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.
#include<iostream>
#include<cstdio>
#include<set>
#include<map>
#include<vector>
#include<cstring>
#include<string>
#include<cstdlib>
#include<algorithm>
#include<queue>
#include<iomanip>
#include<stack>
#include<cmath>

 
using namespace std;

#ifndef POJ
    #define Cpp11
#endif
 
#ifdef Cpp11
    #define _for(i,a,b) for(auto i = (a);i<(b);++i)
    #define _rep(i,a,b) for(auto i = (a);i<=(b);++i)
    #define _dep(i,a,b) for(auto i = (a);i>=(b);--i)
    #define mt(a,b,c) make_tuple(a,b,c) 
    #include<ctime>
    #include<random>
    #include<chrono>
    #include<limits>
    #include<complex>
    #include<unordered_set>
    #include<unordered_map>
    #include<cassert>
    #include<functional>
    #include<bitset>
    #define IO ios::sync_with_stdio(false);cout.tie(nullptr);cin.tie(nullptr);
#endif
 
#ifndef Cpp11
    #define _for(i,a,b) for(int i = (a);i<(b);++i)
    #define _rep(i,a,b) for(int i = (a);i<=(b);++i)
    #define _dep(i,a,b) for(int i = (a);i>=(b);--i)
    #define IO ios::sync_with_stdio(false);cout.tie(NULL);cin.tie(NULL);
#endif
 
 
using namespace std;


 
#define fr first
#define sc second
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define pob pop_back
#define pf push_front
#define pof pop_front
#define sci(x) scanf("%d",&(x))
#define scl(x) scanf("%lld",&(x))
#define debugline fprintf(stderr,"-----------------------\n");
#define szint(x) ((int)(x).size())


 
#ifdef I128IO
typedef __int128 SPLL;
char buff[200];
template<typename T>
void read(T& o)
{
    o = 0;
    scanf("%s",buff);
    //printf("%s\n",buff);
    T f = 1;
    int i = 0;
 
    if(buff[0]=='-')i++,f = -1;
    for(;buff[i];++i)
    {
        o*=10,o+=buff[i]-'0';
    }
    o*=f;
}
 
template<typename T>
void write(T o)
{
    int len = 0;
    buff[0] = '0';
    if(o==0)
    {
        putchar('0');
        return;
    }
    int f = 1;
    if(o<0) f = -1;
    o*=f;
    for(;o;o/=10) buff[len++] = o%10+'0';
    if(f==-1) buff[len++] = '-';
    reverse(buff,buff+len);
    buff[len++] ='\0';
    printf("%s",buff);
}
#endif
 
#ifdef FIO
char buff[100];
template<typename T>
void read(T& o)
{
    o = 0;
    scanf("%s",buff);
    //printf("%s\n",buff);
    T f = 1;
    int i = 0;
    if(buff[0]=='-')i++,f = -1;
    for(;buff[i];++i)
    {
        o*=10,o+=buff[i]-'0';
    }
    o*=f;
}
template<typename T>
void write(T o)
{
    int len = 0;
    buff[0] = '0';
    if(o==0)
    {
        putchar('0');
        return;
    }
    int f = 1;
    if(o<0) f = -1;
    o*=f;
    for(;o;o/=10) buff[len++] = o%10+'0';
    if(f==-1) buff[len++] = '-';
    reverse(buff,buff+len);
    buff[len++] ='\0';
    printf("%s",buff);
}
#endif

#define OIreader


#ifdef OIreader
inline int read(){
    char ch; bool sign=0; int res=0;
    while(!isdigit(ch=getchar()))if(ch=='-')sign=1;
    while(isdigit(ch))res=res*10+(ch^48),ch=getchar();
    if(sign)return -res; else return res;
}
#endif

#define _Random_

#ifdef _Random_
    mt19937 __MT(chrono::system_clock::now().time_since_epoch().count());
#endif
 
#ifndef BigNumber
    typedef unsigned long long uLL;
    typedef long long LL;
    typedef long long ll;
    typedef pair<LL,LL> pLL;
    typedef vector<LL> vL;
    typedef vector<vL> vLL;
#endif

typedef vector<int> vi;
typedef vector<vi > vii;
typedef pair<int,int> pii;

const int maxn = 200000+10;
const int maxm = 20000000+10;
const int maxb = 20+10;
const int apsz = 26;
const int mod = 998244353;

// Think And Code.Just for fun,and also for dream

int fac[maxn],invfac[maxn];
int n;
char s[maxn];

inline int mul(int a,int b)
{
    return 1LL*a*b%mod;
}
inline int add(int a,int b)
{
    a+=b;
    if(a>mod) a-=mod;
    else if(a<0)a+=mod;
    return a;
}

inline int fpow(int a,int b)
{
    int ans(1);
    for(;b;)
    {
        if(b&1) ans = mul(ans,a);
        a = mul(a,a);
        b>>=1;
    }
    return ans;
}



inline void init()
{
    fac[0]++;
    _for(i,1,maxn) fac[i] = mul(fac[i-1],i);
    int now = fpow(fac[maxn-1],mod-2);
    _dep(i,maxn-1,1)
    {
        invfac[i] = mul(now,fac[i-1]);
        now = mul(now,i);
    }
    invfac[0]++;
    _for(i,1,maxn) invfac[i] = mul(invfac[i],invfac[i-1]);
}

inline int C(int n,int m)
{
    if(n<0||m<0||n<m)return 0;
    return mul(fac[n],mul(invfac[n-m],invfac[m]));
}



inline int solve()
{
    vi cnt(2,0);
    _for(i,0,n) cnt[s[i]-'0']++;
    cnt[1] = 0;
    for(int i = 0;i<n;)
    {
        int j = i;
        for(;j<n&&s[j]=='1';)
            ++j;
        int len = j-i;
        cnt[1]+=len/2;
        i = j+1;
    }
    return C(cnt[1]+cnt[0],cnt[0]);
}


int main(void)
{
    int T;
    init();
    sci(T);
    for(;T--;)
    {
        sci(n);
        scanf("%s",s);
        printf("%d\n",solve());
    }
    return 0;
}