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.
					/*
					TO LEARN
					1-segment trees
					2-euler tour
				
					*/
					/*
					TO SOLVE 
					uva 1103
					codeforces 722 kavi on pairing duty
					*/
					/*
					bit manipulation shit
					1-Computer Systems: A Programmer's Perspective
					2-hacker's delight
					3-(02-03-bits-ints)
					4-machine-basics
					5-Bits Manipulation tutorialspoint
					*/
					/*
					TO WATCH
					1-what is bitmasking by kartik arora youtube
					*/
					            import java.util.*;
							    import java.math.*;
							    import java.io.*; 
							    import java.util.stream.Collectors;

							       public class A{
					            static FastScanner scan=new FastScanner();
							     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
				
				static int n,m,k;
				
				static int mod=998244353;
				static long add(long x,long toadd)
				{
					x=x+toadd;
					if(x>=mod)
						x-=mod;
					return x;
				}
				static long fact[];
				static long invfact[];
				  public static long gcdExtended(long a, long b, long arr[])
    {
       
        if (a == 0)
        {
            arr[0] = 0;
            arr[1] = 1;
            return b;
        }
 
        long newarr[]={1,1};
        long gcd = gcdExtended(b%a, a, newarr);
 
       
        arr[0] = newarr[1] - (b/a) * newarr[0];
        arr[1] = newarr[0];
 
        return gcd;
    }
    static long inv(long a,long mod)
    {
    	long arr[]={1,1};
    	gcdExtended(a,mod,arr);
    	return arr[0];
    }
    static void preprosses()
    {
    	fact=new long[(int)1e5+5];
    	invfact=new long[(int)1e5+5];
    	fact[0]=1;
    	invfact[0]=1;
    	for(int i=1;i<(int)1e5+5;i++)
    	{
    		fact[i]=(i*fact[i-1])%mod;
    		invfact[i]=((((inv((long)i,mod)%mod)*invfact[i-1])%mod+mod)%mod);
    		//System.out.println(("INV "+inv(i,mod)));
    	}

    }
    static long ncr(int a,int b)
    {
    	//System.out.println(invfact[a]);
    	return (((fact[a]*invfact[a-b])%mod)*invfact[b])%mod;
    }
			
				public static void main(String[] args)  throws Exception 
					      {
					 

								///scan=new FastScanner("cownomics.in");
							//out = new PrintWriter("cownomics.out");
							 
							 							 /*
							 READING 
						
							 3-Introduction to DP with Bitmasking codefoces
							 4-Bit Manipulation hackerearth
							 5-read more about mobious and inculsion-exclusion 
							 */
		

							    int tt=1;	  
				tt=scan.nextInt();
						    // 0 1 2 3 4 
							    preprosses();
							
						 outer:while(tt-->0)
							    {
							    	int n=scan.nextInt();
							    	String s=scan.next();
							    	int O=0,o=0;
							    	for(int i=0;i<n;i++)
							    	{
							    		if(s.charAt(i)=='1'&&i<n-1&&s.charAt(i+1)=='1')
							    		{
							    			O++;
							    			i++;
							    		}
							    		else if(s.charAt(i)=='0')
							    		{
							    			o++;
							    		}
							    	}
							    //	out.println(o+" "+O);
							    	out.println(ncr(O+o,O));

						

							    	}

							

	out.close();
				}
	    
							static class special{
								boolean bool;
								long n;
								//int id;
								special(boolean bool,long n)
								{
									this.bool=bool;
									this.n=n;
								}
								@Override
								    public int hashCode() {
							                int hash = 7;
				    hash = 31 * hash + (int) n;
				   
				    return hash;
							            }
							              @Override
							            public boolean equals(Object o){
							                if (o == this) return true;
							                if (o.getClass() != getClass()) return false;
							                special t = (special)o;
							                return t.bool == bool && t.n == n;
							            }
							}

							   
							     static long binexp(long a,long n)
							    {
							        if(n==0)
							            return 1;
							        long res=binexp(a,n/2);
							        if(n%2==1)
							            return res*res*a;
							        else 
							            return res*res;
							    }
							     
							    static long powMod(long base, long exp, long mod) {
							           if (base == 0 || base == 1) return base;
							           if (exp == 0) return 1;
							           if (exp == 1) return (base % mod+mod)%mod;
							           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
							           R *= R;
							           R %= mod;
							           if ((exp & 1) == 1) {
							               return (base * R % mod+mod)%mod;
							           }
							           else return (R %mod+mod)%mod;
							       }
							    static double dis(double x1,double y1,double x2,double y2)
							    {
							        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
							    }
							    static long mod(long x,long y)
							        {
							            if(x<0)
							                x=x+(-x/y+1)*y;
							            return x%y;
							        }
							     public static  long pow(long b, long e) {
							                long r = 1;
							                while (e > 0) {
							                    if (e % 2 == 1) r = r * b ;
							                    b = b * b;
							                    e >>= 1;
							                }
							                return r;
							            }
							    private static void sort(long[] arr) {
							            List<Long> list = new ArrayList<>();
							            for (long object : arr) list.add(object);
							            Collections.sort(list);
							        //Collections.reverse(list);
							            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
							        }
							    private static void sort2(long[] arr) {
							            List<Long> list = new ArrayList<>();
							            for (Long object : arr) list.add(object);
							            Collections.sort(list);
							        Collections.reverse(list);
							            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
							        }
							     static class FastScanner
					{
					    private int BS = 1 << 16;
					    private char NC = (char) 0;
					    private byte[] buf = new byte[BS];
					    private int bId = 0, size = 0;
					    private char c = NC;
					    private double cnt = 1;
					    private BufferedInputStream in;
					 
					    public FastScanner() {
					        in = new BufferedInputStream(System.in, BS);
					    }
					 
					    public FastScanner(String s) {
					        try {
					            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
					        } catch (Exception e) {
					            in = new BufferedInputStream(System.in, BS);
					        }
					    }
					 
					    private char getChar() {
					        while (bId == size) {
					            try {
					                size = in.read(buf);
					            } catch (Exception e) {
					                return NC;
					            }
					            if (size == -1) return NC;
					            bId = 0;
					        }
					        return (char) buf[bId++];
					    }
					 
					    public int nextInt() {
					        return (int) nextLong();
					    }
					 
					    public int[] nextInts(int N) {
					        int[] res = new int[N];
					        for (int i = 0; i < N; i++) {
					            res[i] = (int) nextLong();
					        }
					        return res;
					    }
					 
					    public long[] nextLongs(int N) {
					        long[] res = new long[N];
					        for (int i = 0; i < N; i++) {
					            res[i] = nextLong();
					        }
					        return res;
					    }
					 
					    public long nextLong() {
					        cnt = 1;
					        boolean neg = false;
					        if (c == NC) c = getChar();
					        for (; (c < '0' || c > '9'); c = getChar()) {
					            if (c == '-') neg = true;
					        }
					        long res = 0;
					        for (; c >= '0' && c <= '9'; c = getChar()) {
					            res = (res << 3) + (res << 1) + c - '0';
					            cnt *= 10;
					        }
					        return neg ? -res : res;
					    }
					 
					    public double nextDouble() {
					        double cur = nextLong();
					        return c != '.' ? cur : cur + nextLong() / cnt;
					    }
					 
					    public double[] nextDoubles(int N) {
					        double[] res = new double[N];
					        for (int i = 0; i < N; i++) {
					            res[i] = nextDouble();
					        }
					        return res;
					    }
					 
					    public String next() {
					        StringBuilder res = new StringBuilder();
					        while (c <= 32) c = getChar();
					        while (c > 32) {
					            res.append(c);
					            c = getChar();
					        }
					        return res.toString();
					    }
					 
					    public String nextLine() {
					        StringBuilder res = new StringBuilder();
					        while (c <= 32) c = getChar();
					        while (c != '\n') {
					            res.append(c);
					            c = getChar();
					        }
					        return res.toString();
					    }
					 
					    public boolean hasNext() {
					        if (c > 32) return true;
					        while (true) {
					            c = getChar();
					            if (c == NC) return false;
					            else if (c > 32) return true;
					        }
					    }
					}

							     static class Pair implements Comparable<Pair>{
							            public long x, y,z;
							            public Pair(long x1, long y1,long z1) {
							                x=x1;
							                y=y1;
							                z=z1;
							            }
							             public Pair(long x1, long y1) {
							                x=x1;
							                y=y1;
							    
							            }
							            
							            @Override
							            public int hashCode() {
							                return (int)(x + 31 * y);
							            }
							            public String toString() {
							                return x + " " + y+" "+z;
							            }
							            @Override
							            public boolean equals(Object o){
							                if (o == this) return true;
							                if (o.getClass() != getClass()) return false;
							                Pair t = (Pair)o;
							                return t.x == x && t.y == y&&t.z==z;
							            }
							    public int compareTo(Pair o)
							    {
							    	
							   
							    	return (int)(o.x-x);
							     
							        }
							     
							    }
							    
							    }

							     
