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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    static String reverse(String s) {
        return (new StringBuilder(s)).reverse().toString();
    }

    static void sieveOfEratosthenes(int n, int factors[], ArrayList<Integer> ar) 
    { 
        factors[1]=1;
        int p;
        for(p = 2; p*p <=n; p++) 
        { 
            if(factors[p] == 0) 
            { 
                ar.add(p);
                factors[p]=p;
                for(int i = p*p; i <= n; i += p) 
                    if(factors[i]==0)
                        factors[i] = p; 
            } 
        } 
        for(;p<=n;p++){
            if(factors[p] == 0) 
            { 
                factors[p] = p;
                ar.add(p);
            } 
        }
    }

    static void sort(int ar[]) {
        int n = ar.length;
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    static int findMax(int a[], int n, int vis[], int i, int d){
        if(i>=n)
            return 0;
        if(vis[i]==1)
            return findMax(a, n, vis, i+1, d);
        int max = 0;
        for(int j=i+1;j<n;j++){
            if(Math.abs(a[i]-a[j])>d||vis[j]==1)
                continue;
            vis[j] = 1;
            max = Math.max(max, 1 + findMax(a, n, vis, i+1, d));
            vis[j] = 0;
        }
        return max;
    }

    static void findSub(ArrayList<ArrayList<Integer>> ar, int n, ArrayList<Integer> a, int i){
        if(i==n){
            ArrayList<Integer> b = new ArrayList<Integer>();
            for(int y:a){
                b.add(y);
            }
            ar.add(b);
            return;
        }
        for(int j=0;j<n;j++){
            if(j==i)
                continue;
            a.set(i,j);
            findSub(ar, n, a, i+1);
        }
    }
    
    static void build(int t1[], int a[], int v, int tl, int tr) {
        if (tl == tr) {
            t1[v] = a[tl];
        } else {
            int tm = (tl + tr) / 2;
            build(t1, a, v*2, tl, tm);
            build(t1, a, v*2+1, tm+1, tr);
            t1[v] = 0;
        }
    }

    static void update(int t1[], int v, int tl, int tr, int x, int new_val) {
        // if (tl > tr) 
        //     return;
        t1[v] = Math.max(new_val,t1[v]);
        if(tl==tr)
            return;
        int tm = (tl + tr) / 2;
        if(x<=tm)
            update(t1, v*2, tl, tm, x, new_val);
        else
            update(t1, v*2+1, tm+1, tr, x, new_val);
    }

    static int get(int t1[], int v, int tl, int tr, int l, int r) {
        if (tl >= l && tr <= r) {
            return t1[v];
        }
        int tm = (tl + tr) / 2;
        int max = 0;
        if(l<=tm)
            max = Math.max(get(t1, v*2, tl, tm, l, r),max);
        if(r>=tm+1)
            max = Math.max(get(t1, v*2+1, tm+1, tr, l, r), max);
        return max;
    }

    public static void solve(InputReader sc, PrintWriter pw){
        int i, j = 0;
        // int t = 1; 
        int t = sc.nextInt();
        long fact[] = new long[200001];
        long mod = 998244353;
        fact[0] = 1;
        for(i=1;i<200001;i++){
            fact[i] = fact[i-1] * i % mod;
        }
        u: while (t-- > 0) {
            int n = sc.nextInt();
            char ch[] = sc.next().toCharArray();
            int pairs = 0, zeros = 0;
            for(i=0;i<n;i++){
                if(ch[i]=='0'){
                    zeros++;
                }
                else if(i<n-1&&ch[i+1]=='1'){
                    pairs++;
                    i++;
                }
            }
            pw.println(fact[pairs+zeros]*modInverse(fact[pairs], mod)%mod*modInverse(fact[zeros], mod)%mod);
        }
    }

    static void findPrimes(int num, HashMap<Integer, Integer> pos, ArrayList<Integer> ar){
        for(int i=2;i*i<=num;i++){
            if(num%i==0){
                while(num%i==0){
                    num/=i;
                }
                if(pos.containsKey(i))
                    continue;
                ar.add(i);
                pos.put(i,ar.size()-1);
            }
        }
        if(num>1){
            if(!pos.containsKey(num)){
                ar.add(num);
                pos.put(num,ar.size()-1);
            }
        }
    }

    static long[][] matrixMult(long a[][], long b[][], long mod){
        int n = a.length;
        int m = a[0].length;
        int p = b[0].length;
        long c[][] = new long[n][p];
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<p;k++){
                    c[i][k] += a[i][j]*b[j][k]%mod;
                    c[i][k] %= mod;
                }
            }
        }
        return c;
    }

    static long[][] exp(long mat[][], long b, long mod){
        if(b==0){
            int n = mat.length;
            long res[][] = new long[n][n];
            for(int i=0;i<n;i++){
                res[i][i] = 1;
            }
            return res;
        }
        long half[][] = exp(mat, b/2, mod);
        long res[][] = matrixMult(half, half, mod);
        if(b%2==1){
            res = matrixMult(res, mat, mod);
        }
        return res;
    }

    static void countPrimeFactors(int num, int a[], HashMap<Integer,Integer> pos){
        for(int i=2;i*i<=num;i++){
            if(num%i==0){
                int y = pos.get(i);
                while(num%i==0){
                    a[y]++;
                    num/=i;
                }
            }
        }
        if(num>1){
            int y = pos.get(num);
            a[y]++;
        }
    }

    static void assignAnc(ArrayList<Integer> ar[], int depth[], int sz[], int par[][] ,int curr, int parent, int d){
        depth[curr] = d;
        sz[curr] = 1;
        par[curr][0] = parent;
        for(int v:ar[curr]){
            if(parent==v)
                continue;
            assignAnc(ar, depth, sz, par, v, curr, d+1);
            sz[curr] += sz[v];
        }
    }

    static int findLCA(int a, int b, int par[][], int depth[]){
        if(depth[a]>depth[b]){
            a = a^b;
            b = a^b;
            a = a^b;
        }
        int diff = depth[b] - depth[a];
        for(int i=19;i>=0;i--){
            if((diff&(1<<i))>0){
                b = par[b][i];
            }
        }
        if(a==b)
            return a;
        for(int i=19;i>=0;i--){
            if(par[b][i]!=par[a][i]){
                b = par[b][i];
                a = par[a][i];
            }
        }
        return par[a][0];
    }

    static void formArrayForBinaryLifting(int n, int par[][]){
        for(int j=1;j<20;j++){
            for(int i=0;i<n;i++){
                if(par[i][j-1]==-1)
                    continue;
                par[i][j] = par[par[i][j-1]][j-1];
            }
        }
    }

    static long lcm(int a, int b){
        return a*b/gcd(a,b);
    }

    static class Pair1 {
        long a;
        long b;
        
        Pair1(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;
        // int c;
        
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
            // this.c = c;
        }
 
        public int compareTo(Pair p) {
            if(a!=p.a)
                return a-p.a;
            return b-p.b;
        }
    }

    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 9992768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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