#include <bits/stdc++.h>
using namespace std;
#define dbg(x) "[" << #x " = " << (x) << "]"
#define el "\n"
using ll = long long;
const int N = 3e5 + 5, lg = 19, INF = 2e9;
int n, a[N], spt[lg][N];
ll pref[2][N], ans[N], b[N];
int merge_st(int x, int y) {
return b[x] < b[y] ? x : y;
}
int MnPos(int l, int r) {
int k = 31 - __builtin_clz(r - l + 1);
return merge_st(spt[k][l], spt[k][r - (1 << k) + 1]);
}
ll sum(int l, int r, int t) {
assert(l > 0 && t >= 0 && t <= 1);
return pref[t][r] - pref[t][l - 1];
}
ll calc(int l, int r, int Mnp) {
int tl = Mnp - 1, tr = Mnp + 1, t = 1;
ll res = b[Mnp];
for (; l <= tl && tr <= r;) {
if (!t) res += max(b[tl], b[tr]);
(b[tl] > b[tr] ? --tl : ++tr);
t ^= 1;
}
if (tl < l) {
res += sum(tr, r, (tr & 1) ^ t);
} else {
res += sum(l, tl, (tl & 1) ^ t);
}
return res;
}
void DncIterative(int l, int r, ll conE, ll conO) {
using T = tuple<int, int, ll, ll>;
stack<T> stk;
stk.emplace(l, r, conE, conO);
while (!stk.empty()) {
auto [cl, cr, cE, cO] = stk.top();
stk.pop();
if (cl > cr) continue;
int nMnP = MnPos(cl, cr);
ans[nMnP] = cE + calc(cl, cr, nMnP);
if (nMnP != cl) {
ll nconE = cE, nconO = cO;
int bL = (!((nMnP - cl) & 1) ? (nMnP & 1) : ((nMnP & 1) ^ 1));
nconE += sum(nMnP, cr, bL);
nconO += sum(nMnP, cr, bL ^ 1);
stk.emplace(cl, nMnP - 1, nconE, nconO);
}
if (nMnP != cr) {
ll nconE = cE, nconO = cO;
int bR = (!((cr - nMnP) & 1) ? (nMnP & 1) : ((nMnP & 1) ^ 1));
nconE += sum(cl, nMnP, bR);
nconO += sum(cl, nMnP, bR ^ 1);
stk.emplace(nMnP + 1, cr, nconE, nconO);
}
}
}
void Main() {
cin >> n;
int cMn = 0;
a[0] = INF;
for (int i = 1; i <= n; i++) {
cin >> a[i];
if (a[i] < a[cMn]) cMn = i;
}
int i = 1, j = cMn;
while (i <= n) {
b[i] = a[j];
spt[0][i] = i;
(i & 1 ? pref[1][i] : pref[0][i]) += b[i];
pref[0][i] += pref[0][i - 1];
pref[1][i] += pref[1][i - 1];
i++;
j = (j + 1 > n ? j + 1 - n : j + 1);
}
for (int i = 1; i < lg; i++) {
for (int j = 1; j + (1 << i) - 1 <= n; j++) {
spt[i][j] = merge_st(spt[i - 1][j], spt[i - 1][j + (1 << (i - 1))]);
}
}
DncIterative(2, n, (n & 1) * b[1], (!(n & 1)) * b[1]);
// Calculate ans[1]
int l = n, r = 2, state = 1;
ans[1] += b[1];
while (l != r) {
if (!state) ans[1] += max(b[l], b[r]);
(b[l] > b[r] ? --l : ++r);
state ^= 1;
}
if (!state) ans[1] += b[l];
for (int i = 1; i <= n; i++) b[i] = ans[i];
i = cMn, j = 1;
while (j <= n) {
ans[i] = b[j];
j++;
i = (i + 1 > n ? 1 : i + 1);
}
for (int i = 1; i <= n; i++) {
cout << ans[i] << el;
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
#define name "InvMOD"
if (fopen(name ".INP", "r")) {
freopen(name ".INP", "r", stdin);
freopen(name ".OUT", "w", stdout);
}
int t = 1; while (t--) Main();
return 0;
}
