#include 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; using pil = pair; using pli = pair; using pll = pair; //const int MOD = 1000000007; const int MOD = 998244353; const int inf = (1<<30)-1; const ll INF = (1LL<<60)-1; template bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;}; template 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 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(a); return is; } }; using mint = Mod_Int<998244353>; template struct Number_Theorem_Transform{ using T = Mod_Int; vector r, ir; Number_Theorem_Transform(){ r.resize(30), ir.resize(30); for(int i = 0; i < 30; i++){ r[i] = -T(primitive_root).pow((mod-1)>>(i+2)); ir[i] = r[i].inverse(); } } void ntt(vector &a, int n) const{ assert((n&(n-1)) == 0); a.resize(n); for(int k = n; k >>= 1;){ T w = 1; for(int s = 0, t = 0; s < n; s += 2*k){ for(int i = s, j = s+k; i < s+k; i++, j++){ T x = a[i], y = w*a[j]; a[i] = x+y, a[j] = x-y; } w *= r[__builtin_ctz(++t)]; } } } void intt(vector &a, int n) const{ assert((n&(n-1)) == 0); a.resize(n); for(int k = 1; k < n; k <<= 1){ T w = 1; for(int s = 0, t = 0; s < n; s += 2*k){ for(int i = s, j = s+k; i < s+k; i++, j++){ T x = a[i], y = a[j]; a[i] = x+y, a[j] = w*(x-y); } w *= ir[__builtin_ctz(++t)]; } } T inv = T(n).inverse(); for(auto &e: a) e *= inv; } vector convolve(vector a, vector b) const{ int k = (int)a.size()+(int)b.size()-1, n = 1; while(n < k) n <<= 1; ntt(a, n), ntt(b, n); for(int i = 0; i < n; i++) a[i] *= b[i]; intt(a, n), a.resize(k); return a; } }; Number_Theorem_Transform<998244353, 3> NTT; int main(){ int N; cin >> N; vector A(N); rep(i, N) cin >> A[i]; int MAX = 1000000; vector cnt(MAX+1, 0); rep(i, N) cnt[A[i]]++; rep(i, N) A.eb(-A[i]); mint r = 86583718; //虚数単位 mint ans = 0; rep2(i, 1, MAX){ if(cnt[i] == 0) continue; vector f(N+1, 0); f[0] = 1; each(e, A){ if(e == i) continue; mint x = mint(e-i).inverse(); x /= r; vector g(N+1); g[0] = -x; rep(i, N) g[i+1] = g[i]*x; f = NTT.convolve(f, g); f.resize(N+1); } ans += f[cnt[i]-1]*r*2; } cout << ans << '\n'; }