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:
#include <bits/stdc++.h>

#include <unistd.h>
 
using namespace std;
 
#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl
#define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;}
 
 
typedef long long ll;
//#define int ll
 
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx_ori[4] = { -1,0, 1,0 }, dy_ori[4] = { 0,1,0,-1 };
int dx[4] = {0, 0, 0, 0}, dy[4] = {0, 0, 0, 0};
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
//const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'

const int M = 4000;
#define bit bitset<M>

bool eq_less(bit a, bit b) {
  bool is_big = false;
  rrep (i, M) {
    if (a[i] != b[i]) {
      if (a[i]) is_big = true;
      break;
    }
  }
  return not is_big;
}

bit gcd(bit a, bit b) {
  //DEBUG(make_pair(a, b));
  if (eq_less(a, b)) swap(a, b);

  int da = -1, db = -1;
  rrep (i, M) {
    if (da == -1 and a[i]) {
      da = i;
    }
    if (db == -1 and b[i]) {
      db = i;
    }
  }
  //DEBUG(pii(da, db));
  if (db == -1) {
    return a;
  }
  assert(db <= da);
  bit b2 = b << (da - db);
  bit r = a ^ b2;
  return gcd(b, r);
}

bitset<M> convert(string x) {
  int n = x.size();
  string pad(M - n, '0');
  x = pad + x;
  return bitset<M>(x);
}

signed main() {
  int n;
  string _x;
  cin >> n >> _x;
  bitset<M> x = convert(_x);
  
  vector<bitset<M>> a;
  rep (i, n) {
    string _s;
    cin >> _s;
    a.push_back(convert(_s));
  }

  bit p = a[0];
  rep1 (i, n - 1) {
    p = gcd(p, a[i]);
  }
  //DEBUG(p);

  int top;
  rrep (i, M) {
    if (p[i]) {
      top = i;
      break;
    }
  }

  vl power(M + 1);
  power[0] = 1;
  rep (i, M) {
    power[i + 1] = power[i] * 2 % MOD;
  }
  //DEBUG(top);
  bit x2 = x >> (top + 1);
  //DEBUG(x2);
  ll ans = 0;
  rep (i, M) {
    if (x2[i]) (ans += power[i]) %= MOD;
  }
  ans = (ans - 1 + 1) * 2 % MOD;

  bit now;
  int op_num = M - top - 1;
  rep (i, op_num) {
    if (x[M - 1 -i] != now[top]) now = now ^ p;
    now <<= 1;
  }
  
  if (eq_less(now, x)) ans++;
  now = now ^ p;
  if (eq_less(now, x)) ans++;
  cout << ans << endl;
}