// coached by rainboy
#include <algorithm>
#include <iostream>
using namespace std;
const int N = 100000;
const long long INF = 0x3f3f3f3f3f3f3f3fLL;
int aa[N], cc[N], ii0[N], ii1[N];
long long dp[N], xx[N];
__int128_t cross(long long x0, long long y0, long long x1, long long y1) {
return (__int128_t) x0 * y1 - (__int128_t) x1 * y0;
}
__int128_t cross(int i, int j, int k) {
long long xi = aa[i], yi = dp[i] + xi * xi;
long long xj = aa[j], yj = dp[j] + xj * xj;
long long xk = aa[k], yk = dp[k] + xk * xk;
return cross(xj - xi, yj - yi, xk - xi, yk - yi);
}
long long calc(int i, int j) {
return dp[i] + (long long) (aa[i] - aa[j]) * (aa[i] - aa[j]) - cc[j];
}
void solve(int l, int r) {
if (r - l == 1)
return;
int m = l + r >> 1;
solve(l, m);
int k0 = 0;
for (int i = l; i < m; i++)
ii0[k0++] = i;
sort(ii0, ii0 + k0, [] (int i, int j) { return aa[i] != aa[j] ? aa[i] < aa[j] : dp[i] < dp[j]; });
int k0_ = 0;
for (int h0 = 0; h0 < k0; h0++) {
int i = ii0[h0];
if (h0 && aa[i] == aa[ii0[h0 - 1]])
continue;
while (k0_ >= 2 && cross(ii0[k0_ - 2], ii0[k0_ - 1], i) <= 0)
k0_--;
ii0[k0_++] = i;
}
k0 = k0_;
int k1 = 0;
for (int i = m; i < r; i++)
ii1[k1++] = i;
sort(ii1, ii1 + k1, [] (int i, int j) { return aa[i] < aa[j]; });
for (int h0 = 0, h1 = 0; h1 < k1; h1++) {
int i = ii1[h1];
while (h0 + 1 < k0 && calc(ii0[h0], i) > calc(ii0[h0 + 1], i))
h0++;
dp[i] = min(dp[i], calc(ii0[h0], i));
}
solve(m, r);
}
int main() {
ios_base::sync_with_stdio(false), cin.tie(NULL);
int n; cin >> n;
for (int i = 0; i < n; i++)
cin >> aa[i];
for (int i = 0; i < n; i++)
cin >> cc[i];
for (int i = 1; i < n; i++)
dp[0] += cc[i], dp[i] = INF;
solve(0, n);
cout << dp[n - 1] << '\n';
return 0;
}
