#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#define rep(i, n) for(int i=0; i<(n); ++i)
#define FOR(i, m, n) for(int i=(m); i<(n); ++i)
#define rrep(i, m, n) for(int i=(m); i>=(n); --i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define mp make_pair
#define pb push_back
#define eb emplace_back

using namespace std;
using LL = long long;		using VB = vector<bool>;
using VI = vector<int>;		using VL = vector<LL>;
using VS = vector<string>;	using VD = vector<double>;
using VVI = vector<VI>;		using VVL = vector<VL>;
using PII = pair<int, int>;	using PLL = pair<LL, LL>;
using VP = vector<PII>;		using VPL = vector<PLL>;
const int inf = (int)1e9;
const LL inf_ll = (LL)1e18, MOD = 1000000007;
const double PI = acos(-1.0), EPS = 1e-12;

template<class T>void Sort(T& a) { sort(all(a)); }
template<class T>void RSort(T& a) { sort(rall(a)); }
template<class T>void Reverse(T& a) { reverse(all(a)); }
template<class T>void Unique(T& a) { a.erase(unique(all(a)), a.end()); }
template<class T>T Sorted(T a) { Sort(a); return a; }
template<class T>T RSorted(T a) { RSort(a); return a; }
template<class T>T Reversed(T a) { Reverse(a); return a; }
template<class T>T Uniqued(T a) { Unique(a); return a; }
template<class T>auto Max(const T& a) { return *max_element(all(a)); }
template<class T>auto Min(const T& a) { return *min_element(all(a)); }
template<class T>int MaxPos(const T& a) { return max_element(all(a)) - a.begin(); }
template<class T>int MinPos(const T& a) { return min_element(all(a)) - a.begin(); }
template<class T, class U>int Count(const T& a, const  U& v) { return count(all(a), v); }
template<class T, class U>int Find(const T& a, const U& v) { auto pos = find(all(a), v); return pos == a.end() ? -1 : pos - a.begin(); }
template<class T, class U>U Sum(const T& a, const U& v) { return accumulate(all(a), v); }
template<class T, class U>int Lower(const T& a, const U& v) { return lower_bound(all(a), v) - a.begin(); }
template<class T, class U>int Upper(const T& a, const U& v) { return upper_bound(all(a), v) - a.begin(); }
template<class T, class P>void RemoveIf(T& a, P f) { a.erase(remove_if(all(a), f), a.end()); }
template<class T>T Age(T n, T m) { return (n + m - 1) / m; }
template<class T>T Age2(T n, T m) { return Age(n, m) * m; }
template<class T>T Gcd(T n, T m) { return m ? Gcd(m, n % m) : n; }
template<class T>T Lcm(T n, T m) { return n / Gcd(n, m) * m; }
template<class T>T Pow(T a, T n) { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; }return r; }
template<class T>T Powmod(T a, T n, T m = MOD) { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; }
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
template<class T>bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
string operator*(string s, int n) { string ret; rep(i, n)ret += s; return ret; }

// --- input --- //
#if defined(_MSC_VER) || defined(ONLINE_JUDGE)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
inline int gc() { return getchar_unlocked(); }
template<class T>inline void InputF(T& v) { cin >> v; }
inline void InputF(char& v) { while (isspace(v = gc())); }
inline void InputF(string& v) {
	char c; for (InputF(c); !isspace(c); c = gc())v += c;
}
inline void InputF(int& v) {
	int k = 1; v = 0; char c; InputF(c);
	if (c == '-') { k = -1; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	v *= k;
}
inline void InputF(long long& v) {
	int k = 1; v = 0; char c; InputF(c);
	if (c == '-') { k = -1; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	v *= k;
}
inline void InputF(double& v) {
	double dp = 1; int k = 1; bool adp = false; v = 0; char c; InputF(c);
	if (c == '-') { k = -1; c = gc(); }
	for (; isdigit(c) || c == '.'; c = gc()) {
		if (c == '.')adp = true;
		else if (adp)v += (c - '0') * (dp *= 0.1);
		else v = v * 10 + (c - '0');
	}
	v *= k;
}
template<class T, class U>inline void InputF(pair<T, U>& v) {
	InputF(v.first); InputF(v.second);
}
template<class T>inline void InputF(vector<T>& v) {
	for (auto& e : v)InputF(e);
}
struct InputV {
	int n, m;
	InputV(int N) :n(N), m(0) {}
	InputV(pair<int, int> N) :n(N.first), m(N.second) {}
	template<class T>operator vector<T>() {
		vector<T> v(n); InputF(v); return v;
	}
	template<class T>operator vector<vector<T>>() {
		vector<vector<T>> v(n, vector<T>(m)); InputF(v); return v;
	}
};
struct Input {
	template<class T>operator T() { T v; InputF(v); return v; }
	InputV operator[](int n) { return InputV(n); }
	InputV operator[](pair<int, int> n) { return InputV(n); }
}in;

// --- output --- //
struct BoolStr {
	const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {}
}Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {}
}spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{ Yes }; DivStr D{ spc }; bool isPrint = true;
	void p(double v) { printf("%.20f", v); }
	void p(int v) { printf("%d", v); }	void p(LL v) { printf("%lld", v); }
	void p(char v) { putchar(v); }		void p(bool v) { printf(v ? B.t : B.f); }
	template<class T>void p(const T& v) { cout << v; }
	template<class T, class U>void p(const pair<T, U>& v) { p(v.first); printf(D.d); p(v.second); }
	template<class T>void p(const vector<T>& v) { rep(i, sz(v)) { if (i)printf(D.d); p(v[i]); } }
	template<class T>void p(const vector<vector<T>>& v) { rep(i, sz(v)) { if (i)printf(D.l); p(v[i]); } }
	void p(const BoolStr& v) { B = v; isPrint = false; } void p(const DivStr& v) { D = v; isPrint = false; }
public:
	void operator()() { printf(D.l); }
	template<class H>void operator()(H&& h) {
		p(h); if (isPrint)printf(D.l); isPrint = true; B = Yes; D = spc;
	}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		p(h); if (isPrint)printf(D.d); isPrint = true; operator()(forward<T>(t)...);
	}
}out;

#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) (void(0))
#endif


int main() {
	int n = in;
	VI T = in[n], v = in[n];
	v.insert(v.begin(), 0); v.pb(0);

	FOR(i, 1, n + 1) {
		chmin(v[i], v[i - 1] + T[i - 1]);
	}
	rrep(i, n, 1) {
		chmin(v[i], v[i + 1] + T[i - 1]);
	}

	VI t(n + 1);
	FOR(i, 1, n + 1)t[i] = t[i - 1] + T[i - 1];

	double ans = 0;
	rep(i, n) {
		FOR(j, t[i], t[i + 1]) {
			double d1 = v[i] + 0.5 + j - t[i];
			double d2 = v[i + 1];
			double d3 = v[i + 2] - 0.5 + t[i + 1] - j;
			ans += min({ d1 - 0.25,d2,d3 + 0.25 }) * 0.5;
			ans += min({ d1 + 0.25,d2,d3 - 0.25 }) * 0.5;
		}
	}
	out(ans);
}

Measured memory_bytes: 384