#include <bits/stdc++.h>
using ll = long long;
// #define int ll
#define FOR(i, a, b) for (int i = (a); i < int(b); ++i)
#define RFOR(i, a, b) for (int i = (b) - 1; i >= int(a); --i)
#define rep(i, n) FOR(i, 0, n)
#define rep1(i, n) FOR(i, 1, int(n) + 1)
#define rrep(i, n) RFOR(i, 0, n)
#define rrep1(i, n) RFOR(i, 1, int(n) + 1)
#define all(c) begin(c), end(c)

std::string highlight(std::string s) {
#ifdef _MSC_VER
    return s;
#else
    return "\033[33m" + s + "\033[0m";
#endif
}

#ifdef LOCAL
#define dump(...)                                         \
    do {                                                  \
        std::ostringstream os;                            \
        os << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; \
        print_to(os, ", ", "\n", __VA_ARGS__);            \
        std::cerr << highlight(os.str());                 \
    } while (0)
#define dump_(a)                                          \
    do {                                                  \
        std::ostringstream os;                            \
        os << __LINE__ << ":\t" << #a << " = [";          \
        print_to_(os, ", ", "]\n", all(a));               \
        std::cerr << highlight(os.str());                 \
    } while (0)
#else
#define dump(...)
#define dump_(...)
#endif

template <typename T>
void print_to(std::ostream &os, const char *, const char *tail, const T &fst) {
    os << fst << tail;
}
template <typename Fst, typename... Rst>
void print_to(std::ostream &os, const char *del, const char *tail, const Fst &fst, const Rst &... rst) {
    os << fst << del;
    print_to(os, del, tail, rst...);
}
template <typename Iter>
void print_to_(std::ostream &os, const char *del, const char *tail, Iter bgn, Iter end) {
    for (Iter it = bgn; it != end;) {
        os << *it;
        if (++it != end) {
            os << del;
        } else {
            os << tail;
        }
    }
}
template <typename Fst, typename... Rst>
void println(const Fst &fst, const Rst &... rst) {
    print_to(std::cout, "\n", "\n", fst, rst...);
}
template <typename Fst, typename... Rst>
void print(const Fst &fst, const Rst &... rst) {
    print_to(std::cout, " ", "\n", fst, rst...);
}
template <typename Iter>
void println_(Iter bgn, Iter end) {
    print_to_(std::cout, "\n", "\n", bgn, end);
}
template <typename Iter>
void print_(Iter bgn, Iter end) {
    print_to_(std::cout, " ", "\n", bgn, end);
}

// const int MOD = 1000000007;
namespace trush {
    int _ = (std::cout.precision(10), std::cout.setf(std::ios::fixed), std::cin.tie(0),
             std::ios::sync_with_stdio(0), 0);
}

using namespace std;

int main() {
    int n;
    while (cin >> n) {
        vector<double> t(n), v(n);
        rep(i, n) {
            cin >> t[i];
        }
        rep(i, n) {
            cin >> v[i];
        }
        t.push_back(0);
        v.push_back(0);

        double ans = 0;
        double t1 = 0;
        double v1 = 0;
        rep(i, n) {
            double vm = v[i];
            double v2 = min(vm, v1 + t[i]);
            double t2 = t1 + t[i];
            double p = v1;
            FOR(j, i, n) {
                p += t[j];
                // dump(p - (cur_t + t[i]));
                double x = v[j+1] + (p - (v1 + t[i]));
                v2 = min(v2, x);
            }
            // dump(cur_s, end_s);
            // cur_s -> v[i] -> cur_s + t[i]

            double ta = t1 + (vm - v1);
            double tb = t2 - (vm - v2);
            if (ta <= tb) {
                ans += (v1 + vm) * (ta - t1) / 2;
                ans += vm * (tb - ta);
                ans += (v2 + vm) * (t2 - tb) / 2;
            } else {
                double tc = (ta + tb) / 2;
                double vc = v1 + (tc - t1);
                dump(t1, tc, t2);
                dump(v1, vc, v2);
                ans += (v1 + vc) * (tc - t1) / 2;
                ans += (vc + v2) * (t2 - tc) / 2;
            }

            t1 += t[i];
            v1 = v2;
        }
        print(ans);
    }
}

Measured memory_bytes: 384