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 <bits/stdc++.h>             /*Fuck ratings Feel the magic in the code...*/
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
using namespace std;
// using namespace __gnu_pbds;
// template<typename T>
// using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
/*   in log(n) time...
    find_by_order() - Returns an iterator to the k-th largest element (counting from zero)
    order_of_key()  - The number of items in a set that are strictly smaller than our item
    // Rest same as set
*/
#define fastio() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define mod 998244353
#define inf 2e18
#define minf -2e18
#define PI 3.141592653589793238462
#define ll long long
#define lld long double
#define all(x) x.begin(), x.end()
#define min3(a, b, c) min(min(a, b), c)
#define max3(a, b, c) max(max(a, b), c)
#define min4(a, b, c, d) min(min(a, b), min(c, d))
#define max4(a, b, c, d) max(max(a, b), max(c, d))
#define ff first
#define ss second
#define pb push_back
#define ppb pop_back
#define ub upper_bound
#define lb lower_bound
#define sz(v) (ll)v.size()
#define nline "\n"

/*----------------------------Setting up the debugger---------------------*/
#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x);
#endif
  
void _print(int t) {cerr << t;}
void _print(ll t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(lld t) {cerr << t;}
void _print(double t) {cerr << t;}
 
template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.ff); cerr << ","; _print(p.ss); cerr << "}";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {_print(i); cerr << " ";} cerr << "]";}

/* -----------------------------------------------------------------------------*/

ll powr(ll a, ll b, ll p) { if(b == 0) return 1; else if(b == 1) return a; else if(!(b & 1)) return powr((a * a) % p, b / 2, p); else return (a * powr(a, b - 1, p)) % p; }
ll gcd(ll a, ll b){ if(b == 0) return a; else return gcd(b, a % b); }
ll lcm(ll a, ll b){ return a * b / gcd(a, b); }
void extendgcd(ll a, ll b, ll *v) {if (b == 0) {v[0] = 1; v[1] = 0; v[2] = a; return ;} extendgcd(b, a % b, v); ll x = v[1]; v[1] = v[0] - v[1] * (a / b); v[0] = x; return;} //pass an arry of size1 3
ll mminv(ll a, ll b) {ll arr[3]; extendgcd(a, b, arr); return (arr[0] + b) % b ; } //for non prime b 
ll mod_inv(ll a, ll p){ return powr(a,p-2,p); } /*For prime p  "Fermet lill theorem"*/
ll mod_add(ll a, ll b, ll m) { a = a % m; b = b % m; return ((a + b) % m + m) % m; }
ll mod_mul(ll a, ll b, ll m) { a = a % m; b = b % m; return ((a * b) % m + m) % m; }
ll mod_sub(ll a, ll b, ll m) { a = a % m; b = b % m; return ((a - b) % m + m) % m; }
ll mod_div(ll a, ll b, ll m) { a = a % m; b = b % m; return (mod_mul(a, mod_inv(b, m), m) + m) % m; } /*For prime p*/
// void swap(ll &a, ll &b) { ll temp = a; a = b; b = temp; }
ll spf(ll n) { for(ll i = 2; i * i <= n; i++) { if(n % i == 0) return i; } return n; }/* spf in sqrt(n) time... */
vector<ll> fact_modp(ll n, ll p) { vector<ll> fact(n + 1); fact[0] = 1; for(ll i = 1; i <= n; i++){ fact[i] = (i * fact[i - 1]) % p; } return fact; }
vector<ll> fact = fact_modp(1e5 + 10, mod);

/*For prime p "Fermet lill theorem..."*/
ll nCr_modp(ll n, ll r, ll p) {  if(n < r) return 0; if(r == 0) return 1; else { return ((fact[n] * mod_inv(fact[r], p)) % p * mod_inv(fact[n - r], p)) % p; } }


vector<ll> prime_sieve(ll n) { /*Returns vector of prime <= n  in nloglogn time*/
    vector<ll> t;
    vector<bool> a(n + 1, true);
    a[0] = a[1] = false;
    for(ll i = 2; i * i <= n; i++) {
        if(a[i]) {
            for(ll j = i * i; j <= n; j += i)
            a[j] = false;
        }
    }
    for(ll i = 0; i <= n; i++) {
        if(a[i])
        t.push_back(i);
    }
    return t;
}
vector<ll> spf_sieve(ll n) { /*Returns vector of spf[n] in nloglogn time*/
    vector<ll> a(n + 1, -1);
    for(ll i = 2; i * i <= n; i++) {
        if(a[i] == -1) {
            a[i] = i;
            for(ll j =i * i; j <= n; j += i) { if(a[j] == -1) a[j] = i;}
        }
    }
    for(ll i = 2; i <= n; i++) { if(a[i] == -1) a[i] = i;}
    return a;
}
     /* --------------------------------------Template ends, Dee codes---------------------------------------*/


int main()
{
    fastio();

#ifndef ONLINE_JUDGE
    freopen("error.txt", "w", stderr);
#endif
    
    vector<ll> fac = fact_modp(1e5 + 10, mod);          
    int tests = 1;                                               
    cin >> tests;        
    while(tests--)
    {
        int n;
        cin >> n;
        string s;
        cin >> s;
        ll n0 = 0, n1 = 0;
        ll key = 0, temp = 0;
        for(auto x : s) {
            if(x == '0') {
                n0++;
                n1 += temp / 2;
                key = 0;
                temp = 0;
            }
            else {
                temp++;
            }
        }
        debug(n0); debug(n1);
        n1 += temp / 2;
        ll nn = n1 + n0;
        cout << nCr_modp(nn, n0, mod) << nline;



    } //end of while
    return 0;
} // end of main
