#include <bits/stdc++.h>

using namespace std;

#define int long long

const int N = 500'000 + 10;
int n;
int c[N], a[N];

struct Line { 
  long long a, b;
  Line() : a(0), b(0) {}
  Line(long long a, long long b) : a(a), b(b) {}
  double x(Line rhs) { return 1.0 * (b - rhs.b) / (rhs.a - a); }
};
struct CHT { 
  Line convex[N];
  int top;
  void clear() { top = 0; }
  void add(Line line) { 
    while (top > 1 && convex[top - 1].x(convex[top]) <= convex[top - 1].x(line)) 
      top -= 1;
    convex[++top] = line;
  }
} T;

int bwd[N], fwd[N];

long long f[N];
void dnc(int l, int r) { 
  if (l == r) return;
  int mid = (l + r) >> 1;
  dnc(l, mid);

  bwd[mid] = c[mid];
  for (int i = mid - 1; i >= l; --i) bwd[i] = max(bwd[i + 1], c[i]);

  fwd[mid + 1] = c[mid];
  for (int i = mid + 2; i <= r; ++i) fwd[i] = max(fwd[i - 1], c[i - 1]);

  { //max at right side
    T.clear();

    int it = mid;
    for (int i = mid + 1; i <= r; ++i) { 
      const int ma = fwd[i];
      while (it >= l && ma >= bwd[it]) { 
        T.add({-it, f[it]});
        it -= 1;
      }
      if (!T.top) continue;

      auto get = [&](int it) { 
        return 1ll * (T.convex[it].a + i) * ma + T.convex[it].b + a[i];
      };

      int l = 1, r = T.top - 1, pos = 1;
      while (l <= r) { 
        int mid = (l + r) >> 1;
        if (get(mid) >= get(mid + 1)) l = pos = mid + 1;
        else r = mid - 1;
      }

      f[i] = min(f[i], get(pos));
    }
  } 

  { //max at left side
    T.clear();

    int it = l;
    for (int i = r; i >= mid + 1; --i) { 
      while (it <= mid && bwd[it] >= fwd[i]) { 
        T.add({bwd[it], f[it] - 1ll * bwd[it] * it});
        it += 1;
      }
      if (!T.top) continue;

      auto get = [&](int it) { 
        return 1ll * T.convex[it].a * i + T.convex[it].b + a[i];
      };

      int l = 1, r = T.top - 1, pos = 1;
      while (l <= r) { 
        int mid = (l + r) >> 1;
        if (get(mid) >= get(mid + 1)) l = pos = mid + 1;
        else r = mid - 1;
      }

      f[i] = min(f[i], get(pos));
    }
  }

  dnc(mid + 1, r);
}

int32_t main() { 
  cin.tie(0)->sync_with_stdio(0);

  cin >> n;
  for (int i = 0; i < n; ++i) cin >> c[i];
  for (int i = 1; i < n; ++i) cin >> a[i];

  memset(f, 14, sizeof f);
  f[0] = 0;
  dnc(0, n + 1);

  cout << f[n + 1] << "\n";
}