Problem: You have c_1 letters 'a', c_2 letters 'b', ..., c_{26} letters 'z'. You want to build a beautiful string of length n from them (obviously, you cannot use the i-th letter more than c_i times). Each c_i is greater than n/3.

A string is called beautiful if there are no palindromic contiguous substrings of odd length greater than 1 in it. For example, the string "abacaba" is not beautiful, it has several palindromic substrings of odd length greater than 1 (for example, "aca"). Another example: the string "abcaa" is beautiful.

Calculate the number of different strings you can build, and print the answer modulo 998244353.

Input

The first line contains one integer n (3 ≤ n ≤ 400).

The second line contains 26 integers c_1, c_2, ..., c_{26} (n/3 < c_i ≤ n).

Output

Print one integer — the number of strings you can build, taken modulo 998244353.

Examples

Input


4
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2


Output


422500


Input


3
2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 3 2 2 3 2 2


Output


16900


Input


400
348 322 247 158 209 134 151 267 268 176 214 379 372 291 388 135 147 304 169 149 193 351 380 368 181 340


Output


287489790

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#ifdef ALGO
#include "el_psy_congroo.hpp"
#else
#define DUMP(...) 1145141919810
#define CHECK(...) (__VA_ARGS__)
#endif

template<int MOD>
struct Integral {
  int v_ = 0;

  template<typename T> Integral(T v) : v_(norm(v)) {  // Implicit conversion is allowed.
    static_assert(std::is_integral<T>::value, "input should be an integral.");
  }
  Integral() = default;
  ~Integral() = default;

  template<typename T> T norm(T v) const {
    if constexpr(std::is_same<long long, T>::value) {
      v %= MOD;
      if (v < 0) v += MOD;
    } else {
      if (v >= MOD) v -= MOD;
      if (v < 0) v += MOD;
      if (v >= MOD || v < 0) {
        v %= MOD;
        if (v < 0) v += MOD;
      }
    }
    return v;
  }

  int val() const { return v_; }
  Integral& operator += (const Integral& rhs) { v_ += rhs.val(); if (v_ >= MOD) v_ -= MOD; return *this; }
  Integral& operator -= (const Integral& rhs) { v_ += MOD - rhs.val(); if (v_ >= MOD) v_ -= MOD; return *this; }
  Integral& operator *= (const Integral& rhs) { v_ = v_ * 1LL * rhs.val() % MOD; return *this; }
  Integral& operator /= (const Integral& rhs) { v_ = v_ * 1LL * rhs.inv().val() % MOD; return *this; }
  Integral operator + (const Integral& rhs) const { Integral ret = *this; return ret += rhs; }
  Integral operator - (const Integral& rhs) const { Integral ret = *this; return ret -= rhs; }
  Integral operator * (const Integral& rhs) const { Integral ret = *this; return ret *= rhs; }
  Integral operator / (const Integral& rhs) const { Integral ret = *this; return ret /= rhs; }
  bool operator == (const Integral& rhs) const { return val() == rhs.val(); }
  bool operator != (const Integral& rhs) const { return !(*this == rhs); }
  const Integral operator - () const { return Integral(-val()); }
  const Integral& operator ++ () { v_ += 1; if (v_ >= MOD) v_ -= MOD; return *this; }
  const Integral operator ++ (int) { Integral ret = *this; ++(*this); return ret; }
  const Integral& operator -- () { v_ += MOD - 1; if (v_ >= MOD) v_ -= MOD; return *this; }
  const Integral operator -- (int) { Integral ret = *this; --(*this); return ret; }

  Integral power(long long b) const {
    long long ret = 1 % MOD, a = v_;
    for ( ; b; b >>= 1, a = a * a % MOD) if (b & 1) ret = ret * a % MOD; return ret;
  }
  Integral inv() const { return power(MOD - 2); }
};

template<int MOD>
std::string to_string(const Integral<MOD>& v) {
  return std::string("{") + std::to_string(v.val()) + "}";
}

template<int MOD, bool kAllowBruteForce = false>
struct Binomial {
  std::vector<Integral<MOD>> factor, inv_factor;

  explicit Binomial(int n = 0) : factor(n + 1), inv_factor(n + 1) {
    factor[0] = 1;
    for (int i = 1; i <= n; ++i) factor[i] = factor[i - 1] * i;
    inv_factor[n] = factor[n].inv();
    for (int i = n; i >= 1; --i) inv_factor[i - 1] = inv_factor[i] * i;
  }
  ~Binomial() = default;

  template<typename T>
  Integral<MOD> operator () (T a, T b) const {
    if (a < b || b < 0) return 0;
    if (a < factor.size()) return factor[a] * inv_factor[b] * inv_factor[a - b];
    if constexpr(!kAllowBruteForce) {
      throw std::out_of_range("Binomial");
    } else {
      b = std::min(b, a - b);
      Integral<MOD> ret = 1;
      for (T i = 1; i <= b; ++i) ret = ret * (a + 1 - i) / i;
      return ret;
    }
  }
};

template<int MOD>
struct PowerTable : public std::vector<Integral<MOD>> {
  PowerTable(int n, const Integral<MOD>& g) {
    static_assert(sizeof(PowerTable) == sizeof(std::vector<Integral<MOD>>), "");
    this->resize(n + 1);
    this->at(0) = 1;
    this->at(1) = g;
    for (int i = 2; i < this->size(); ++i) this->at(i) = this->at(i - 1) * this->at(1);
  }
};

const int MOD = 998244353;
using Mint = Integral<MOD>;
using Binom = Binomial<MOD>;

Binom binom(400);
// PowerTable<MOD> pw2(200000, 2);

int n;
int c[26];

using State = std::array<Mint[400 + 5][3][3], 400 + 5>;

State dp[2];

int solve() {
  State& f = dp[0];
  State& g = dp[1];
  f[0][0][0][0] = 1;
  for (int at = 0; at < n; ++at) {
    for (int i = 0; i <= at; ++i) {
      for (int j = 0; i + j <= at; ++j) {
        for (int A = 0; A < 3; ++A) {
          for (int B = 0; B < 3; ++B) if (f[i][j][A][B].val()) {
            const Mint& val = f[i][j][A][B];
            if (at < 2 || A != 0) {
              g[i + 1][j][B][0] += val;
            }
            if (at < 2 || A != 1) {
              g[i][j + 1][B][1] += val;
            }
            g[i][j][B][2] += val * (at >= 2 && A == 2 ? 23 : 24);
          }
        }
      }
    }
    f.swap(g);
    memset(&g, 0, sizeof(State));
  }
  Mint result = 0;
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; i + j <= n; ++j) {
      for (int A = 0; A < 3; ++A) {
        for (int B = 0; B < 3; ++B) {
          result += f[i][j][A][B];
        }
      }
    }
  }
  for (int C = 0; C < 26; ++C) {
    for (int i = c[C] + 1; i <= n; ++i) {
      for (int j = 0; i + j <= n; ++j) {
        for (int A = 0; A < 3; ++A) {
          for (int B = 0; B < 3; ++B) {
            result -= f[i][j][A][B];
          }
        }
      }
    }
  }
  for (int C = 0; C < 26; ++C) {
    for (int D = C + 1; D < 26; ++D) {
      for (int i = c[C] + 1; i <= n; ++i) {
        for (int j = c[D] + 1; i + j <= n; ++j) {
          for (int A = 0; A < 3; ++A) {
            for (int B = 0; B < 3; ++B) {
              result += f[i][j][A][B];
            }
          }
        }
      }
    }
  }
  return result.val();
}

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::istream& reader = std::cin;

  reader >> n;
  for (int i = 0; i < 26; ++i) {
    reader >> c[i];
  }
  std::cout << solve() << std::endl;
}