#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // MITライセンスなのでお借りしました // https://github.com/iwiwi/radix-heap /* The MIT License (MIT) Copyright (c) 2015 Takuya Akiba Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ namespace radix_heap { namespace internal { template class find_bucket_impl; template<> class find_bucket_impl { public: static inline constexpr size_t find_bucket(uint32_t x, uint32_t last) { return x == last ? 0 : 32 - __builtin_clz(x ^ last); } }; template<> class find_bucket_impl { public: static inline constexpr size_t find_bucket(uint64_t x, uint64_t last) { return x == last ? 0 : 64 - __builtin_clzll(x ^ last); } }; template inline constexpr size_t find_bucket(T x, T last) { return find_bucket_impl::find_bucket(x, last); } template class encoder_impl_integer; template class encoder_impl_integer { public: typedef KeyType key_type; typedef KeyType unsigned_key_type; inline static constexpr unsigned_key_type encode(key_type x) { return x; } inline static constexpr key_type decode(unsigned_key_type x) { return x; } }; template class encoder_impl_integer { public: typedef KeyType key_type; typedef typename std::make_unsigned::type unsigned_key_type; inline static constexpr unsigned_key_type encode(key_type x) { return static_cast(x) ^ (unsigned_key_type(1) << unsigned_key_type(std::numeric_limits::digits - 1)); } inline static constexpr key_type decode(unsigned_key_type x) { return static_cast (x ^ (unsigned_key_type(1) << (std::numeric_limits::digits - 1))); } }; template class encoder_impl_decimal { public: typedef KeyType key_type; typedef UnsignedKeyType unsigned_key_type; inline static constexpr unsigned_key_type encode(key_type x) { return raw_cast(x) ^ ((-(raw_cast(x) >> (std::numeric_limits::digits - 1))) | (unsigned_key_type(1) << (std::numeric_limits::digits - 1))); } inline static constexpr key_type decode(unsigned_key_type x) { return raw_cast (x ^ (((x >> (std::numeric_limits::digits - 1)) - 1) | (unsigned_key_type(1) << (std::numeric_limits::digits - 1)))); } private: template union raw_cast { public: constexpr raw_cast(T t) : t_(t) {} operator U() const { return u_; } private: T t_; U u_; }; }; template class encoder : public encoder_impl_integer::value> {}; template<> class encoder : public encoder_impl_decimal {}; template<> class encoder : public encoder_impl_decimal {}; } // namespace internal template> class radix_heap { public: typedef KeyType key_type; typedef EncoderType encoder_type; typedef typename encoder_type::unsigned_key_type unsigned_key_type; radix_heap() : size_(0), last_(), buckets_() { buckets_min_.fill(std::numeric_limits::max()); } void push(key_type key) { const unsigned_key_type x = encoder_type::encode(key); assert(last_ <= x); ++size_; const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(x); buckets_min_[k] = std::min(buckets_min_[k], x); } key_type top() { pull(); return encoder_type::decode(last_); } void pop() { pull(); buckets_[0].pop_back(); --size_; } size_t size() const { return size_; } bool empty() const { return size_ == 0; } void clear() { size_ = 0; last_ = key_type(); for (auto &b : buckets_) b.clear(); buckets_min_.fill(std::numeric_limits::max()); } void swap(radix_heap &a) { std::swap(size_, a.size_); std::swap(last_, a.last_); buckets_.swap(a.buckets_); buckets_min_.swap(a.buckets_min_); } private: size_t size_; unsigned_key_type last_; std::array, std::numeric_limits::digits + 1> buckets_; std::array::digits + 1> buckets_min_; void pull() { assert(size_ > 0); if (!buckets_[0].empty()) return; size_t i; for (i = 1; buckets_[i].empty(); ++i); last_ = buckets_min_[i]; for (unsigned_key_type x : buckets_[i]) { const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(x); buckets_min_[k] = std::min(buckets_min_[k], x); } buckets_[i].clear(); buckets_min_[i] = std::numeric_limits::max(); } }; template> class pair_radix_heap { public: typedef KeyType key_type; typedef ValueType value_type; typedef EncoderType encoder_type; typedef typename encoder_type::unsigned_key_type unsigned_key_type; pair_radix_heap() : size_(0), last_(), buckets_() { buckets_min_.fill(std::numeric_limits::max()); } void push(key_type key, const value_type &value) { const unsigned_key_type x = encoder_type::encode(key); assert(last_ <= x); ++size_; const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(x, value); buckets_min_[k] = std::min(buckets_min_[k], x); } void push(key_type key, value_type &&value) { const unsigned_key_type x = encoder_type::encode(key); assert(last_ <= x); ++size_; const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(x, std::move(value)); buckets_min_[k] = std::min(buckets_min_[k], x); } template void emplace(key_type key, Args&&... args) { const unsigned_key_type x = encoder_type::encode(key); assert(last_ <= x); ++size_; const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(std::piecewise_construct, std::forward_as_tuple(x), std::forward_as_tuple(args...)); buckets_min_[k] = std::min(buckets_min_[k], x); } key_type top_key() { pull(); return encoder_type::decode(last_); } value_type &top_value() { pull(); return buckets_[0].back().second; } void pop() { pull(); buckets_[0].pop_back(); --size_; } size_t size() const { return size_; } bool empty() const { return size_ == 0; } void clear() { size_ = 0; last_ = key_type(); for (auto &b : buckets_) b.clear(); buckets_min_.fill(std::numeric_limits::max()); } void swap(pair_radix_heap &a) { std::swap(size_, a.size_); std::swap(last_, a.last_); buckets_.swap(a.buckets_); buckets_min_.swap(a.buckets_min_); } private: size_t size_; unsigned_key_type last_; std::array>, std::numeric_limits::digits + 1> buckets_; std::array::digits + 1> buckets_min_; void pull() { assert(size_ > 0); if (!buckets_[0].empty()) return; size_t i; for (i = 1; buckets_[i].empty(); ++i); last_ = buckets_min_[i]; for (size_t j = 0; j < buckets_[i].size(); ++j) { const unsigned_key_type x = buckets_[i][j].first; const size_t k = internal::find_bucket(x, last_); buckets_[k].emplace_back(std::move(buckets_[i][j])); buckets_min_[k] = std::min(buckets_min_[k], x); } buckets_[i].clear(); buckets_min_[i] = std::numeric_limits::max(); } }; } // namespace radix_heap using namespace std; #define REP(i,a,b) for(int i=a;i<(int)b;i++) #define rep(i,n) REP(i,0,n) typedef long long ll; int main() { int N; cin >> N; double p[N], q[N]; rep(i, N) cin >> p[i], p[i] /= 1000; rep(i, N) cin >> q[i], q[i] /= 100; radix_heap::radix_heap h; rep(k, 1000) { rep(i, N) { h.push(-p[i] * pow(1-q[i], k) * q[i]); } } double res = 0.0; int cnt = 1; while(!h.empty()) { res += (cnt++) * -h.top(); h.pop(); } cout << setprecision(6) << res << endl; return 0; }