#define _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <chrono>
#include <random>
#include <numeric>
#include <queue>
#include <map>
#include <list>
#include <vector>
#include <string>
#include <stack>
#include <limits>
#include <climits>
#include <cassert>
#include <fstream>
#include <cstring>
#include <cmath>
#include <bitset>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <cstdio>
#include <ciso646>
#include <set>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <type_traits>

using namespace std;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define REP(i, n) for (int i = 0; i < (n); i++)
#define RREP(i, n) for (int i = (n)-1; i >= 0; i--)
#define inf 0x3f3f3f3f3f3f3f3f
#define ALL(a) (a).begin(), (a).end()
#define DEBUG(x) // cerr<<#x<<": "<<x<<endl
#define ll long long
#define ull unsigned long long
using pii = pair<ll, ll>;
#define eps 1e-14
#define SETUP cin.tie(0), ios::sync_with_stdio(false), cout << setprecision(15) << std::fixed;
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)

template <class T>
using vec2 = std::vector<vector<T>>;

//// bit ////
#ifdef _MSC_VER
#ifdef _WIN32
inline unsigned int __builtin_ctz(unsigned int x) { unsigned long r; _BitScanForward(&r, x); return r; }
inline unsigned int __builtin_clz(unsigned int x) { unsigned long r; _BitScanReverse(&r, x); return 31 - r; }
inline unsigned int __builtin_ffs(unsigned int x) { unsigned long r; return _BitScanForward(&r, x) ? r + 1 : 0; }
// inline unsigned int __builtin_popcount(unsigned int x){ return __popcnt(x); }
#ifdef _WIN64
inline unsigned long long __builtin_ctzll(unsigned long long x) { unsigned long r; _BitScanForward64(&r, x); return r; }
inline unsigned long long __builtin_clzll(unsigned long long x) { unsigned long r; _BitScanReverse64(&r, x); return 63 - r; }
inline unsigned long long __builtin_ffsll(unsigned long long x) { unsigned long r; return _BitScanForward64(&r, x) ? r + 1 : 0; }
inline unsigned long long __builtin_popcountll(unsigned long long x) { return __popcnt64(x); }
#else
inline unsigned int hidword(unsigned long long x) { return static_cast<unsigned int>(x >> 32); }
inline unsigned int lodword(unsigned long long x) { return static_cast<unsigned int>(x & 0xFFFFFFFF); }
inline unsigned long long __builtin_ctzll(unsigned long long x) { return lodword(x) ? __builtin_ctz(lodword(x)) : __builtin_ctz(hidword(x)) + 32; }
inline unsigned long long __builtin_clzll(unsigned long long x) { return hidword(x) ? __builtin_clz(hidword(x)) : __builtin_clz(lodword(x)) + 32; }
inline unsigned long long __builtin_ffsll(unsigned long long x) { return lodword(x) ? __builtin_ffs(lodword(x)) : hidword(x) ? __builtin_ffs(hidword(x)) + 32 : 0; }
// inline unsigned long long __builtin_popcountll(unsigned long long x) { return __builtin_popcount(lodword(x)) + __builtin_popcount(hidword(x)); }
#endif // _WIN64
#endif // _WIN32
#endif // _MSC_VER

namespace
{
	struct input_returnner
	{
		ll N;
		input_returnner(ll N_ = 0) : N(N_) {}
		template <typename T>
		operator vector<T>() const
		{
			vector<T> res(N);
			for (auto& a : res)
				cin >> a;
			return std::move(res);
		}
		template <typename T>
		operator T() const
		{
			T res;
			cin >> res;
			return res;
		}
		template <typename T>
		T operator-(T right) { return T(input_returnner()) - right; }
		template <typename T>
		T operator+(T right) { return T(input_returnner()) + right; }
		template <typename T>
		T operator*(T right) { return T(input_returnner())* right; }
		template <typename T>
		T operator/(T right) { return T(input_returnner()) / right; }
		template <typename T>
		T operator<<(T right) { return T(input_returnner()) << right; }
		template <typename T>
		T operator>>(T right) { return T(input_returnner()) >> right; }
	};
	template <typename T>
	input_returnner in() { return in<T>(); }
	input_returnner in() { return input_returnner(); }
	input_returnner in(ll N) { return std::move(input_returnner(N)); }
} // namespace

template <typename T>
istream& operator>>(istream& is, vector<T>& vec)
{
	for (T& x : vec)
		is >> x;
	return is;
}

template <typename T>
struct is_vector : std::false_type
{
};

template <typename T>
struct is_vector<std::vector<T>> : std::true_type
{
};

template <typename T>
constexpr bool is_vector_v = is_vector<T>::value;

template <typename T>
std::ostream& operator<<(std::ostream & out, const std::vector<T> & v)
{
	if (!v.empty())
	{
		for (int i = 0; i < v.size(); ++i)
		{
			out << v[i] << (i == v.size() - 1 ? "\n" : (is_vector_v<T> ? "" : ", "));
		}
	}
	return out;
}

namespace std
{
	// ref: https://stackoverflow.com/questions/7110301/generic-hash-for-tuples-in-unordered-map-unordered-set
	template <class T>
	inline void hash_combine(std::size_t& seed, T const& v)
	{
		seed ^= std::hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
	}

	// Recursive template code derived from Matthieu M.
	template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
	struct HashValueImpl
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
			hash_combine(seed, std::get<Index>(tuple));
		}
	};

	template <class Tuple>
	struct HashValueImpl<Tuple, 0>
	{
		static void apply(size_t& seed, Tuple const& tuple)
		{
			hash_combine(seed, std::get<0>(tuple));
		}
	};
	template <typename... TT>
	struct hash<std::tuple<TT...>>
	{
		size_t operator()(std::tuple<TT...> const& tt) const
		{
			size_t seed = 0;
			HashValueImpl<std::tuple<TT...>>::apply(seed, tt);
			return seed;
		}
	};

	template <class T, class U>
	class hash<std::pair<T, U>>
	{
	public:
		size_t operator()(const std::pair<T, U>& x) const
		{
			return hash<std::tuple<T, U>>()(std::tie(x.first, x.second));
		}
	};
} // namespace std

// ref: https://stackoverflow.com/questions/6245735/pretty-print-stdtuple
namespace aux
{
	template <std::size_t...>
	struct seq
	{
	};

	template <std::size_t N, std::size_t... Is>
	struct gen_seq : gen_seq<N - 1, N - 1, Is...>
	{
	};

	template <std::size_t... Is>
	struct gen_seq<0, Is...> : seq<Is...>
	{
	};

	template <class Ch, class Tr, class Tuple, std::size_t... Is>
	void print_tuple(std::basic_ostream<Ch, Tr>& os, Tuple const& t, seq<Is...>)
	{
		using swallow = int[];
		(void)swallow {
			0, (void(os << (Is == 0 ? "" : ", ") << std::get<Is>(t)), 0)...
		};
	}
} // namespace aux

template <class Ch, class Tr, class... Args>
auto operator<<(std::basic_ostream<Ch, Tr> & os, std::tuple<Args...> const& t)
-> std::basic_ostream<Ch, Tr> &
{
	os << "(";
	aux::print_tuple(os, t, aux::gen_seq<sizeof...(Args)>());
	return os << ")";
}

template <class S, class T>
std::ostream& operator<<(std::ostream & os, const std::pair<S, T> & p)
{
	return os << "(" << p.first << ", " << p.second << ")";
}

// ref: https://stackoverflow.com/questions/8542591/c11-reverse-range-based-for-loo�Fp
template <typename T>
struct reversion_wrapper
{
	T& iterable;
};

template <typename T>
auto begin(reversion_wrapper<T> w) { return std::rbegin(w.iterable); }

template <typename T>
auto end(reversion_wrapper<T> w) { return std::rend(w.iterable); }

template <typename T>
reversion_wrapper<T> REV(T && iterable) { return { iterable }; }

template <class T>
bool inside(T left, T val, T right)
{
	return left <= val and val < right;
}

template <class T>
T bitCount(T num)
{
	T res = 0;
	while (num > 0)
	{
		if (num & 1)
			++res;
		num >>= 1;
	}
	return res;
}

ll MOD = 1e9 + 7;
//ll MOD = 998244353;

void solve();

signed main()
{
	SETUP;
#ifdef _DEBUG
	while (true)
	{
#endif
		solve();
#ifdef _DEBUG
		cout << "-------" << endl;
	}
#endif
#ifdef _DEBUG
	system("pause");
#endif
	return 0;
}

#define int ll

// template

bool f(string & s, string & T) {
	REP(i, s.size()) {
		if (s[i] != '?' and s[i] != T[i]) {
			return false;
		}
	}
	return true;
}

void solve() {
	int N; cin >> N;
	vector<int> T(N); for (auto& a : T) cin >> a;
	vector<int> V(N); for (auto& a : V) cin >> a;

	vector<int> Tsum(N+1);
	Tsum[0] = 0;
	FOR(i, 1, N+1) Tsum[i] = Tsum[i - 1] + T[i-1];

	vector<tuple<int, int, int> > Vtuple;

	REP(i, N) {
		int from = Tsum[i];
		int to = Tsum[i + 1];
		int v = V[i];
		Vtuple.emplace_back(from, to, v);
	}
	Vtuple.emplace_back(-1, 0, 0);
	Vtuple.emplace_back(Tsum.back(), Tsum.back()+1, 0);

	vector<double> tv;
	for (double t = 0.0; t <= Tsum.back(); t += 0.5) {
		double mi = inf;
		for (auto& a : Vtuple) {
			int from, to, v; tie(from, to, v) = a;
			if (from <= t and t <= to) {
				mi = min(double(v), mi);
			}
			else if (to <= t) {
				mi = min((t - to) + v, mi);
			}
			else if (t <= from) {
				mi = min((from - t) + v, mi);
			}
		}
		tv.emplace_back(mi);
	}

	double res = 0;
	REP(i, tv.size()-1) {
		res += (tv[i] + tv[i+1]) * 0.5 / 2.0;
	}
	cout << res << endl;
}


Measured memory_bytes: 892