte _byte = 0;for (int i = 48; i < 58; i++) bytes[i] = _byte++;for (int i = 48; i < 58; i++) ints[i] = value++;for (int i = 32; i < 128; i++) chars[i] = ch++; }private static final double[][] doubles = {{0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d, 0.0000000000d, 0.00000000000d, 0.000000000000d, 0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d, 0.00000000000000000d, 0.000000000000000000d, 0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d}, {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d, 0.0000000001d, 0.00000000001d, 0.000000000001d, 0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d, 0.00000000000000001d, 0.000000000000000001d, 0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d}, {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d, 0.0000000002d, 0.00000000002d, 0.000000000002d, 0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d, 0.00000000000000002d, 0.000000000000000002d, 0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d}, {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d, 0.0000000003d, 0.00000000003d, 0.000000000003d, 0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d, 0.00000000000000003d, 0.000000000000000003d, 0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d}, {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d, 0.0000000004d, 0.00000000004d, 0.000000000004d, 0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d, 0.00000000000000004d, 0.000000000000000004d, 0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d}, {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d, 0.0000000005d, 0.00000000005d, 0.000000000005d, 0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d, 0.00000000000000005d, 0.000000000000000005d, 0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d}, {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d, 0.0000000006d, 0.00000000006d, 0.000000000006d, 0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d, 0.00000000000000006d, 0.000000000000000006d, 0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d}, {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d, 0.0000000007d, 0.00000000007d, 0.000000000007d, 0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d, 0.00000000000000007d, 0.000000000000000007d, 0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d}, {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d, 0.0000000008d, 0.00000000008d, 0.000000000008d, 0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d, 0.00000000000000008d, 0.000000000000000008d, 0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d}, {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d, 0.0000000009d, 0.00000000009d, 0.000000000009d, 0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d, 0.00000000000000009d, 0.000000000000000009d, 0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}};
        public InputReader() { this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE); }
        public InputReader(int bufferSize) { this(DEFAULT_STREAM, bufferSize); }
        public InputReader(InputStream stream) { this(stream, DEFAULT_BUFFER_SIZE); }
        public InputReader(InputStream stream, int bufferSize) { if (stream == null || bufferSize <= 0) throw new IllegalArgumentException();buf = new byte[bufferSize];charBuffer = new char[128];this.bufferSize = bufferSize;this.stream = stream; }
        private byte read() throws IOException { if (numBytesRead == EOF) throw new IOException();if (bufIndex >= numBytesRead) { bufIndex = 0;numBytesRead = stream.read(buf);if (numBytesRead == EOF) return EOF; }return buf[bufIndex++]; }
        private int readJunk(int token) throws IOException { if (numBytesRead == EOF) return EOF;
            do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > token) return 0;bufIndex++; }
                numBytesRead = stream.read(buf);if (numBytesRead == EOF) return EOF;bufIndex = 0; } while (true); }
        public byte nextByte() throws IOException {return (byte) nextInt(); }
        public int nextInt() throws IOException { if (readJunk(DASH - 1) == EOF) throw new IOException();int sgn = 1, res = 0;c = buf[bufIndex];if (c == DASH) { sgn = -1;bufIndex++; } do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { res = (res << 3) + (res << 1);res += ints[buf[bufIndex++]]; } else { bufIndex++;return res * sgn; } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return res * sgn;bufIndex = 0; } while (true); }
        public long nextLong() throws IOException { if (readJunk(DASH - 1) == EOF) throw new IOException();int sgn = 1;long res = 0L;c = buf[bufIndex];if (c == DASH) { sgn = -1;bufIndex++; } do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { res = (res << 3) + (res << 1);res += ints[buf[bufIndex++]]; } else { bufIndex++;return res * sgn; } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return res * sgn;bufIndex = 0; } while (true); }
        private void doubleCharBufferSize() { char[] newBuffer = new char[charBuffer.length << 1];for (int i = 0; i < charBuffer.length; i++) newBuffer[i] = charBuffer[i];charBuffer = newBuffer; }
        public String nextLine() throws IOException { try { c = read(); } catch (IOException e) { return null; }if (c == NEW_LINE) return "";if (c == EOF) return null;int i = 0;charBuffer[i++] = (char) c;do { while (bufIndex < numBytesRead) { if (buf[bufIndex] != NEW_LINE && buf[bufIndex] != CARRIAGE_RETURN) { if (i == charBuffer.length) doubleCharBufferSize();charBuffer[i++] = (char) buf[bufIndex++]; } else { if(buf[bufIndex] == CARRIAGE_RETURN) bufIndex++;bufIndex++;return new String(charBuffer, 0, i); } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return new String(charBuffer, 0, i);bufIndex = 0; } while (true); }
        public String nextString() throws IOException { if (numBytesRead == EOF) return null;if (readJunk(SPACE) == EOF) return null;for (int i = 0; ; ) { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { if (i == charBuffer.length) doubleCharBufferSize();charBuffer[i++] = (char) buf[bufIndex++]; } else {bufIndex++;return new String(charBuffer, 0, i); } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return new String(charBuffer, 0, i);bufIndex = 0; } }
        public double nextDoubleFast() throws IOException {c = read();int sgn = 1;while (c <= SPACE) c = read();if (c == DASH) { sgn = -1;c = read(); }double res = 0.0;while (c > DOT) { res *= 10.0;res += ints[c];c = read(); }if (c == DOT) { int i = 0;c = read();while (c > SPACE && i < MAX_DECIMAL_PRECISION) { res += doubles[ints[c]][i++];c = read(); } }return res * sgn; }
        public void close() throws IOException {stream.close(); }
    }

    // region variables
    static InputReader sc = new InputReader();
    static OutputStream outputStream = System.out;
    static PrintWriter w = new PrintWriter(outputStream);
    static final long mod = 998244353L;
    // endregion

    private static void initiateIO()
            throws IOException {if (System.getProperty("ONLINE_JUDGE") == null) { try { w = new PrintWriter("output.txt");sc = new InputReader(new FileInputStream("input.txt")); } catch (Exception e) { throw new IOException(); }} }

    public static void main(String[] args)
            throws IOException {

        initiateIO();

        int t = sc.nextInt();
        while(t-- > 0) {
            solve();
        }

        w.close();

    }

    // region pow(a, b, mod) -> a^b
    static long fast_pow_mod (long b, long x, long mod) {
        if (x == 0) return 1;
        if (x == 1) return b;
        if (x % 2 == 0) return fast_pow_mod (b * b % mod, x / 2, mod) % mod;

        return b * fast_pow_mod (b * b % mod, x / 2, mod) % mod;
    }
    // endregion

    static long ncr(long n, long r) {
        // numerator calculation
        long num = 1;
        for(long i = n; i > r; i--) {
            num *= i;
            num %= mod;
        }

        // denominator calculation
        long den = 1;
        for(long i = n-r; i > 0; i--) {
            den *= i;
            den %= mod;
        }

        return ((num % mod) * (fast_pow_mod(den % mod, mod-2L, mod) % mod))%mod;
    }

    static void solve() throws IOException {
        int len = sc.nextInt();
        String str = sc.nextString();
        int m = 0;
        int n = 0;
        // answer is ncr where n = number of pairs of one + number of zeroes and
        // r = number of zeroes
        for(int i = 0; i < len-1; i++) {
            if(str.charAt(i) == '1' && str.charAt(i+1) == '1') {
                m++;
                i++;
            }
        }

        for(int i = 0; i < len; i++) {
            if(str.charAt(i) == '0') n++;
        }
        w.println(ncr(m+n, n));
    }
}