#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < int(n); i++)
#define rep1(i,n) for (int i = 1; i <= int(n); i++)
#define repR(i,n) for (int i = int(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = int(n); i >= 1; i--)
#define loop(i,a,b) for (int i = int(a); i < int(b); i++)
#define loop1(i,a,b) for (int i = int(a); i <= int(b); i++)
#define loopR(i,a,b) for (int i = int(b)-1; i >= int(a); i--)
#define loop1R(i,a,b) for (int i = int(b); i >= int(a); i--)
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#define cauto const auto
#ifdef LOCAL
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", _dmp_(#__VA_ARGS__, __VA_ARGS__);
void _dmp_(const char*) { cerr << endl; }
template <class T, class... U>
void _dmp_(const char *s, T const& x, U const& ...y) { const char *o = "({[", *e = "]})"; for (int i = 0; *s != '\0'; cerr << *s++) { if (count(o,o+3,*s)) i++; if (count(e,e+3,*s)) i--; if (!i && *s == ',') break; } cerr << " = " << x; if (*s == ',') cerr << ", ", s++; _dmp_(s, y...); }
#else
#define dump(...)
#endif
using ll = long long;
#define int ll
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
#define CONAINER_OUTPUT os << "{"; for (auto const& x : v) os << " " << x; return os << " }";
template <class T> ostream& operator<<(ostream& os, vector<T> const& v) { CONAINER_OUTPUT }
template <class T> ostream& operator<<(ostream& os, deque<T> const& v) { CONAINER_OUTPUT }
template <class T> ostream& operator<<(ostream& os, set<T> const& v) { CONAINER_OUTPUT }
template <class T, class U> ostream& operator<<(ostream& os, map<T,U> const& v) { CONAINER_OUTPUT }
#undef CONAINER_OUTPUT
template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S> const& p) { return is >> p.first >> p.second; }
struct _Init_ { _Init_() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); } } _init_;

template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
#define YesNo(c) ((c) ? "Yes" : "No")
////////////////////////////////

const int NN = 205, MM = 4e4 + 5, inf = 1e10;
double dp[NN][MM];
int n;
int t[NN], v[NN], vm[MM];

int32_t main() {
    cin >> n;
    rep (i,n) cin >> t[i+1], t[i+1] *= 2;
    rep (i,n) cin >> v[i], v[i] *= 2;

    rep (i,n) t[i+1] += t[i];
    const int total = t[n];
    
    loop1 (t,0,total) vm[t] = inf;
    rep (i,n) loop1 (s,t[i],t[i+1]) chmin(vm[s], v[i]);

    rep (i,NN) rep (j,MM) dp[i][j] = -inf;
    dp[0][0] = 0;
    rep1 (s,total) loop1 (u,0,vm[s]) {
        chmax(dp[u][s], dp[u+1][s-1]+u+0.5);
        chmax(dp[u][s], dp[u][s-1]+u);
        if (u >= 1) chmax(dp[u][s], dp[u-1][s-1]+u-0.5);
    }
    cout << dp[0][total]/4.0 << endl;
}


Measured memory_bytes: 64640