// たすけて~ #pragma warning(disable : 4146) #include #include #include #include #include #include #include #include #include namespace n91 { using i32 = std::int32_t; using i64 = std::int64_t; using u32 = std::uint32_t; using u64 = std::uint64_t; using isize = std::ptrdiff_t; using usize = std::size_t; using f64 = double; struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct revrep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr revrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; template auto md_vec(const usize n, const T &value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T &a, const T &b) noexcept { return a < b ? b - a : a - b; } template void chmin(T &a, const T &b) noexcept { if (b < a) a = b; } template void chmax(T &a, const T &b) noexcept { if (a < b) a = b; } template class rec_lambda { F f; public: rec_lambda(F &&f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; template T scan() { T ret; std::cin >> ret; return ret; } constexpr char eoln = '\n'; i64 floor_div(const i64 n, const i64 d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } i64 ceil_div(const i64 n, const i64 d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } #ifdef N91_LOCAL #define OJ_LOCAL(a, b) b #else #define OJ_LOCAL(a, b) a #endif } // namespace n91 #include namespace n91 { void main_() { using mint = atcoder::modint998244353; static constexpr usize MAX = OJ_LOCAL(100, 100); const usize n = scan(); std::vector s(MAX + 1, 0); for (const usize i : rep(0, n)) { s[scan()]++; } mint ans = 0; { auto dp = md_vec(n + 1, n + 1, mint()); dp[0][0] = 1; for (const usize i : revrep(1, MAX + 1)) { auto nx = md_vec(n + 1, n + 1, mint()); for (const usize z : rep(0, n + 1)) { for (const usize r : rep(0, n + 1)) { if (dp[z][r].val() == 0) { continue; } for (const usize c : rep(0, n + 1)) { if (c + r <= s[i]) { nx[z + (s[i] - c - r)][r] += dp[z][r]; } else if (r + (c + r - s[i]) <= n) { nx[z][r + (c + r - s[i])] += dp[z][r]; } } } } dp = std::move(nx); } for (const usize z : rep(0, n + 1)) { for (const usize r : rep(0, n + 1)) { if (z + s[0] >= r) { ans += (z + s[0] - r + 1) * dp[z][r]; } } } } { for (const usize min : rep(1, MAX + 1)) { if (s[min] == 0) { continue; } std::vector dp(n + 1, 0); for (const usize c : rep(1, s[min] + 1)) { dp[c] = 1; } for (const usize i : rep(min + 1, MAX + 1)) { std::vector nx(n + 1, 0); for (const usize c : rep(0, s[i] + 1)) { for (const usize j : rep(c, n + 1)) { nx[j] += dp[j - c]; } } dp = std::move(nx); } usize r = 1; usize amari = 0; for (const usize i : revrep(1, min)) { if(s[i] >= r)amari += s[i] - r; r *= 2; r -= std::min(r / 2, s[i]); chmin(r, n + 1); } r -= std::min(r, s[0]); r -= std::min(r, amari); for (const usize j : rep(0, n + 1)) { if (j < r) { ans -= dp[j]; } } } } if (s[0] == 0 && s[1] == 0) { ans += 1; } ans -= 1; std::cout << ans.val() << eoln; } } // namespace n91 int main() { //* std::ios::sync_with_stdio(false); std::cin.tie(nullptr); //*/ std::cout << std::fixed << std::setprecision(20); n91::main_(); return 0; }