Problem: There are N non-negative integers written on a blackboard. The i-th integer is A_i.

Takahashi can perform the following two kinds of operations any number of times in any order:

* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.



How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.

Constraints

* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.

Input

Input is given from Standard Input in the following format:


N X
A_1
:
A_N


Output

Print the number of different integers not exceeding X that can be written on the blackboard.

Examples

Input

3 111
1111
10111
10010


Output

4


Input

4 100100
1011
1110
110101
1010110


Output

37


Input

4 111001100101001
10111110
1001000110
100000101
11110000011


Output

1843


Input

1 111111111111111111111111111111111111111111111111111111111111111
1


Output

466025955

Solution (in CPP):

Solution:
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize(3)
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC target("sse3","sse2","sse")
//#pragma GCC target("avx","sse4","sse4.1","sse4.2","ssse3")
//#pragma GCC target("f16c")
//#pragma GCC optimize("inline","fast-math","unroll-loops","no-stack-protector")
//#pragma GCC diagnostic error "-fwhole-program"
//#pragma GCC diagnostic error "-fcse-skip-blocks"
//#pragma GCC diagnostic error "-funsafe-loop-optimizations"
//#pragma GCC diagnostic error "-std=c++14"
#include "bits/stdc++.h"
//#include "ext/pb_ds/tree_policy.hpp"
//#include "ext/pb_ds/assoc_container.hpp"
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fr(x) freopen(x,"r",stdin)
#define fw(x) freopen(x,"w",stdout)
#define iout(x) printf("%d\n",x)
#define lout(x) printf("%lld\n",x)
#define REP(x,l,u) for(ll x = l;x<u;x++)
#define RREP(x,l,u) for(ll x = l;x>=u;x--)
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define PII pair<int,int>
#define PLL pair<ll,ll>
#define MP make_pair
#define lowbit(x) ((x)&(-(x)))
#define lson (ind<<1)
#define rson (ind<<1|1)
#define se second
#define fi first
#define sz(x) ((int)x.size())
#define EX0 exit(0);

typedef  long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
using namespace std;
typedef vector<ll> VLL;
typedef vector<int> VI;
const int block_size = 320;
typedef complex<ll> point;
const ll mod = 998244353;
const ll inf = 1e9+7;
const ld eps = 1e-9;
const db PI = atan(1)*4;
template<typename T>
inline int sign(const T&a) {if(a<0)return -1;if(a>0)return 1;return 0;}
string to_string(string s) {return '"' + s + '"';}string to_string(const char* s) {return to_string((string) s);}string to_string(bool b) {return (b ? "true" : "false");}template <typename A, typename B>string to_string(pair<A, B> p) {return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}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;}void debug_out() { cerr << endl; }template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {cerr << " " << to_string(H);debug_out(T...);}

#ifndef ONLINE_JUDGE
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define dbg(...) {}
#endif

template<typename T,typename S>inline bool upmin(T&a,const S&b){return a>b?a=b,1:0;}
template<typename T,typename S>inline bool upmax(T&a,const S&b){return a<b?a=b,1:0;}

template<typename T> inline void in(T &x) {x = 0;T f = 1;char ch = getchar();while (!isdigit(ch)) {if (ch == '-') f = -1;ch = getchar();}while (isdigit(ch))  {x = x * 10 + ch - '0';ch = getchar();}x *= f;}
ll twop(int x) {return 1LL<<x;}
template<typename T>T MOD(T a, T m){a %= m;if (a < 0)a += m;return a;}
template<typename T>T inverse(T a, T m){a = MOD(a, m);if (a <= 1)return a;return MOD((1 - inverse(m, a) * m) / a, m);}template<typename A,typename B > inline void in(A&x,B&y) {in(x);in(y);}
template<typename A,typename B,typename C>inline void in(A&x,B&y,C&z) {in(x);in(y);in(z);}
template<typename A,typename B,typename C,typename D> inline void in(A&x,B&y,C&z,D&d) {in(x);in(y);in(z);in(d);}
template <typename T>T sqr(T x){return x*x;}
ll gcd(ll a,ll b){while(b!=0){a%=b;swap(a,b);}return a;}
ll fast(ll a,ll b,ll mod){ll ans = 1;while(b){if(b&1){b--;ans = ans * a % mod;}else{a = a * a % mod;b/=2;}}return ans%mod;}


const ll len = 4020;
typedef bitset<len> bs;
namespace SOLVE {
    bs gcd(bs a, bs b){
        while (a.count() and b.count()) {
            int h[2] = {0,0};
            REP(i,0,len){
                if(a[i])h[0] = i;
                if(b[i])h[1] = i;
            }
            if(h[0]<=h[1]){
                b^=a<<(h[1]-h[0]);
            }else{
                a^=b<<(h[0]-h[1]);
            }
        }
        if(a.count())return a;
        return b;
    }
    bs g,x;
    int get_deg(bs x){
        RREP(i,len-1,0)if(x[i])return i;
        return -1;
    }
    bool operator<(const bs&a,const bs&b){
        RREP(i,len-1,0)if(a[i]!=b[i])return a[i]<b[i];
        return false;
    }
    ll ans = 0;
    void main(){
        int n;
        cin>>n>>x;
        
        REP(i,0,n){
            bs b;
            cin>>b;
            g = gcd(b, g);
        }
        int deg = get_deg(g);
        RREP(i,len-1,deg){
            if(x[i]){
                ans += fast(2, i-deg, mod);
                
            }
        }
//        dbg(x.to_string());
//        dbg(g.to_string());
        if(x<g){
            cout<<1<<endl;
            return;
        }
        bs tmp;
        RREP(i,len-1,deg){
            if(x[i] != tmp[i]){
                tmp ^= g<<(i-deg);
            }
        }
        ans += tmp < x or tmp == x;
        cout<< MOD(ans,mod)<<endl;
    }
}


signed main() {
#ifndef ONLINE_JUDGE
#endif
    
    
    
    
    
    int t = 1;
//    in(t);
    while(t--){
        SOLVE::main();

    }
    
    
    
    
    
    
    
    
//    clock_t st = clock();
//    while(clock() - st < 3.0 * CLOCKS_PER_SEC){
//
//    }
    
    
    
    
    
    
    return 0;
}