#include <iostream>
#include <algorithm>
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <array>
#include <unordered_map>
#include <complex>
#include <deque>
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>
#include <tuple>
#include <cstring>
using namespace std;

#define forr(x,arr) for(auto&& x:arr)
#define _overload3(_1,_2,_3,name,...) name
#define _rep2(i,n) _rep3(i,0,n)
#define _rep3(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload3(__VA_ARGS__,_rep3,_rep2,)(__VA_ARGS__)
#define _rrep2(i,n) _rrep3(i,0,n)
#define _rrep3(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define rrep(...) _overload3(__VA_ARGS__,_rrep3,_rrep2,)(__VA_ARGS__)
#define all(x) (x).begin(),(x).end()
#define bit(n) (1LL<<(n))
#define sz(x) ((int)(x).size())
#define TEN(n) ((ll)(1e##n))
#define fst first
#define snd second

string DBG_DLM(int &i){return(i++==0?"":", ");}
#define DBG_B(exp){int i=0;os<<"{";{exp;}os<<"}";return os;}
template<class T>ostream&operator<<(ostream&os,vector<T>v);
template<class T>ostream&operator<<(ostream&os,set<T>v);
template<class T>ostream&operator<<(ostream&os,queue<T>q);
template<class T>ostream&operator<<(ostream&os,priority_queue<T>q);
template<class T,class K>ostream&operator<<(ostream&os,pair<T,K>p);
template<class T,class K>ostream&operator<<(ostream&os,map<T,K>mp);
template<class T,class K>ostream&operator<<(ostream&os,unordered_map<T,K>mp);
template<int I,class TPL>void DBG(ostream&os,TPL t){}
template<int I,class TPL,class H,class...Ts>void DBG(ostream&os,TPL t){os<<(I==0?"":", ")<<get<I>(t);DBG<I+1,TPL,Ts...>(os,t);}
template<class T,class K>void DBG(ostream&os,pair<T,K>p,string delim){os<<"("<<p.first<<delim<<p.second<<")";}
template<class...Ts>ostream&operator<<(ostream&os,tuple<Ts...>t){os<<"(";DBG<0,tuple<Ts...>,Ts...>(os,t);os<<")";return os;}
template<class T,class K>ostream&operator<<(ostream&os,pair<T,K>p){DBG(os,p,", ");return os;}
template<class T>ostream&operator<<(ostream&os,vector<T>v){DBG_B(forr(t,v){os<<DBG_DLM(i)<<t;});}
template<class T>ostream&operator<<(ostream&os,set<T>s){DBG_B(forr(t,s){os<<DBG_DLM(i)<<t;});}
template<class T>ostream&operator<<(ostream&os,queue<T>q){DBG_B(for(;q.size();q.pop()){os<<DBG_DLM(i)<<q.front();});}
template<class T>ostream&operator<<(ostream&os,priority_queue<T>q){DBG_B(for(;q.size();q.pop()){os<<DBG_DLM(i)<<q.top();});}
template<class T,class K>ostream&operator<<(ostream&os,map<T,K>m){DBG_B(forr(p,m){os<<DBG_DLM(i);DBG(os,p,"->");});}
template<class T,class K>ostream&operator<<(ostream&os,unordered_map<T,K>m){DBG_B(forr(p,m){os<<DBG_DLM(i);DBG(os,p,"->");});}
#define DBG_OVERLOAD(_1,_2,_3,_4,_5,_6,macro_name,...)macro_name
#define DBG_LINE(){char s[99];sprintf(s,"line:%3d | ",__LINE__);cerr<<s;}
#define DBG_OUTPUT(v){cerr<<(#v)<<"="<<(v);}
#define DBG1(v,...){DBG_OUTPUT(v);}
#define DBG2(v,...){DBG_OUTPUT(v);cerr<<", ";DBG1(__VA_ARGS__);}
#define DBG3(v,...){DBG_OUTPUT(v);cerr<<", ";DBG2(__VA_ARGS__);}
#define DBG4(v,...){DBG_OUTPUT(v);cerr<<", ";DBG3(__VA_ARGS__);}
#define DBG5(v,...){DBG_OUTPUT(v);cerr<<", ";DBG4(__VA_ARGS__);}
#define DBG6(v,...){DBG_OUTPUT(v);cerr<<", ";DBG5(__VA_ARGS__);}
#define DEBUG0(){DBG_LINE();cerr<<endl;}
#ifdef LOCAL
#define out(...){DBG_LINE();DBG_OVERLOAD(__VA_ARGS__,DBG6,DBG5,DBG4,DBG3,DBG2,DBG1)(__VA_ARGS__);cerr<<endl;}
#else
#define out(...)
#endif

using ll=long long;
using pii=pair<int,int>;using pll=pair<ll,ll>;using pil=pair<int,ll>;using pli=pair<ll,int>;
using vs=vector<string>;using vvs=vector<vs>;using vvvs=vector<vvs>;
using vb=vector<bool>;using vvb=vector<vb>;using vvvb=vector<vvb>;
using vi=vector<int>;using vvi=vector<vi>;using vvvi=vector<vvi>;
using vl=vector<ll>;using vvl=vector<vl>;using vvvl=vector<vvl>;
using vd=vector<double>;using vvd=vector<vd>;using vvvd=vector<vvd>;
using vpii=vector<pii>;using vvpii=vector<vpii>;using vvvpii=vector<vvpii>;
template<class A,class B>bool amax(A&a,const B&b){return b>a?a=b,1:0;}
template<class A,class B>bool amin(A&a,const B&b){return b<a?a=b,1:0;}
ll ri(){ll l;cin>>l;return l;} string rs(){string s;cin>>s;return s;}

double solve() {
	int n = ri();
	vector<int> T(n);
	rep(i, n) T[i] = ri();
	vector<int> V(n);
	rep(i, n) V[i] = ri();

	rep(i, 1, n) T[i] += T[i-1];
	out(n, T, V);

	int LAS = T.back();
	int MAS = *max_element(all(V));

	out(T);
	out(V);

	vi LIM(LAS+1);
	{
		rep(i, T[0]) {
			LIM[i+1] = V[0];
		}
		rep(i, 1, n) {
			rep(t, T[i-1], T[i]) {
				LIM[t+1] = V[i];
			}
		}
	}
	out(LIM);

	vvd dp(LAS+1, vd(MAS+1, -1));
	dp[0][0] = 0;

	rep(i, LAS) {
		int lim0 = LIM[i];
		int lim = LIM[i+1];
		rep(j, lim0+1) if (dp[i][j] >= 0) {
			if (lim >= j) {
        		amax(dp[i+1][j], dp[i][j] + j);
			}
			if (lim >= j && j > 0 && lim0 >= j - 1) {
				amax(dp[i+1][j-1], dp[i][j] + (j+j-1)/2.0);
			}
			if (lim >= j + 1) {
				amax(dp[i+1][j+1], dp[i][j] + (j+j+1)/2.0);
				amax(dp[i+1][j],   dp[i][j] + j + 0.25);
			}
		}
	}
	double ans = dp[LAS][0];
	return ans;
}

void Main() {
	cout << fixed << setprecision(10);
	cout << solve() << endl;
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  Main();
  return 0;
}


Measured memory_bytes: 9088