CIRCLE (THT)

#define task "CIRCLE"

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>

using namespace std;

using ll = long long;
using ld = long double;

constexpr int N = 1e5 + 5;
constexpr int Inf = 1e9 + 7;

int id[] = {0, 1, 2};
int n, a[N], b[N], ans[N], tmp[N];
bool ck[N];
vector<int> s[3];

void Read()
{
    cin >> n;
    for (int i = 0; i < n; ++i)
        cin >> a[i];
}

void Sub_1()
{
    int x = 0, sum(0);
    do
    {
        sum += a[(x + 1) % n] - a[(x + 2) % n];
        (x += 3) %= n;
        b[x] = -sum;
    } while (x != 0);

    int minn = *min_element(b, b + n);
    for (int i = 0; i < n; ++i)
        cout << b[i] - minn + 1 << " ";
}

void Sub_2()
{
    for (int i = 0; i < 3; ++i)
    {
        int x = i, sum(0);
        while (x < n)
        {
            s[i].emplace_back(x);
            b[x] = -sum;
            sum += a[(x + 1) % n] - a[(x + 2) % n];
            x += 3;
        }
    }

    do
    {
        fill(tmp, tmp + n, 0);
        fill(ck + 1, ck + n + 1, false);

        int mex(1);

        for (int i = 0; i < 3; ++i)
        {
            int minn(Inf);
            for (auto j : s[id[i]])
                minn = min(minn, b[j]);

            for (auto j : s[id[i]])
            {
                tmp[j] = b[j] + mex - minn;
                if (tmp[j] > n || ck[tmp[j]])
                    goto done;
                ck[tmp[j]] = 1;
            }

            for (int j = 1; j <= n; ++j)
                if (!ck[j])
                {
                    mex = j;
                    break;
                }
        }

        for (int i = 0; i < n; ++i)
            if (ans[i] == 0 || ans[i] > tmp[i])
            {
                for (int j = 0; j < n; ++j)
                    ans[j] = tmp[j];
                break;
            }
            else if (ans[i] < tmp[i])
                goto done;

    done:;

    } while (next_permutation(id, id + 3));

    for (int i = 0; i < n; ++i)
        cout << ans[i] << " ";
}

int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    if (fopen(task ".INP", "r"))
    {
        freopen(task ".INP", "r", stdin);
        freopen(task ".OUT", "w", stdout);
    }
    Read();
    if (n % 3 != 0)
        Sub_1();
    else
        Sub_2();
}