#include<bits/stdc++.h>
using namespace std;


#define uli         unsigned long long int
#define li          long long int
#define rep(i,to)   for(li i=0;i<((li)(to));i++)
#define repp(i,start,to)    for(li i=(li)(start);i<((li)(to));i++)
#define pb          push_back
#define sz(v)       ((li)(v).size())
#define bgn(v)      ((v).begin())
#define eend(v)     ((v).end())
#define allof(v)    (v).begin(), (v).end()
#define dodp(v,n)       memset(v,(li)n,sizeof(v))
#define bit(n)      (1ll<<(li)(n))
#define mp(a,b)     make_pair(a,b)
#define rin rep(i,n)
#define EPS 1e-12
#define ETOL 1e-8
#define MOD 1000000007
typedef pair<li, li> PI;

#define INF bit(60)

#define DBGP 1


#define idp if(DBGP)
#define F first
#define S second
#define p2(a,b)     idp cout<<a<<"\t"<<b<<endl
#define p3(a,b,c)       idp cout<<a<<"\t"<<b<<"\t"<<c<<endl
#define p4(a,b,c,d)     idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<endl
#define p5(a,b,c,d,e)       idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<endl
#define p6(a,b,c,d,e,f)     idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<"\t"<<f<<endl
#define p7(a,b,c,d,e,f,g)       idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<"\t"<<f<<"\t"<<g<<endl
#define p8(a,b,c,d,e,f,g,h)     idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<"\t"<<f<<"\t"<<g<<"\t"<<h<<endl
#define p9(a,b,c,d,e,f,g,h,i)       idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<"\t"<<f<<"\t"<<g<<"\t"<<h<<"\t"<<i<<endl
#define p10(a,b,c,d,e,f,g,h,i,j)        idp cout<<a<<"\t"<<b<<"\t"<<c<<"\t"<<d<<"\t"<<e<<"\t"<<f<<"\t"<<g<<"\t"<<h<<"\t"<<i<<"\t"<<j<<endl
#define foreach(it,v)   for(__typeof((v).begin()) it=(v).begin(); it!=(v).end(); ++it)
#define p2p(x)      idp p2((x).F, (x).S)
#define dump(x,n)   idp{rep(i,n){cout<<x[i]<<" ";}puts("");}
#define dump2(x,n)  idp{rep(i,n){cout<<"["<<x[i].F<<" , "<<x[i].S<<"] ";}puts("");}
#define dumpi(x)    idp{foreach(it, x){cout<<(*it)<<" ";}puts("");}
#define dumpi2(x)   idp{foreach(it, x){cout<<"["<<(it)->F<<" , "<<(it)->S<<"] ";}puts("");}

#define read2d(a,w,h)   rep(i,h)rep(j,w)cin>>a[i][j]
#define dump2d(a,w,h)   rep(i,h){rep(j,w)cout<<a[i][j]<<" ";puts("");}

typedef pair<li, li> PI;

li n;
li t[222];
li v[222];

li left_[222];
li right_[222];

inline double calc(li l, li r, li lim, li len) {
    //p4(l,  r,  lim, len);
    // 山のてっぺんがvに達しない場合
    if (l > r)swap(l, r);
    assert(l <= r);
    if (lim - l + lim - r > len) {
        double ll = (l + r) * (r - l) / 2.0;
        len -= (r - l);
        double len2 = len / 2.0;
        double yama = (r + len2 + r) * len2;
        return ll + yama;
    }
    double base = lim * len;
    base -= (lim - l) * (lim - l) / 2.0;
    base -= (lim - r) * (lim - r) / 2.0;
    return base;
}

int main() {
    cin >> n;
    rin{
        cin >> t[i];
    }
    rin{
        cin >> v[i];
    }
    left_[0] = 0;
    repp(i, 1, n) {
        left_[i] = min(left_[i - 1] + t[i - 1], min(v[i - 1], v[i]));
        right_[i - 1] = left_[i];
    }
    right_[n - 1] = 0;
    for (li i = n - 2; i >= 0; i--) {
        right_[i] = min(right_[i + 1] + t[i + 1], min(v[i], v[i + 1]));
        right_[i] = min(right_[i], left_[i + 1]);
        left_[i + 1] = min(left_[i + 1], right_[i]);
    }
    double res = 0.0;
    rin{
        res += calc(left_[i], right_[i], v[i], t[i]);
    }
    printf("%.12f\n", res);


    return 0;
}

Measured memory_bytes: 256