#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define mid ((l+r) >> 1)
struct block {
ll s[2];
int sz, L, R;
block operator + (const block &a) const {
int c = a.sz % 2;
return {{s[c]+a.s[0], s[!c]+a.s[1]}, sz+a.sz, L, a.R};
}
} o, t[1200120];
int n, a[300300], b[300300], r[300300];
ll ans[300300];
void update(int id, block &x, int node = 1, int l = 1, int r = n) {
if(id < l || r < id) return;
if(l == r) {
t[node] = x;
return;
}
update(id, x, node*2, l, mid), update(id, x, node*2+1, mid+1, r);
t[node] = t[node*2] + t[node*2+1];
}
block find(int nl, int nr, int node = 1, int l = 1, int r = n) {
if(r < nl || nr < l) return o;
if(nl <= l && r <= nr) return t[node];
return find(nl, nr, node*2, l, mid) + find(nl, nr, node*2+1, mid+1, r);
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n;
for(int i=1;i<=n;i++) cin >> a[i];
iota(r+1, r+1+n, 1);
sort(r+1, r+1+n, [&](auto x, auto y){ return a[x] < a[y]; });
for(int i=1;i<=n;i++) b[r[i]] = i;
int mn = r[1];
rotate(a+1, a+mn, a+1+n), rotate(b+1, b+mn, b+1+n);
ans[1] = a[1];
for(int i=2, L = 2, R = n;i<=n;i++) {
int C = a[L] > a[R] ? a[L++] : a[R--];
if(i % 2) ans[1] += C;
}
vector<vector<block>> op(n+1);
vector<block> st(1, o);
for(int i=n;i>1;i--) {
block u = {{a[i], 0}, 1, b[i], b[i]};
while(st.back().L > b[i]) {
auto P = st.back(); st.pop_back();
op[i].push_back(P);
update(P.L, o);
int c = u.sz % 2;
u.s[0] += P.s[c], u.s[1] += P.s[!c];
u.sz += P.sz, u.R = P.R;
}
update(b[i], u);
st.push_back(u);
}
st = {o};
for(int i=2;i<=n;i++) {
update(b[i], o);
for(auto B : op[i]) update(B.L, B);
ans[i] = t[1].s[1] + a[i] + (n%2 ? a[1] : 0);
block u = {{a[i], 0}, 1, b[i], b[i]};
while(st.back().R > b[i]) {
auto P = st.back(); st.pop_back();
update(P.R, o);
int c = u.sz % 2;
u.s[0] += P.s[c], u.s[1] += P.s[!c];
u.sz += P.sz, u.L = P.L;
}
update(b[i], u);
st.push_back(u);
}
for(int i=0;i<n;i++) cout << ans[(i-mn+1+n)%n+1] << "\n";
}
