#include <bits/stdc++.h>
#include <stdio.h>

using namespace std;
#define inputInt(a) int a; cin >> a; 
#define inputInt2(a,b) int a; int b; cin >> a >> b; 
#define inputInt3(a,b,c) int a; int b; int c; cin >> a >> b >> c;
#define inputLong(a) long a;cin >> a; 
#define inputIntArray(a,N) int a[N];for(int i=0;i<N;i++){cin >> a[i];}
#define inputLongArray(a,N) long a[N];for(int i=0;i<N;i++){cin >> a[i];}
#define inputIntArray2(a,b,N) int a[N]; int b[N]; for(int i=0;i<N;i++){cin >> a[i] >> b[i];}
#define output(answer) cout << answer << endl;
#define fN(i,N)    for(int i=0; i<N; i++)
#define fSE(i,s,e) for(int i=s; i<=e; i++)
#define ll long long
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define FOR(i,N) for(int i=0; i<N; i++)
#define cinv(v,N) vector<int> v(N); for(int i=0; i<N; i++){ cin >> v[i]; }
#define mt make_tuple
#define vll vector<long long int>
#define vvll vector<vector<long long int>>
#define all(v) (v).begin(),(v).end()
#define show(v) FOR(i,v.size()){ cout << v[i] << " "; } cout << endl;
#define showshow(v) FOR(i,v.size()){ FOR(j,v[i].size()){ cout << v[i][j] << " "; } cout << endl; }
const ll MOD = 1e9+7;
const ll MOD2 = 998244353;
const ll INF = 1e18;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

//Combination計算 //ComInitしないと何もできません。
const int LIMIT = 1e6;//1e6→50ms,1e7→500ms,1e8→5000ms程度。
//const ll MOD = 1e9+7;
vector<ll> FacMod(LIMIT), InvMod(LIMIT), FacInvMod(LIMIT);
const int dpComTableLIMIT = 3e3+1;
vector<vector<ll>> Com(dpComTableLIMIT,vector<ll>(dpComTableLIMIT,0));
const int ComKTableLIMIT = 1e7;
vector<ll> ComK(ComKTableLIMIT);

void DPComInit(){
  //Com[0][j]は0で初期化されている。
  for(int i=0; i<dpComTableLIMIT; i++){ Com[i][0] = 1; }
  
  for(int i=1; i<dpComTableLIMIT; i++){
    for(int j=1; j<dpComTableLIMIT; j++){
      Com[i][j] = (Com[i-1][j-1]+Com[i-1][j])%MOD;
    }
  }
}

void ComKInit(ll N){
  for(int i=0; i<=ComKTableLIMIT; i++){
    if(0<i && i<=N/2){
      ComK[i] = (ComK[i-1]*(N-i+1)/i)%MOD;
    }else if(i==0){
      ComK[i] = 1;
    }else if(N/2<i && i<=N){
      ComK[i] = ComK[N-i];
    }else{//i>Nの時
      ComK[i] = -1;
    }
  }
}

void ComInit(){//tableを作成
  FacMod[0] = FacMod[1] = 1;
  InvMod[0] = 0; InvMod[1] = 1; //InvMod[0]は定義できない
  FacInvMod[0] = FacInvMod[1] = 1;
  
  for(int i=2; i<LIMIT; i++){
    FacMod[i] = FacMod[i-1]*i%MOD;
    InvMod[i] = -InvMod[MOD%i]*(MOD/i)%MOD + MOD;
    FacInvMod[i] = FacInvMod[i-1] * InvMod[i]%MOD;
  }
}

ll ComMod(int n, int k){
  if(n>=0 && k>=0 && n>=k){
    return FacMod[n]*(FacInvMod[k]*FacInvMod[n-k]%MOD)%MOD;
  }else{
    return 0; //戻り値を0にする方が計算結果に影響が少ない。
  }
}


//繰り返し2乗法
ll power(ll x, ll y){//繰り返し2乗法
  if(y < 0){
    return 0;
  }else if(y == 0){
    return 1LL;
  }else if(y%2 == 0){//偶数
    return power(x,y/2)*power(x,y/2);
  }else{//奇数
    return power(x,y-1)*x;
  }
}

//繰り返し2乗法
ll mpower(ll x, ll y, ll m){//繰り返し2乗法
  if(y < 0){
    return 0;
  }else if(y == 0){
    return 1LL;
  }else if(y%2 == 0){//偶数
    return mpower(x,y/2,m)*mpower(x,y/2,m)%m;
  }else{//奇数
    return mpower(x,y-1,m)*x%m;
  }
}

//互除法
ll GCD(ll a, ll b){
  return b ? GCD(b,a%b) : a;
}

ll LCM(ll a, ll b){
  return (a / GCD(a,b))*b;
}

//素因数分解
pair<map<ll,ll>,bool> PrimeFactorization(ll N){
  pair<map<ll,ll>,bool> ret;//<素因数分解,素数判定>
  ret.second = true;
  
  //素因数分解
  if(N != 2){
    while(N%2 == 0){//p=2の時。
      N /= 2;
      ret.first[2] ++;
      ret.second = false;
    }
  }
  for(ll i=3; i*i<=N; i+=2){//p>=3の時。
    while(N%i == 0){
      N /= i; 
      ret.first[i] ++;
      ret.second = false;
    }
  }
  if(N != 1){//Nが素数の時
    ret.first[N] ++;
  }
  
  //返り値
  return ret;
}

//pair型のソート
bool compare_by_second(pair<ll,ll> a, pair<ll,ll> b){
  return a.second != b.second ? a.second < b.second : a.first < b.first;
}

class UnionFind {
  vector<int> parent;
  vector<int> rank;
  vector<int> size;
  
  public:
  
  UnionFind(int N);
  int root(int x);
  void unite(int x, int y);
  bool isUnited(int x, int y);
  int getRank(int x);
  int getSize(int x);
};

UnionFind::UnionFind(int N):parent(N),rank(N,1),size(N,1){
  for(int i=0; i<N; i++){parent[i]=i;}
}

int UnionFind::root(int x){
  if(parent[x] == x) return x;
  return root(parent[x]);
  /*parent[x] = parent[parent[x]];
  if(parent[x]!=parent[parent[x]]) rank[x]-=1;*/
}

void UnionFind::unite(int x, int y) { // xとyの木を併合
  int rx = root(x); //xの根をrx
  int ry = root(y); //yの根をry
  //cout << x << " " << y << " " << parent[x] << " " << parent[y] << endl; 
  if (rx == ry) return; //xとyの根が同じ(=同じ木にある)時はそのまま
  
  ll xs = size[root(x)]; ll ys = size[root(y)];
  size[root(x)] += ys;
  size[root(y)] += xs;
  //cout << x << " " << y << " " << size[root(x)] << " " << size[root(y)] << endl; 
  if(rank[x] >= rank[y]){parent[ry] = rx; rank[y]+=1;}//大きい木に小さい木が併合される
  else{parent[rx] = ry; rank[x]+=1;}//根に直接辺を張る
}

bool UnionFind::isUnited(int x, int y) { // 2つのデータx, yが属する木が同じならtrueを返す
  int rx = root(x);
  int ry = root(y);
  parent[x]=rx; parent[y]=ry;rank[x]=2;rank[y]=2;
  return rx == ry;
}

int UnionFind::getRank(int x){
  return rank[x];
}

int UnionFind::getSize(int x){
  return size[root(x)];
}

bool isOK(ll condition){
  //return false;
  return true;
}

ll binary_search(){
  //最小値を求める時
  ll ok = 1e18;//解が存在する最大値
  ll ng = -1;//解が存在しない最小値
  /*
  //最大値を求める時
  ll ok = -1;//解が存在する最小値
  ll ng = 1e18;//解が存在しない最大値
  */
  
  while(abs(ok-ng) > 1){
    ll mid = (ok+ng)/2;
    if(isOK(mid)){
      ok = mid; 
    }else{
      ng = mid;
    }
  }
  return ok;
}

int main()
{
  //input
  cin.tie(0);
  ios::sync_with_stdio(false);
  
  ll N; cin >> N;
  vector<ll> T(N); vector<ll> Tsum(N+1,0); 
  FOR(i,N){ cin >> T[i]; } FOR(i,N){ Tsum[i+1] = Tsum[i]+T[i]; }
  vector<ll> V(N); ll Vmax = 0;
  FOR(i,N){ cin >> V[i]; Vmax = max(Vmax,V[i]); }
  
  //main
  double def = -1e10;
  vector<vector<double>> dp(2*Tsum[N]+1,vector<double>(2*Vmax+1,def));
  dp[0][0] = 0; ll state = 0;
  for(ll t=1; t<=2*Tsum[N]; t++){
    if(2*Tsum[state+1] < t){
      state ++; 
    }
    for(ll v=0; v<=2*V[state]; v++){
      if(v+1<=2*V[state] && dp[t-1][v] != def){//加速
        dp[t][v+1] = max(dp[t][v+1],dp[t-1][v]+(0.25*v+0.125));  
      }
      if(v-1>=0 && dp[t-1][v] != def){//減速
        dp[t][v-1] = max(dp[t][v-1],dp[t-1][v]+(0.25*v-0.125)); 
      }
      //維持
      if(dp[t-1][v] != def){
        dp[t][v] = max(dp[t][v],dp[t-1][v]+0.25*v); 
      }
    }
  }
  
  double ans = dp[2*Tsum[N]][0];
  
  // output
  cout << fixed << setprecision(10) << ans << endl;
  
  return 0;
}

Measured memory_bytes: 209248