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.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;

public class four {
    static StringBuilder sb;
    static dsu dsu;
    static long fact[];
    static int mod = (int)998244353;

    static void solve() {
        int n=i();
        String str=s();

        int count=0;
        int val=0;
        boolean []vis=new boolean [str.length()];

        for(int i=0;i<n;i++){
            vis[i]=false;
            if(str.charAt(i)=='0')count++;
        }

        for(int i=1;i<n;i++){
            if(str.charAt(i)=='1' && str.charAt(i-1)=='1' && vis[i-1]==false){
                val++;
                vis[i]=true;
            }
        }

        
        sb.append(ncr(count+val, val)+"\n");
    }

    public static void main(String[] args) {
        sb = new StringBuilder();
        fact=new long[(int)1e6+10]; 
        fact[0]=fact[1]=1;
        for(int i=2;i<fact.length;i++){ 
            fact[i]=((long)(i%mod)*(long)(fact[i-1]%mod))%mod; 
        }
        int test = i();
        while (test-- > 0) {
            solve();
        }
        System.out.println(sb);
    }

    /*
     * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
     * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
     */
    // **************NCR%P******************
    static long ncr(int n, int r) {
        if (r > n)
            return (long) 0;

        long res = fact[n] % mod;
        // System.out.println(res);
        res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
        res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
        // System.out.println(res);
        return res;

    }

    static long p(long x, long y)// POWER FXN //
    {
        if (y == 0)
            return 1;

        long res = 1;
        while (y > 0) {
            if (y % 2 == 1) {
                res = (res * x) % mod;
                y--;
            }

            x = (x * x) % mod;
            y = y / 2;

        }
        return res;
    }

    // **************END******************

    // *************Disjoint set
    // union*********//
    static class dsu {
        int parent[];

        dsu(int n) {
            parent = new int[n];
            for (int i = 0; i < n; i++)
                parent[i] = -1;
        }

        int find(int a) {
            if (parent[a] < 0)
                return a;
            else {
                int x = find(parent[a]);
                parent[a] = x;
                return x;
            }
        }

        void merge(int a, int b) {
            a = find(a);
            b = find(b);
            if (a == b)
                return;
            parent[b] = a;
        }
    }

    // **************PRIME FACTORIZE **********************************//
    static TreeMap<Integer, Integer> prime(long n) {
        TreeMap<Integer, Integer> h = new TreeMap<>();
        long num = n;
        for (int i = 2; i <= Math.sqrt(num); i++) {
            if (n % i == 0) {
                int nt = 0;
                while (n % i == 0) {
                    n = n / i;
                    nt++;
                }
                h.put(i, nt);
            }
        }
        if (n != 1)
            h.put((int) n, 1);
        return h;

    }

    // ****CLASS PAIR ************************************************
    static class Pair implements Comparable<Pair> {
        int x;
        long y;

        Pair(int x, long y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair o) {
            return (int) (this.y - o.y);

        }

    }
    // ****CLASS PAIR **************************************************

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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 int Int() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String String() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return String();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }
    }

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);

    public static long[] sort(long[] a2) {
        int n = a2.length;
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a2)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a2[i] = l.get(i);
        return a2;
    }

    public static long pow(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                res = (res * x);// % modulus;
                y--;

            }
            x = (x * x);// % modulus;
            y = y / 2;
        }
        return res;
    }

    // GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }
    // ******LOWEST COMMON MULTIPLE
    // *********************************************

    public static long lcm(long x, long y) {
        return (x * (y / gcd(x, y)));
    }

    // INPUT PATTERN********************************************************
    public static int i() {
        return in.Int();
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static String s() {
        return in.String();
    }

    public static int[] readArray(int n) {
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = i();
        }
        return A;
    }

    public static long[] readArrayL(int n) {
        long A[] = new long[n];
        for (int i = 0; i < n; i++) {
            A[i] = l();
        }
        return A;
    }

}