#include <bits/stdc++.h>
using namespace std;
#define all(x) (x).begin(), (x).end() 
#define sz(x) (int) (x).size() 
typedef long long lint;
typedef pair<lint,lint> ii;

int n; 
lint A[500005], B[500005];
lint ans[500005];

void add(int l, int r, lint val){
	ans[l] += val;
	ans[r+1] -= val;
}

struct sumtool{
	lint total = 0;
	vector<lint> v, psum;
	
	void push(lint x){
		if(v.empty()) v.push_back(x);
		else v.push_back(max(v.back(), x));
		total += v.back();
		psum.push_back(total);
	}

	lint query(lint x){
		int pos = upper_bound(all(v), x) - v.begin();
		lint res = total;
		if(pos != 0) res -= psum[pos-1];
		res += x * pos;
		return res;
	}
};
struct thing{ lint val, total, cnt; };

lint val[500005], total[500005], tempans[500005];

void dnc(int l, int r){
	if(l == r){
		add(0, l-1, A[l]);
		add(l, n, B[l]);
		return;
	}
	
	lint res = 0;
	int m = (l+r)/2;
	
	///compute for [l, m] first
	sumtool R;
	for(int i = m+1;i <= r;i++) R.push(A[i]);
	
	lint acc = 0;
	for(int i = m;i >= l;i--){
		acc = max(acc, A[i]);
		val[i] = acc;
		
		total[i] = R.query(acc);
		res += total[i];
	}
		
	tempans[l-1] = res;
	
	stack<thing> S;
	for(int i = l;i <= m;i++){
		res -= total[i];
		val[i] = max(val[i], B[i]);
		int cnt = 1;
		while(!S.empty()){
			if(S.top().val <= val[i]){
				cnt += S.top().cnt;
				res -= S.top().total * S.top().cnt;
				S.pop();
			}
			else break;
		}
			
		lint total = R.query(val[i]);
		res += total * cnt;
		S.push({val[i], total, cnt});
		
		tempans[i] = res;
	}
	
	///compute for [m+1, R] first
	sumtool L; 
	while(!S.empty()) S.pop();
	for(int i = m;i >= l;i--) L.push(B[i]);
		
	acc = 0, res = 0;
	for(int i = m+1;i <= r;i++){
		acc = max(acc, A[i]);
		val[i] = acc;
		
		total[i] = L.query(acc);
		res += total[i];
	}
	
	for(int i = r;i >= m+1;i--){
		if(S.empty() || S.top().val > val[i]) S.push({val[i], total[i], 1});
		else S.top().cnt++;
	}
			
	for(int i = m+1;i <= r;i++){
		res -= S.top().total;
		if(S.top().cnt == 1) S.pop();
		else S.top().cnt--;
		
		val[i] = max(val[i], B[i]);
		if(i != m+1) val[i] = max(val[i], val[i-1]);
		
		int cnt = 1;
		while(!S.empty()){
			if(S.top().val <= val[i]){
				cnt += S.top().cnt;
				res -= S.top().total * S.top().cnt;
				S.pop();
			}
			else break;
		}
		
		lint total = L.query(val[i]);
		res += total * cnt;
		S.push({val[i], total, cnt});
		
		tempans[i] = res;
		
		if(S.top().cnt == 1) S.pop();
		else S.top().cnt--;
	}
	
	add(0, l-1, tempans[l-1]);
	add(r, n, tempans[r]);
	for(int i = l;i < r;i++) add(i, i, tempans[i]);
	
	dnc(l, m); dnc(m+1, r);
}

int main(){
	ios_base::sync_with_stdio(false); cin.tie(0);
	
	cin >> n;
	for(int i = 1;i <= n;i++) cin >> A[i];
	for(int i = 1;i <= n;i++) cin >> B[i], B[i] += A[i];

	dnc(1, n);
	
	lint acc = 0;
	for(int i = 0;i <= n;i++){
		acc += ans[i];
		cout << acc << "\n";
	}
}