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>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const int MOD = 1000000007;
const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};

struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

template<int mod>
struct Mod_Int{
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    Mod_Int &operator += (const Mod_Int &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator -= (const Mod_Int &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator *= (const Mod_Int &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator /= (const Mod_Int &p){
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator ++ () {return *this += Mod_Int(1);}

    Mod_Int operator ++ (int){
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator -- () {return *this -= Mod_Int(1);}

    Mod_Int operator -- (int){
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator - () const {return Mod_Int(-x);}

    Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;}

    Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;}

    Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;}

    Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;}

    bool operator == (const Mod_Int &p) const {return x == p.x;}

    bool operator != (const Mod_Int &p) const {return x != p.x;}

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod-2);
    }

    Mod_Int pow(long long k) const{
        Mod_Int now = *this, ret = 1;
        for(; k > 0; k >>= 1, now *= now){
            if(k&1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }

    friend istream &operator >> (istream &is, Mod_Int &p){
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

int main(){
    int N; cin >> N;

    vector<int> c(26);
    rep(i, 26) cin >> c[i];

    int n = N/2, m = N-n;
    mint ans = mint(25).pow(N-2)*mint(26).pow(2);
    rep(i, 26){
        vector<mint> dp1(N+1, 0), dp2(N+1, 0);
        dp1[0] = 1;
        rep(j, N){
            vector<mint> tmp1(N+1, 0), tmp2(N+1, 0);
            rep(k, N){
                tmp2[k+1] += dp1[k];
                tmp1[k] += dp1[k]*24+dp2[k]*25;
                if(j == 0) tmp1[k] += dp1[k];
                if(j == n){
                    tmp1[k] += dp1[k];
                    tmp2[k+1] += dp2[k];
                }
            }
            swap(dp1, tmp1), swap(dp2, tmp2);
        }
        rep2(j, c[i]+1, N) ans -= dp1[j]+dp2[j];
    }

    vector<vector<mint>> dp1(N+1, vector<mint>(N+1, 0)), dp2(N+1, vector<mint>(N+1, 0)), dp3(N+1, vector<mint>(N+1, 0));
    dp1[0][0] = 1;
    rep(i, N){
        vector<vector<mint>> tmp1(N+1, vector<mint>(N+1, 0)), tmp2(N+1, vector<mint>(N+1, 0)), tmp3(N+1, vector<mint>(N+1, 0));
        rep(j, N) rep(k, N){
            tmp2[j+1][k] += dp1[j][k]+dp3[j][k];
            tmp3[j][k+1] += dp2[j][k]+dp1[j][k];
            tmp1[j][k] += dp1[j][k]*23+dp2[j][k]*24+dp3[j][k]*24;
            if(i == 0) tmp1[j][k] += dp1[j][k];
            if(i == n){
                tmp1[j][k] += dp1[j][k];
                tmp2[j+1][k] += dp2[j][k];
                tmp3[j][k+1] += dp3[j][k];
            }
        }
        swap(dp1, tmp1), swap(dp2, tmp2), swap(dp3, tmp3);
    }

    rep(i, 26) rep(j, i){
        rep2(k, c[i]+1, N){
            rep2(l, c[j]+1, N){
                ans += dp1[k][l]+dp2[k][l]+dp3[k][l];
            }
        }
    }

    cout << ans << '\n';
}