#include<stdio.h>
#include<assert.h>
#include<vector>
#include<string.h>
#include<algorithm>
#include<memory.h>
#include<cmath>
#include<string>
#include<iostream>
#include<set>
#include<unordered_set>
#include<map>
#include<queue>
#include<functional>
#include<list>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<double, double> pdd;
typedef tuple<int,int,int> t3;
const int MX = 1<<19;
const int MM = 1000000007;
struct node{
node(){}
node(ll f, ll s, int c, int v):f(f), s(s), c(c), v(v){}
ll f, s;
int c, v;
};
node merge(node l, node r){
if( l.c == 0 ) return node(l.f + r.f, l.s + r.s, l.c^r.c, min(l.v, r.v));
return node(l.f + r.s, l.s + r.f, l.c^r.c, min(l.v, r.v));
}
struct Tree{
node t[MX*2];
node read(){ return t[1]; }
void update(node n){
// printf("update %d %d %d %d\n", n.f, n.s, n.c, n.v);
int x = n.v + MX;
t[x] = n;
while(x > 1){
x /= 2; t[x] = merge(t[x*2+1], t[x*2]);
}
}
void remove(node n){
// printf("remove %d %d %d %d\n", n.f, n.s, n.c, n.v);
int x = n.v + MX;
t[x] = node(0, 0, 0, x);
while(x > 1){
x /= 2; t[x] = merge(t[x*2+1], t[x*2]);
}
}
} tree;
vector<node> rm[MX], add[MX];
vector<int> X;
int N, M, a, b;
int D[MX], A[MX];
ll ans[MX], R[MX];
ll get_ans(int st){
auto n = [](int s){ return s%N+1; };
auto b = [](int s){ return (s+N-2)%N+1; };
ll ans = D[st];
int c = 1, l = b(st), r = n(st);
while(l != r){
int p = 0;
if( D[l] < D[r] ) p = D[r], r = n(r);
else p = D[l], l = b(l);
if( !c ) ans += p;
c ^= 1;
}
if( !c ) ans += D[l];
return ans;
}
int main()
{
scanf("%d", &N);
for(int i = 1; i <= N; i++) scanf("%d", D+i);
int mn = 1;
for(int i = 2; i <= N; i++) if( D[i] < D[mn] ) mn = i;
ans[0] = get_ans(mn);
for(int i = mn%N+1, j = 1; i != mn; i = i%N+1, j++) A[j] = D[i]; N--;
for(int i = 1; i <= N; i++) X.push_back(A[i]);
sort(X.begin(), X.end());
auto t = [](vector<int> &X, int a){ return lower_bound(X.begin(), X.end(), a) - X.begin(); };
vector<node> stack;
for(int i = N; i >= 1; i--){
int v = t(X, A[i]);
node c = node(A[i], 0, 1, v);
while( stack.size() && stack.back().v > v ){
c = merge(c, stack.back());
add[i].push_back(stack.back());
tree.remove(stack.back());
stack.pop_back();
}
stack.push_back(c);
tree.update(c);
rm[i].push_back(c);
}
stack.clear();
for(int i = 1; i <= N; i++){
for(node c : rm[i]) tree.remove(c);
for(node c : add[i]) tree.update(c);
ans[i] = tree.read().s + A[i];
int v = t(X, A[i]);
node c = node(A[i], 0, 1, v);
while( stack.size() && stack.back().v > v ){
c = merge(c, stack.back());
add[i].push_back(stack.back());
tree.remove(stack.back());
stack.pop_back();
}
stack.push_back(c);
tree.update(c);
}
for(int i = 0; i <= N; i++){
R[(i+mn-1)%(N+1)] = ans[i] + (N%2 == 0 && i ? D[mn] : 0);
}
for(int i = 0; i <= N; i++) printf("%lld\n", R[i]);
}
