#include <algorithm>
#include <cstdio>
#include <cstring>
using namespace std;
#define forn(i, n) for (int i = 0; i < (n); ++i)
#define MAXT (1 << 17)
struct L {
long m = 0, c = 1e18;
long operator()(long x) { return x * m + c; }
} t[MAXT * 2];
int x[MAXT];
void add_line(L cn, int s = 1, int l = 0, int r = MAXT) {
if (r - l == 1) {
t[s] = t[s](x[l]) < cn(x[l]) ? t[s] : cn;
} else {
int m = (l + r) / 2;
bool cl = cn(x[l]) < t[s](x[l]);
bool cm = cn(x[m]) < t[s](x[m]);
if (cm) swap(cn, t[s]);
cl != cm ? add_line(cn, s * 2, l, m) : add_line(cn, s * 2 + 1, m, r);
}
}
long get_min(int k, int s = 1, int l = 0, int r = MAXT) {
if (r - l == 1) {
return t[s](x[k]);
} else {
long cur = t[s](x[k]);
int m = (l + r) / 2;
return min(cur, k < m ? get_min(k, s * 2, l, m) : get_min(k, s * 2 + 1, m, r));
}
}
#define MAXN 100000
int n, h[MAXN], w[MAXN], p[MAXN], pr[MAXN];
long dp[MAXN];
int main() {
scanf("%d", &n);
forn (i, n) scanf("%d", h + i);
forn (i, n) scanf("%d", w + i);
long wsum = 0;
forn (i, n) wsum += w[i];
// dp[i] =
// = min_{j < i} dp[j] + (h[j] - h[i]) ^ 2 + w[i]
// = min_{j < i} dp[j] + h[j] ^ 2 - 2h[j]h[i] + h[i] ^ 2 + w[i]
// f_j(x) := h[j] ^ 2 - 2h[j]x + dp[j]
// = h[i] ^ 2 + w[i] + min_{j < i} f_j(h[i])
memset(x, 0x3f, sizeof(x));
forn (i, n) x[i] = h[i];
forn (i, n) p[i] = i;
sort(p, p + n, [&](int i, int j) {
return x[i] < x[j];
});
forn (i, n) pr[p[i]] = i;
sort(x, x + n);
add_line({-2l * h[0], 1l * h[0] * h[0] - w[0]});
for (int i = 1; i < n; ++i) {
dp[i] = 1l * h[i] * h[i] - w[i] + get_min(pr[i]);
add_line({-2l * h[i], 1l * h[i] * h[i] + dp[i]});
}
printf("%ld\n", dp[n - 1] + wsum);
}
