#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
template <const int MOD>
struct modular_int {
  int x;
  static vector<int> inverse_list;
  const static int inverse_limit;
  const static bool is_prime;
  modular_int() { x = 0; }
  template <typename T>
  modular_int(const T z) {
    x = (z % MOD);
    if (x < 0) x += MOD;
  }
  modular_int(const modular_int<MOD>* z) { x = z->x; }
  modular_int(const modular_int<MOD>& z) { x = z.x; }
  modular_int operator-(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = x - m.x;
    if (U.x < 0) U.x += MOD;
    return U;
  }
  modular_int operator+(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = x + m.x;
    if (U.x >= MOD) U.x -= MOD;
    return U;
  }
  modular_int& operator-=(const modular_int<MOD>& m) {
    x -= m.x;
    if (x < 0) x += MOD;
    return *this;
  }
  modular_int& operator+=(const modular_int<MOD>& m) {
    x += m.x;
    if (x >= MOD) x -= MOD;
    return *this;
  }
  modular_int operator*(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = (x * 1ull * m.x) % MOD;
    return U;
  }
  modular_int& operator*=(const modular_int<MOD>& m) {
    x = (x * 1ull * m.x) % MOD;
    return *this;
  }
  template <typename T>
  friend modular_int operator+(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) + p);
  }
  template <typename T>
  friend modular_int operator-(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) - p);
  }
  template <typename T>
  friend modular_int operator*(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) * p);
  }
  template <typename T>
  friend modular_int operator/(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) / p);
  }
  int value() const { return x; }
  modular_int operator^(const modular_int<MOD>& cpower) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    int power = cpower.x;
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  modular_int operator^(long long power) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    if (power >= MOD && is_prime) {
      power %= (MOD - 1);
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  modular_int operator^(int power) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  template <typename T>
  modular_int& operator^=(T power) {
    modular_int<MOD> res = (*this) ^ power;
    x = res.x;
    return *this;
  }
  template <typename T>
  modular_int pow(T x) {
    return (*this) ^ x;
  }
  pair<long long, long long> gcd(const int a, const int b) const {
    if (b == 0) return {1, 0};
    pair<long long, long long> c = gcd(b, a % b);
    return {c.second, c.first - (a / b) * c.second};
  }
  inline void init_inverse_list() const {
    vector<int>& dp = modular_int<MOD>::inverse_list;
    dp.resize(modular_int<MOD>::inverse_limit + 1);
    int n = modular_int<MOD>::inverse_limit;
    dp[0] = 1;
    if (n > 1) dp[1] = 1;
    for (int i = 2; i <= n; ++i) {
      dp[i] = (dp[MOD % i] * 1ull * (MOD - MOD / i)) % MOD;
    }
  }
  modular_int<MOD> get_inv() const {
    if (modular_int<MOD>::inverse_list.size() <
        modular_int<MOD>::inverse_limit + 1)
      init_inverse_list();
    if (this->x <= modular_int<MOD>::inverse_limit) {
      return modular_int<MOD>::inverse_list[this->x];
    }
    pair<long long, long long> G = gcd(this->x, MOD);
    return modular_int<MOD>(G.first);
  }
  modular_int<MOD> operator-() const {
    modular_int<MOD> v(0);
    v -= (*this);
    return v;
  }
  modular_int operator/(const modular_int<MOD>& m) const {
    modular_int<MOD> U(this);
    U *= m.get_inv();
    return U;
  }
  modular_int& operator/=(const modular_int<MOD>& m) {
    (*this) *= m.get_inv();
    return *this;
  }
  bool operator==(const modular_int<MOD>& m) const { return x == m.x; }
  bool operator<(const modular_int<MOD>& m) const { return x < m.x; }
  template <typename T>
  bool operator==(const T& m) const {
    return (*this) == (modular_int<MOD>(m));
  }
  template <typename T>
  bool operator<(const T& m) const {
    return x < (modular_int<MOD>(m)).x;
  }
  template <typename T>
  bool operator>(const T& m) const {
    return x > (modular_int<MOD>(m)).x;
  }
  template <typename T>
  friend bool operator==(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x == m.x;
  }
  template <typename T>
  friend bool operator<(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x < m.x;
  }
  template <typename T>
  friend bool operator>(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x > m.x;
  }
  friend istream& operator>>(istream& is, modular_int<MOD>& p) {
    int64_t val;
    is >> val;
    p.x = (val % MOD);
    if (p.x < 0) p.x += MOD;
    return is;
  }
  friend ostream& operator<<(ostream& os, const modular_int<MOD>& p) {
    return os << p.x;
  }
};
extern const int MOD = 998244353;
using mod_int = modular_int<MOD>;
template <typename T>
vector<T> mobius_transform(int n, vector<T> f) {
  assert(f.size() == (1 << n));
  for (int mask = 0; mask < (1 << n); mask++) {
    if ((__builtin_popcount(mask) % 2) == 1) {
      f[mask] *= -1;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int mask = 0; mask < (1 << n); mask++) {
      if ((mask & (1 << i)) != 0) {
        f[mask] += f[mask ^ (1 << i)];
      }
    }
  }
  for (int mask = 0; mask < (1 << n); mask++) {
    if ((__builtin_popcount(mask) % 2) == 1) {
      f[mask] *= -1;
    }
  }
  vector<T> mu(1 << n);
  for (int mask = 0; mask < (1 << n); mask++) mu[mask] = f[mask];
  return mu;
}
const int ALPHABET = 26;
const char MIN_CHAR = 'a';
const int S_MAX = 20005;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  vector<array<uint16_t, ALPHABET>> S(N);
  for (int i = 0; i < N; i++) {
    S[i].fill(0);
    string str;
    cin >> str;
    for (auto& ch : str) S[i][ch - MIN_CHAR]++;
  }
  vector<array<uint16_t, ALPHABET>> mins(1 << N);
  mins[0].fill(S_MAX);
  for (int mask = 1; mask < 1 << N; mask++) {
    int low = __builtin_ctz(mask);
    mins[mask] = mins[mask ^ 1 << low];
    for (int c = 0; c < ALPHABET; c++)
      mins[mask][c] = min(mins[mask][c], S[low][c]);
  }
  vector<mod_int> dp(1 << N, 1);
  dp[0] = 0;
  for (int mask = 1; mask < 1 << N; mask++)
    for (int x : mins[mask]) dp[mask] *= x + 1;
  dp = mobius_transform<mod_int>(N, dp);
  for (int mask = 1; mask < 1 << N; mask++)
    if (__builtin_popcount(mask) % 2 == 0) dp[mask] = -dp[mask];
  vector<int16_t> sums(1 << N, 0);
  int64_t ans = 0;
  for (int mask = 1; mask < 1 << N; mask++) {
    int low = __builtin_ctz(mask);
    sums[mask] = int16_t(sums[mask ^ 1 << low] + (low + 1));
    int k = __builtin_popcount(mask);
    ans ^= int64_t(dp[mask].x) * k * sums[mask];
  }
  cout << ans << '\n';
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

For a sequence of strings [t_1, t_2, ..., t_m], let's define the function f([t_1, t_2, ..., t_m]) as the number of different strings (including the empty string) that are subsequences of at least one string t_i. f([]) = 0 (i. e. the number of such strings for an empty sequence is 0).

You are given a sequence of strings [s_1, s_2, ..., s_n]. Every string in this sequence consists of lowercase Latin letters and is sorted (i. e., each string begins with several (maybe zero) characters a, then several (maybe zero) characters b, ..., ends with several (maybe zero) characters z).

For each of 2^n subsequences of [s_1, s_2, ..., s_n], calculate the value of the function f modulo 998244353.

Input

The first line contains one integer n (1 ≤ n ≤ 23) — the number of strings.

Then n lines follow. The i-th line contains the string s_i (1 ≤ |s_i| ≤ 2 ⋅ 10^4), consisting of lowercase Latin letters. Each string s_i is sorted.

Output

Since printing up to 2^{23} integers would be really slow, you should do the following:

For each of the 2^n subsequences (which we denote as [s_{i_1}, s_{i_2}, ..., s_{i_k}]), calculate f([s_{i_1}, s_{i_2}, ..., s_{i_k}]), take it modulo 998244353, then multiply it by k ⋅ (i_1 + i_2 + ... + i_k). Print the XOR of all 2^n integers you get.

The indices i_1, i_2, ..., i_k in the description of each subsequences are 1-indexed (i. e. are from 1 to n).

Examples

Input


3
a
b
c


Output


92


Input


2
aa
a


Output


21


Input


2
a
a


Output


10


Input


2
abcd
aabb


Output


124


Input


3
ddd
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaabbbbbbbbbbbcccccccccccciiiiiiiiiiiiiiiiiiiiiiooooooooooqqqqqqqqqqqqqqqqqqvvvvvzzzzzzzzzzzz


Output


15706243380

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
template <const int MOD>
struct modular_int {
  int x;
  static vector<int> inverse_list;
  const static int inverse_limit;
  const static bool is_prime;
  modular_int() { x = 0; }
  template <typename T>
  modular_int(const T z) {
    x = (z % MOD);
    if (x < 0) x += MOD;
  }
  modular_int(const modular_int<MOD>* z) { x = z->x; }
  modular_int(const modular_int<MOD>& z) { x = z.x; }
  modular_int operator-(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = x - m.x;
    if (U.x < 0) U.x += MOD;
    return U;
  }
  modular_int operator+(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = x + m.x;
    if (U.x >= MOD) U.x -= MOD;
    return U;
  }
  modular_int& operator-=(const modular_int<MOD>& m) {
    x -= m.x;
    if (x < 0) x += MOD;
    return *this;
  }
  modular_int& operator+=(const modular_int<MOD>& m) {
    x += m.x;
    if (x >= MOD) x -= MOD;
    return *this;
  }
  modular_int operator*(const modular_int<MOD>& m) const {
    modular_int<MOD> U;
    U.x = (x * 1ull * m.x) % MOD;
    return U;
  }
  modular_int& operator*=(const modular_int<MOD>& m) {
    x = (x * 1ull * m.x) % MOD;
    return *this;
  }
  template <typename T>
  friend modular_int operator+(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) + p);
  }
  template <typename T>
  friend modular_int operator-(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) - p);
  }
  template <typename T>
  friend modular_int operator*(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) * p);
  }
  template <typename T>
  friend modular_int operator/(const T& l, const modular_int<MOD>& p) {
    return (modular_int<MOD>(l) / p);
  }
  int value() const { return x; }
  modular_int operator^(const modular_int<MOD>& cpower) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    int power = cpower.x;
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  modular_int operator^(long long power) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    if (power >= MOD && is_prime) {
      power %= (MOD - 1);
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  modular_int operator^(int power) const {
    modular_int<MOD> ans;
    ans.x = 1;
    modular_int<MOD> curr(this);
    if (curr.x <= 1) {
      if (power == 0) curr.x = 1;
      return curr;
    }
    while (power > 0) {
      if (power & 1) {
        ans *= curr;
      }
      power >>= 1;
      if (power) curr *= curr;
    }
    return ans;
  }
  template <typename T>
  modular_int& operator^=(T power) {
    modular_int<MOD> res = (*this) ^ power;
    x = res.x;
    return *this;
  }
  template <typename T>
  modular_int pow(T x) {
    return (*this) ^ x;
  }
  pair<long long, long long> gcd(const int a, const int b) const {
    if (b == 0) return {1, 0};
    pair<long long, long long> c = gcd(b, a % b);
    return {c.second, c.first - (a / b) * c.second};
  }
  inline void init_inverse_list() const {
    vector<int>& dp = modular_int<MOD>::inverse_list;
    dp.resize(modular_int<MOD>::inverse_limit + 1);
    int n = modular_int<MOD>::inverse_limit;
    dp[0] = 1;
    if (n > 1) dp[1] = 1;
    for (int i = 2; i <= n; ++i) {
      dp[i] = (dp[MOD % i] * 1ull * (MOD - MOD / i)) % MOD;
    }
  }
  modular_int<MOD> get_inv() const {
    if (modular_int<MOD>::inverse_list.size() <
        modular_int<MOD>::inverse_limit + 1)
      init_inverse_list();
    if (this->x <= modular_int<MOD>::inverse_limit) {
      return modular_int<MOD>::inverse_list[this->x];
    }
    pair<long long, long long> G = gcd(this->x, MOD);
    return modular_int<MOD>(G.first);
  }
  modular_int<MOD> operator-() const {
    modular_int<MOD> v(0);
    v -= (*this);
    return v;
  }
  modular_int operator/(const modular_int<MOD>& m) const {
    modular_int<MOD> U(this);
    U *= m.get_inv();
    return U;
  }
  modular_int& operator/=(const modular_int<MOD>& m) {
    (*this) *= m.get_inv();
    return *this;
  }
  bool operator==(const modular_int<MOD>& m) const { return x == m.x; }
  bool operator<(const modular_int<MOD>& m) const { return x < m.x; }
  template <typename T>
  bool operator==(const T& m) const {
    return (*this) == (modular_int<MOD>(m));
  }
  template <typename T>
  bool operator<(const T& m) const {
    return x < (modular_int<MOD>(m)).x;
  }
  template <typename T>
  bool operator>(const T& m) const {
    return x > (modular_int<MOD>(m)).x;
  }
  template <typename T>
  friend bool operator==(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x == m.x;
  }
  template <typename T>
  friend bool operator<(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x < m.x;
  }
  template <typename T>
  friend bool operator>(const T& x, const modular_int<MOD>& m) {
    return (modular_int<MOD>(x)).x > m.x;
  }
  friend istream& operator>>(istream& is, modular_int<MOD>& p) {
    int64_t val;
    is >> val;
    p.x = (val % MOD);
    if (p.x < 0) p.x += MOD;
    return is;
  }
  friend ostream& operator<<(ostream& os, const modular_int<MOD>& p) {
    return os << p.x;
  }
};
extern const int MOD = 998244353;
using mod_int = modular_int<MOD>;
template <typename T>
vector<T> mobius_transform(int n, vector<T> f) {
  assert(f.size() == (1 << n));
  for (int mask = 0; mask < (1 << n); mask++) {
    if ((__builtin_popcount(mask) % 2) == 1) {
      f[mask] *= -1;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int mask = 0; mask < (1 << n); mask++) {
      if ((mask & (1 << i)) != 0) {
        f[mask] += f[mask ^ (1 << i)];
      }
    }
  }
  for (int mask = 0; mask < (1 << n); mask++) {
    if ((__builtin_popcount(mask) % 2) == 1) {
      f[mask] *= -1;
    }
  }
  vector<T> mu(1 << n);
  for (int mask = 0; mask < (1 << n); mask++) mu[mask] = f[mask];
  return mu;
}
const int ALPHABET = 26;
const char MIN_CHAR = 'a';
const int S_MAX = 20005;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  vector<array<uint16_t, ALPHABET>> S(N);
  for (int i = 0; i < N; i++) {
    S[i].fill(0);
    string str;
    cin >> str;
    for (auto& ch : str) S[i][ch - MIN_CHAR]++;
  }
  vector<array<uint16_t, ALPHABET>> mins(1 << N);
  mins[0].fill(S_MAX);
  for (int mask = 1; mask < 1 << N; mask++) {
    int low = __builtin_ctz(mask);
    mins[mask] = mins[mask ^ 1 << low];
    for (int c = 0; c < ALPHABET; c++)
      mins[mask][c] = min(mins[mask][c], S[low][c]);
  }
  vector<mod_int> dp(1 << N, 1);
  dp[0] = 0;
  for (int mask = 1; mask < 1 << N; mask++)
    for (int x : mins[mask]) dp[mask] *= x + 1;
  dp = mobius_transform<mod_int>(N, dp);
  for (int mask = 1; mask < 1 << N; mask++)
    if (__builtin_popcount(mask) % 2 == 0) dp[mask] = -dp[mask];
  vector<int16_t> sums(1 << N, 0);
  int64_t ans = 0;
  for (int mask = 1; mask < 1 << N; mask++) {
    int low = __builtin_ctz(mask);
    sums[mask] = int16_t(sums[mask ^ 1 << low] + (low + 1));
    int k = __builtin_popcount(mask);
    ans ^= int64_t(dp[mask].x) * k * sums[mask];
  }
  cout << ans << '\n';
}

```