////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// [Tips]
// XCodeでのEOF入力はCtrl+D
// ¥はAlt+\
// ansは結構INTの範囲2,147,483,647を超えることがあるのでlong long使っておいたほうが良い
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////



////////////////////////////////////////
//
////////////////////////////////////////

//#define debug //*******************************************************************************************************************************************
#ifdef debug
#include <chrono>
#endif

#include <iostream>
#include <algorithm> // next_permutation
#include <iomanip>
#include <cmath>
#include <vector>
#include <sstream>
#include <string>
#include <cstring> //memcpy
#include <cstdio>
#include <stack>
#include <queue>
#include <list>
#include <numeric> //accumulate
//#include <map>
//#include <unordered_map> //hash func.
#include <fstream> //ifstream, ofstream
#include <iterator> //insert_iterator::inserter
#include <set>


#define NDEBUG //If NDEBUG is defined before #include <cassert>, assert will be ignored. You had better define NDEBUG when u submit the code.
#include <cassert> //assert

using namespace std;


#define dout cout
//If u wanna output to a text file instead of standard output, plz define OUTPUTFILE.
//#define OUTPUTFILE "output.txt" //************************************************************
#ifdef OUTPUTFILE
#define dout outputfile
ofstream outputfile(OUTPUTFILE);
#define OutputFilePath "/Users/Nag/Documents/Prgm/Test/DerivedData/Test/Build/Products/Debug/output.txt"
#endif


#define din cin
//If u wanna input from a text file instead of standard input, plz define INPUTFROMTEXTFILEを.
//#define INPUTFILE "input.txt" //**************************************************************
#ifdef INPUTFILE
#define din inputfile
ifstream inputfile(INPUTFILE);
#endif

#define scand(A) scanf("%d", &(A))
#define scans(A) scanf("%s", (A))
#define printd(A) printf("%d\n", (A))
#define prints(A) printf("%s\n", (A))
#define disp(A) dout << #A << " = " << setw(3) << (A) << endl
#define disP(A) dout << setw(3) << (A) << " "
#define rep(i,a,n) for(int (i)=(a); (i)<(n); (i)++)
#define show(A,n) dout << #A << " = "; rep(j, 0, (n)) {disP(A[j]);} dout << endl
#define showi(n) dout << "i = "; rep(j, 0, (n)) {disP(j);} dout << endl










//#define dispAll(A,n) cout << #A << " = "; rep(j, 0, (n)) {cout << setw(3) << A[j] << " ";} cout << endl

#define sign(x) ((x)>0)-((x)<0) //x<0: -1, x=0: 0, x>0: +1
#define p(i) ((i)/2)
#define l(i) ((i)*2)
#define r(i) ((i)*2+1)
#define sibling(i) (i^1) //the other sibling of i (ex. 16^1 = 17, 17^1 = 16)
#define isRightChild(i) (i&1) // ex. 16&1 = 0, 17&1 = 1
#define isLeftChild(i) (!(i&1)) // ex. 16&1 = 1, 17&1 = 0

int dx[] = {1,-1, 0, 0, 1, 1,-1,-1}; //右左上下、右上から時計回りに右下、左下、左上
int dy[] = {0, 0,-1, 1,-1, 1, 1,-1};

typedef pair<int,int> ii;
typedef pair<ii, int> iii;
typedef vector<int> vi;
typedef long long ll;
typedef unsigned long long ull;

const int INF = (1LL<<31)-1;
const ll INF_LL = (ll)9e18-1LL; //Be careful for overflow.
const ull INF_ULL = (ull)1e19-1ULL;
const int NONE = -1;
const ll MOD = (ll)1e9+7; //大きい素数の代表といえばこの人、10億7さん

const int N_MAX = 110; //num of vertex or element
const int M_MAX = 100010; //num of edge
const int DATA_MAX = 1010;

int N;
int T[N_MAX];
int V[N_MAX];
int TT[N_MAX];
vector <pair<int, int> > Xi;



void display() {
#ifdef debug
    dout << "---------------------\n";
    showi(N);
    show(T, N+1);
    show(TT, N+1);
    show(V, N+1);
#endif
}





int main() {
    
    //cin, coutの高速化  ＊注意：cinを使うなら全部cinで、scanfを使うなら全部scanfで統一するように！
    cin.tie(0); //cinとcoutの同期を切る
    ios::sync_with_stdio(false); //iostreamとstdioの同期を切る
    
    //read input data
//    scand(N);

    din >> N;
    
    din >> T[0];
    TT[0] = T[0];
    
    rep(i,1,N) {
        din >> T[i];
        TT[i] = TT[i-1] + T[i];
    }
    T[N] = 0;
    TT[N] = TT[N-1];
    
    rep(i,0,N) {
        din >> V[i];
    }
    V[N] = 0;
    
    
    //------------------------------------------------------------------------------------------
#ifdef debug
    //start timer
    auto startTime = chrono::system_clock::now();
#endif
    //------------------------------------------------------------------------------------------
    

#ifdef debug
    display();
#endif
    
    double v = 0;
    double t = 0;

    double ans = 0;
    
    int X;
    
    //calc. X[j]
    rep(i,0,N) {
        X = V[i+1] + TT[i];
        Xi.push_back(make_pair(X, i));
    }
    
    sort(Xi.begin(), Xi.end());
    
    
    //calc. ans
    int j, j_min;
    double X_min, XX_min;
    
    rep(i,0,N) {
        
        //get X_min, j_min
        X = Xi[0].first;
        j = Xi[0].second;
        
        while(j<i) {
            Xi.erase(Xi.begin());
            X = Xi[0].first;
            j = Xi[0].second;
        }
        
        X_min = (X-v+t)/2.0;
        XX_min = X-V[i];
        j_min = j;
        
#ifdef debug
        disp(X_min);
        disp(XX_min);
        disp(j_min);
#endif
        
        
        //i-a
        if( t+T[i] <= V[i]+t-v ) {
            
            //i-a-(1)
            if( t+T[i] <= X_min ) {
#ifdef debug
                dout << "i-a-(1)\n";
#endif
                ans += (v + t+T[i]-t+v)*T[i]/2.0;
                t = t + T[i];
                v = t+T[i]-t+v;
            }
            
            //i-a-(2)
            else {
#ifdef debug
                dout << "i-a-(2)\n";
#endif
                assert(t<=X_min);
                
                ans += (v + X_min-t+v)*(X_min-t)/2.0 + (X_min-t+v + V[j_min+1])*(TT[j_min]-X_min)/2.0;
                t = TT[j_min];
                v = V[j_min+1];
                
                i = j_min;
            }
            
        }
        
        //i-b
        else {
            
            //i-b-(1)
            if( t+T[i] <= XX_min ) {
#ifdef debug
                dout << "i-b-(1)\n";
#endif
                ans += (v+V[i])*(V[i]+t-v - t)/2.0 + V[i]*(t+T[i] - (V[i]+t-v));
                t = t + T[i];
                v = V[i];
            }
            
            //i-b-(2)
            else if( V[i]+t-v <= XX_min ) {
#ifdef debug
                dout << "i-b-(2)\n";
#endif
                ans += (v+V[i])*(V[i]+t-v - t)/2.0 + V[i]*(XX_min - (V[i]+t-v)) + (V[i]+V[j_min+1])*(TT[j_min] - XX_min)/2.0;
                t = TT[j_min];
                v = V[j_min+1];
                i = j_min;
            }
            
            //i-b-(3)
            else {
#ifdef debug
                dout << "i-b-(3)\n";
#endif
                assert(t<=XX_min);
                
                ans += (v + X_min-t+v)*(X_min-t)/2.0 + (X_min-t+v + V[j_min+1])*(TT[j_min]-X_min)/2.0;
                t = TT[j_min];
                v = V[j_min+1];
                
                i = j_min;
            }
            
        }
#ifdef debug
        disp(ans);
        dout << endl;
#endif
        
    }
    
    
#ifdef debug
    dout << "=== OUTPUT ===\n";
#endif
    dout << fixed << setprecision(6) << ans << endl;
    
    
    
    //------------------------------------------------------------------------------------------
#ifdef debug
    //stop timer
    auto endTime = chrono::system_clock::now();
    auto dur = endTime - startTime;
    auto msec = chrono::duration_cast<chrono::milliseconds>(dur).count();
    dout << fixed << setprecision(4) << (double)msec/1000 << " sec \n";
#endif
    //------------------------------------------------------------------------------------------
    
#ifdef INPUTFILE
    inputfile.close();
#endif
    
#ifdef OUTPUTFILE
    outputfile.close();
    cout << "\"" << OutputFilePath << "\"" << endl;
#endif
    
    return 0;
}


Measured memory_bytes: 384