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.
//Har Har Mahadev
using namespace std;
#include <bits/stdc++.h>
#define ll long long int
#define ld long double
#define pb push_back
#define mp make_pair
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)
mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
#ifdef bhole_ka_saaya
	#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__);
	#define booga cerr << "booga" << endl;
#else
	#define debug(...) 42;
	#define booga 42;
#endif

template <typename T> std::ostream& operator<<(std::ostream& stream, const vector<T>& vec){ for(size_t i = 0; i < vec.size(); i++){stream << vec[i];if(i != vec.size() - 1)stream << ' ';}; return stream; }
template <typename T> std::istream& operator>>(std::istream& stream, vector<T>& vec) { for(T &x : vec)stream >> x;return stream; }
template <typename T,typename U> std::ostream& operator<<(std::ostream& stream, const pair<T,U>& pr){ stream << pr.first << ' ' << pr.second; return stream; }
template <typename T,typename U> std::istream& operator>>(std::istream& stream, pair<T,U>& pr){ stream >> pr.first >> pr.second; return stream; }
template <typename T> void operator+=(vector<T>& vec, const T value) { for(T &x : vec)x += value; }
template <typename T> void operator-=(vector<T>& vec, const T value) { for(T &x : vec)x -= value; }
template <typename T> void operator++(vector<T>& vec) { vec += 1; }
template <typename T> void operator++(vector<T>& vec,T) { vec += 1; }
template <typename T> void operator--(vector<T>& vec) { vec -= 1; }
template <typename T> void operator--(vector<T>& vec,T) { vec -= 1; }
template <typename T> void operator*=(vector<T>& vec, const T value) { for(T &x : vec)x *= value; }
template <typename T> void operator/=(vector<T>& vec, const T value) { for(T &x : vec)x /= value; }
template <typename T,typename U> void operator+=(pair<T,U>& vec, const T value) { vec.first += value;vec.second += value; }
template <typename T,typename U> void operator-=(pair<T,U>& vec, const T value) { vec.first -= value;vec.second -= value; }
template <typename T,typename U> void operator++(pair<T,U>& vec) { vec += 1; } 
template <typename T,typename U> void operator++(pair<T,U>& vec,T) { vec += 1; } 
template <typename T,typename U> void operator--(pair<T,U>& vec) { vec -= 1; } 
template <typename T,typename U> void operator--(pair<T,U>& vec,T) { vec -= 1; } 
template <typename T,typename U> void operator*=(pair<T,U>& vec, const T value) { vec.first *= value;vec.second *= value; } 
template <typename T,typename U> void operator/=(pair<T,U>& vec, const T value) { vec.first /= value;vec.second /= value; } 

template <typename A, typename B>string to_string(pair<A, B> p);
template <typename A, typename B, typename C>string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(char c) {string s;s += c;return s; }
string to_string(const char* s) {return to_string((string) s); }
string to_string(bool b) {return (b ? "1" : "0"); }
string to_string(vector<bool> v) {bool first = true;string res = "{";for (int i = 0; i < static_cast<int>(v.size()); i++) {if (!first) {res += ", ";}first = false;res += to_string(v[i]);}res += "}";return res;}
template <size_t N>string to_string(bitset<N> v) {string res = "";for (size_t i = 0; i < N; i++) {res += static_cast<char>('0' + v[i]);}return res;}
template <typename A>string to_string(A v) {bool first = true;string res = "{";for (const auto &x : v) {if (!first) {res += ", ";}first = false;res += to_string(x);}res += "}";return res;}
template <typename A, typename B>string to_string(pair<A, B> p) {return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}
template <typename A, typename B, typename C>string to_string(tuple<A, B, C> p) {return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";}
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }

void debug_out() { cerr << endl; } template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {cerr << " " << to_string(H);debug_out(T...);}
void bharo(int N_N) { return; }template <typename Head, typename... Tail>void bharo(int N_N, Head &H, Tail & ... T) {H.resize(N_N);bharo(N_N,T...);}
void safai() { return; }template <typename Head, typename... Tail>void safai(Head &H, Tail & ... T) {H.clear();safai(T...);}

template <typename T>
T inverse(T a, T m) {
	T u = 0, v = 1;
	while (a != 0) {
		T t = m / a;
		m -= t * a; swap(a, m);
		u -= t * v; swap(u, v);
	}
	assert(m == 1);
	return u;
}
 
template <typename T>
class Modular {
 public:
	using Type = typename decay<decltype(T::value)>::type;
	constexpr Modular() : value() {}
	template <typename U>
	Modular(const U& x) {
		value = normalize(x);
	}
	template <typename U>
	static Type normalize(const U& x) {
		Type v;
		if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
		else v = static_cast<Type>(x % mod());
		if (v < 0) v += mod();
		return v;
	}
	const Type& operator()() const { return value; }
	template <typename U>
	explicit operator U() const { return static_cast<U>(value); }
	constexpr static Type mod() { return T::value; }
	Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
	Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
	template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
	template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
	Modular& operator++() { return *this += 1; }
	Modular& operator--() { return *this -= 1; }
	Modular operator++(int) { Modular result(*this); *this += 1; return result; }
	Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
	Modular operator-() const { return Modular(-value); }
	template <typename U = T>
	typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
		uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
		uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
		asm(
			"divl %4; "
			: "=a" (d), "=d" (m)
			: "d" (xh), "a" (xl), "r" (mod())
		);
		value = m;
#else
		value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
		return *this;
	}
	template <typename U = T>
	typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
		long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
		value = normalize(value * rhs.value - q * mod());
		return *this;
	}
	template <typename U = T>
	typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
		value = normalize(value * rhs.value);
		return *this;
	}
	Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
	friend const Type& abs(const Modular& x) { return x.value; }
	template <typename U>
	friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
	template <typename U>
	friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
	template <typename V, typename U>
	friend V& operator>>(V& stream, Modular<U>& number);
	private: Type value;
};
 
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
 
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
	assert(b >= 0);
	Modular<T> x = a, res = 1;
	U p = b;
	while (p > 0) {
		if (p & 1) res *= x;
		x *= x;
		p >>= 1;
	}
	return res;
}
 
template <typename T>
bool IsZero(const Modular<T>& number) {
	return number() == 0;
}
 
template <typename T>
string to_string(const Modular<T>& number) {
	return to_string(number());
}
 
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
	return stream << number();
}
 
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
	typename common_type<typename Modular<T>::Type, long long>::type x;
	stream >> x;
	number.value = Modular<T>::normalize(x);
	return stream;
}
 

//using ModType = int;
 
//struct VarMod { static ModType value; };
//ModType VarMod::value;
//ModType& md = VarMod::value;
//using Mint = Modular<VarMod>;
 
constexpr int md = (int) 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
 

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);


const int MXN = 1e5 + 50;

void prep(){ // Don't forget to call this to use nCr
	fact.resize(MXN);
	inv_fact.resize(MXN);
	fact[0] = 1;
	for(int i = 1; i < MXN; i++){
		fact[i] = fact[i-1]*i;
	}
	inv_fact[MXN-1] = power(fact[MXN-1],md-2);
	for(int i = MXN-2; i >= 0; i--){
		inv_fact[i] = inv_fact[i+1]*(i+1);
	}
}
 

Mint C(int n, int k) {
	if (k < 0 || k > n) {
		return 0;
	}
	while ((int) fact.size() < n + 1) {
		fact.push_back(fact.back() * (int) fact.size());
		inv_fact.push_back(1 / fact.back());
	}
	return fact[n] * inv_fact[k] * inv_fact[n - k];
}



void testcase(){
	int n;string s;
	cin >> n >> s;
    vector<bool> state(n,false);
    int cnt = 0,tot = 0;
    for(ll i = 0;i < n;i++){
        cnt += s[i] == '0';
    }
    for(ll i = 1;i < n;i++){
        if(s[i] == '1' && s[i-1]=='1' && !state[i-1]){
            tot++;
            state[i] = true;
        }
    }
    cout << C(cnt+tot,tot) << '\n';
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int tt = 1;
	cin >> tt;
	while(tt--){
		testcase();
	}
	return 0;
}

