/*
СТРОИМ СТЕНУ РАБОТЯГИ!
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*/

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
    
     
     
using namespace std;
template<typename T1, typename T2>inline void chkmin(T1 &x, T2 y) { if (x > y) x = y; }
template<typename T1, typename T2>inline void chkmax(T1 &x, T2 y) { if (x < y) x = y; }
/** Interface */
     
inline int readChar();
template <class T = int> inline T readInt(); 
template <class T> inline void writeInt( T x, char end = 0 );
inline void writeChar( int x ); 
inline void writeWord( const char *s );
     
/** Read */
     
static const int buf_size = 4096;
     
inline int getChar() {
    static char buf[buf_size];
    static int len = 0, pos = 0;
    if (pos == len) {
        pos = 0, len = fread(buf, 1, buf_size, stdin);
    }
    if (pos == len) {
        return -1;
    }
    return buf[pos++];
}
     
inline int readChar() {
    int c = getChar();
    while (c <= 32) {
        c = getChar();
    }
    return c;
}
     
template <class T>
inline T readInt() {
    int s = 1, c = readChar();
    T x = 0;
    if (c == '-')
        s = -1, c = getChar();
    while ('0' <= c && c <= '9')
        x = x * 10 + c - '0', c = getChar();
    return s == 1 ? x : -x;
}
     
/** Write */
     
static int write_pos = 0;
static char write_buf[buf_size];
     
inline void writeChar( int x ) {
    if (write_pos == buf_size)
        fwrite(write_buf, 1, buf_size, stdout), write_pos = 0;
    write_buf[write_pos++] = x;
}
     
template <class T> 
inline void writeInt( T x, char end ) {
    if (x < 0)
        writeChar('-'), x = -x;
     
    char s[24];
    int n = 0;
    while (x || !n)
        s[n++] = '0' + x % 10, x /= 10;
    while (n--)
        writeChar(s[n]);
    if (end)
        writeChar(end);
}
     
inline void writeWord( const char *s ) {     while (*s)
writeChar(*s++); }
     
struct Flusher {
    ~Flusher() {
        if (write_pos)
            fwrite(write_buf, 1, write_pos, stdout), write_pos = 0;
    }
} flusher;   
#define sz(c) (int)(c).size()
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define left left228
#define right right228
#define rank rank228
#define prev prev228
#define y1 y1228  



int n;
int t[100], v[100];
int ogr[100];


double get(double l, double r, double ts, double ms) {
    double ans = l * ts;
    r = r - l;
    ms = ms - l;
    l = 0;
    ans += r * r / 2.0 + r * (ts - r);
    if ((ts - r) / 2.0 + r <= ms) {
        ans += (ts - r) * (ts - r) / 4.0;
    } else {
        ans += (ms - r) * (ms - r) + (ms - r) * (ts - r - 2 * (ms - r));
    }
        //cout << ans << endl;
    return ans;
}


int main() {
    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> t[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> v[i];
    }
    for (int i = 0; i < n - 1; i++) {
        ogr[i] = min(v[i], v[i + 1]);
    }
    ogr[0] = min(ogr[0], t[0]);
    for (int i = 0; i < n - 2; i++) {
        ogr[i + 1] = min(ogr[i + 1], ogr[i] + t[i + 1]);
    }
    ogr[n - 2] = min(ogr[n - 2], t[n - 1]);
    for (int i = n - 2; i >= 1; i--) {
        ogr[i - 1] = min(ogr[i - 1], ogr[i] + t[i]);
    }
    if (n == 1) {
        if (double(t[0]) / 2.0 <= v[0]) {
            printf("%.10lf\n", double(t[0]) / 2.0 * double(t[0]) / 2.0);
        } else {
            printf("%.10lf\n", double(v[0]) * double(v[0]) + double(v[0]) * double(t[0] - 2 * v[0]));
        }
    } else {
        double cur = 0;
        double ans = 0.0;
        for (int i = 0; i <= n - 2; i++) {
            if (i == 0) {
                cur = 0;
            } else {
                cur = ogr[i - 1];           
            }
            double nxt = ogr[i];
            double l = cur;
            double r = nxt;
            double ts = t[i];
            if (l > r) {
                swap(l, r);
            }
            ans += get(l, r, ts, v[i]);
        }
        double kek = ogr[n - 2];
        ans += get(0.0, kek, t[n - 1], v[n - 1]);;
        printf("%.10lf\n", ans);
    }
    return 0;
}


Measured memory_bytes: 256