#ifndef __INTMOD_H__0001__
#define __INTMOD_H__0001__

#include <vector>
#include <iostream>
#include <cassert>

template <unsigned int Modulus>
class IntMod {
	typedef unsigned long long ULL;
private:
	unsigned int value_m;

	void Copy(const IntMod& other) { value_m = other.value_m; }
	bool Modulus_is_valid() { return Modulus != 0; }
public:
	IntMod() { value_m = 0; }
	IntMod(unsigned int value) { value_m = value % Modulus; }
	IntMod(unsigned long long value) { value_m = value % Modulus; }
	IntMod(int value) {
		if (Modulus >= 0x80000000UL) {
			value_m = value >= 0 ? (unsigned int)value % Modulus : Modulus - (unsigned int)(-value);
		} else {
			int tmp = value % (int)Modulus;
			value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
		}
	}
	IntMod(const IntMod& other) { Copy(other); }
	IntMod& operator=(const IntMod& other) { Copy(other); return *this; }
	bool operator==(const IntMod& right) const { return value_m == right.value_m; }
	bool operator!=(const IntMod& right) const { return value_m != right.value_m; }
	IntMod& operator++() {
		++value_m;
		value_m %= Modulus;
		return *this;
	}
	IntMod& operator--() {
		if (value_m == 0) { value_m = Modulus - 1; } else { --value_m; }
		return *this;
	}
	IntMod operator-() const {
		if (value_m == 0) return IntMod(0);
		return IntMod(Modulus - value_m);
	}
	IntMod& operator+=(const IntMod& right) {
		ULL sum = (ULL)value_m + right.value_m;
		if (sum >= (ULL)Modulus) { value_m = (unsigned int)(sum - (ULL)Modulus); } else { value_m = (unsigned int)sum; }
		return *this;
	}
	IntMod& operator-=(const IntMod& right) {
		(*this) += (-right);
		return *this;
	}
	IntMod operator+(const IntMod& right) const {
		IntMod ret(*this);
		ret += right;
		return ret;
	}
	IntMod operator-(const IntMod& right) const {
		IntMod ret(*this);
		ret -= right;
		return ret;
	}
	IntMod& operator*=(const IntMod& right) {
		ULL tmp = (ULL)value_m * right.value_m;
		value_m = tmp % (ULL)Modulus;
		return *this;
	}
	IntMod& operator/=(const IntMod& right) {
		(*this) *= (right.Inverse());
		return *this;
	}
	IntMod operator*(const IntMod& right) const {
		IntMod ret(*this);
		ret *= right;
		return ret;
	}
	IntMod operator/(const IntMod& right) const {
		IntMod ret(*this);
		ret /= right;
		return ret;
	}
	// for power
	IntMod operator[](unsigned int exp) const {
		return Pow(exp);
	}

	/* 素数判定は自分でしろ */
	IntMod Inverse() const {
		return (*this).Pow(Modulus - 2);
	}
	IntMod Pow(unsigned int exp) const {
		unsigned int arr[32];		// TODO
		ULL sum = 1;
		arr[0] = value_m;
		for (int i = 1; i < 32; ++i) {
			arr[i] = ((ULL)arr[i - 1] * arr[i - 1]) % (ULL)Modulus;
		}
		for (int i = 0; i < 32; ++i) {
			if (exp & (0x1 << i)) {
				sum *= arr[i]; sum %= (ULL)Modulus;
			}
		}
		return (unsigned int)sum;
	}
	IntMod Fact() const {
		static std::vector<IntMod> table;
		int factoriand = Get_value();
		if (table.size() > factoriand) {
			return table[factoriand];
		}

		int old_size = table.size();
		table.resize(factoriand + 1);
		for (int i = old_size; i <= factoriand; i++) {
			table[i] = (i == 0 ? 1 : table[i - 1] * i);
		}
		return table[factoriand];
	}
	IntMod Combination(const IntMod& right) const {
		if (value_m < right.value_m) throw "okashii";
		return Fact() / ((*this - right).Fact() * right.Fact());
	}
	unsigned int Get_value() const {
		return value_m;
	}
	static std::vector<IntMod> Inverse_list(int size) {
		assert(size < Modulus);
		std::vector<IntMod> ret_arr(size + 1);
		ret_arr[1] = 1;
		for (int i = 2; i <= size; ++i) {
			ret_arr[i] = ((ULL)(Modulus - Modulus / i) * ret_arr[Modulus % i].Get_value()) % Modulus;
		}
		return ret_arr;
	}
};
typedef IntMod<1000000007> MInt;

//template <unsigned int Modulus>
//IntMod<Modulus> operator*(const int left, const IntMod<Modulus>& right) {
//	IntMod<Modulus> ret(left);
//	ret *= right;
//	return ret;
//}
//template <unsigned int Modulus>
//IntMod<Modulus> operator/(const int left, const IntMod<Modulus>& right) {
//	IntMod<Modulus> ret(left);
//	ret /= right;
//	return ret;
//}

#if 0
MInt operator"" _m(unsigned long long num) { return MInt(num); }
#endif

template <unsigned int Modulus>
std::ostream& operator<<(std::ostream& ost, const IntMod<Modulus>& val) {
	ost << val.Get_value();
	return ost;
}

#endif

#define _CRT_SECURE_NO_WARNINGS
#define _SCL_SECURE_NO_WARNINGS
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <utility>
#include <algorithm>
#include <functional>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <limits>
#include <numeric>
#include <valarray>
#include <fstream>

using namespace std;
typedef unsigned int uint;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<LL, LL> PP;
#define REP(i, a, n) for(LL i = (a), i##_max = (n); i < i##_max; ++i)
#define REM(i, a, n) for(LL i = (LL)(n) - 1, i##min = (a); i >= i##min; --i)
#define ALL(arr) (arr).begin(), (arr).end()
#define FLOAT fixed << setprecision(16)
#define SPEEDUP {cin.tie(NULL); ios::sync_with_stdio(false);}
const int INF = 0x3FFFFFFF;
const LL INFLL = 0x3FFFFFFF3FFFFFFF;
const double INFD = 1.0e+308;
const double EPS = 1.0e-9;

void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
template <class T, class U>
istream& operator >> (istream& ist, pair<T, U>& right) { return ist >> right.first >> right.second; }
template <class T, class U>
ostream& operator<<(ostream& ost, const pair<T, U>& right) { return ost << right.first << ' ' << right.second; }
template <class T, class TCompatible, size_t N>
void Fill(T(&dest)[N], const TCompatible& val) { fill(dest, dest + N, val); }
template <class T, class TCompatible, size_t M, size_t N>
void Fill(T(&dest)[M][N], const TCompatible& val) { for (int i = 0; i < M; ++i) Fill(dest[i], val); }
template<class T>
T Compare(T left, T right) { return left > right ? 1 : (left < right ? -1 : 0); }
istream& Ignore(istream& ist) { string s; ist >> s; return ist; }
bool Inside(int i, int j, int h, int w) { return i >= 0 && i < h && j >= 0 && j < w; }
template <class T>
T Next() { T buf; cin >> buf; return buf; }

#ifdef ONLY_MY_ENVIR
#include "IntMod.h"
#include "Graph.h"
#include "Math.h"
#include "Matrix.h"
#include "MinMax.h"
#include "Range.h"
#include "Tree.h"
#include "Union_Find.h"
#endif

#ifdef __GNUC__
typedef __int128 LLL;
istream& operator >> (istream& ist, __int128& val) { LL tmp;  ist >> tmp; val = tmp; return ist; }
ostream& operator<< (ostream& ost, __int128 val) { LL tmp = val; ost << tmp; return ost; }
#endif

#if 1234567891
#include <array>
#include <random>
#include <unordered_set>
#include <unordered_map>
template<typename T>
using PriorityQ = priority_queue<T, vector<T>, greater<T> >;
// template <class T>
// auto Is(const T& value) { return [value](const auto& comparand) -> bool { return comparand == value; }; }
#endif

const int M = 4064;
using Bits = bitset<M>;
using Mit = IntMod<998244353>;

int Digit(const Bits& a) {
	REM(i, 0, M) {
		if (a[i]) {
			return i + 1;
		}
	}
	return 0;
}

Bits GCD(Bits a, Bits b) {
	Bits* p = &a;
	Bits* q = &b;
	int as = Digit(a) - 1;
	int bs = Digit(b) - 1;

	while (bs >= 0) {
		while (as >= bs) {
			*p ^= *q << (as - bs);
			while (as >= 0 && (*p)[as] == 0) {
				--as;
			}
		}
		swap(p, q);
		swap(as, bs);
	}
	return *p;
}

bool Less(const Bits& a, const Bits& b) {
	REM(i, 0, M) {
		if (a[i] < b[i]) return true;
		if (a[i] > b[i]) return false;
	}
	return false;
}

Bits Inc(const Bits& a) {
	Bits ret(a);

	REP(i, 0, M) {
		if (ret[i]) {
			ret[i] = 0;
		} else {
			ret[i] = 1;
			return ret;
		}
	}
}

int N;
Bits X;
Bits A[6];
Mit P[M];
int main() {
	cin >> N >> X;
	REP(i, 0, N) {
		cin >> A[i];
	}
	X = Inc(X);
	
	P[0] = 1;
	REP(i, 1, M) {
		P[i] = P[i - 1] * 2;
	}
	
	Bits gcd = 0;
	REP(i, 0, N) {
		gcd = GCD(gcd, A[i]);
	}
	
	int xs = Digit(X);
	int gs = Digit(gcd);

	Mit sum = 0;
	REM(i, gs - 1, xs) {
		if (X[i]) {
			sum += P[i - gs + 1];
		}
	}

	Bits Y = 0;
	REM(i, gs - 1, xs) {
		if (Y[i] != X[i]) {
			Y ^= gcd << (i - gs + 1);
		}
	}

	cout << sum + Less(Y, X) << endl;
	return 0;
}


Measured memory_bytes: 256