Problem:
Score : 800 points

Problem Statement

Niwango has N cards, numbered 1,2,\ldots,N.
He will now arrange these cards in a row.

Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.
To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.

To the immediate right of Card 1 (if any) is NOT Card a_1.

To the immediate right of Card 2 (if any) is NOT Card a_2.

\vdots

To the immediate right of Card N (if any) is NOT Card a_N.

Constraints

2 \leq N \leq 10^{5}

1 \leq a_i \leq N

a_i \neq i

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:

b_1 b_2 \ldots b_N

Here, b_i represents the i-th card from the left.

Sample Input 1

4
2 3 4 1

Sample Output 1

1 3 2 4

The arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition "to the immediate right of Card 1 is not Card 2."

Sample Input 2

2
2 1

Sample Output 2

-1

If no arrangements satisfy the conditions, print -1.

Sample Input 3

13
2 3 4 5 6 7 8 9 10 11 12 13 12

Sample Output 3

1 3 2 4 6 5 7 9 8 10 12 11 13

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

// >>> TEMPLATES

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#define INF (numeric_limits<int>::max()/2-1)
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }

// <<<
// >>> segment tree

template <class Handler>
struct Segtree : Handler {
    using Value = typename Handler::Value;
    using Handler::unit; // () -> Value
    using Handler::merge; // (Value,Value) -> Value

    vector<Value> v; // use v[1..2*cap-1]
    int cap; // capacity: power of 2
    int n; // original size

    Segtree() {}
    Segtree(int n) { init(n); }
    template <class It> Segtree(It first, It last) { init(first, last); }
    void init(int n) {
        assert(n >= 0); this->n = n;
        for (cap = 1; cap < n; cap <<= 1) ;;
		v.assign(2*cap, unit());
    }
    template <class It> void init(It first, It last) {
        init(distance(first,last));
        copy(first, last, next(v.begin(), cap));
        for (int i = cap-1; i >= 1; i--) v[i] = merge(v[2*i],v[2*i+1]);
    }
    int size() const { return n; }
    void set(int i, Value const& x) {
        assert(0 <= i && i < size());
        i += cap; v[i] = x;
        while (i > 1) i >>= 1, v[i] = merge(v[2*i],v[2*i+1]);
    }
    Value operator[](int i) const { return get(i); }
    Value get(int i) const {
        assert(0 <= i && i < size());
        return v[cap + i];
    }
    // [l,r)
    Value get(int l, int r) const {
        assert(0 <= l && l <= r && r <= size());
        Value x = unit(), y = unit();
        for (l += cap, r += cap; l < r; l >>= 1, r >>= 1) {
            if (l&1) x = merge(x, v[l++]);
            if (r&1) y = merge(v[--r], y);
        }
        return merge(x,y);
    }
    vector<Value> dat() const {
        vector<Value> ret(size());
        for (int i = 0; i < size(); i++) ret[i] = get(i);
        return ret;
    }
};

// <<<

struct RangeMax {
    using Value = pair<int,int>;
    constexpr static Value unit() { return {-INF,-1}; }
    constexpr static Value merge(Value x, Value y) { return max(x,y); }
};

int32_t main() {
    int n; cin >> n;
    vector<int> a(n); cin >> a;
    rep (i,n) a[i]--;
    if (n == 2) quit(-1);

    Segtree<RangeMax> seg(n);
    {
        vector<pair<int,int> > cnt(n);
        rep (i,n) cnt[a[i]].fst++;
        rep (i,n) cnt[i].snd = i;
        seg.init(all(cnt));
    }
    set<int> s;
    rep (i,n) s.insert(i);

    vector<int> ans;
    auto add = [&](int i) {
        ans.eb(i);
        seg.set(a[i],{seg[a[i]].fst-1,seg[a[i]].snd});
        seg.set(i,RangeMax::unit());
        s.erase(i);
        dump(ans,s);
    };
    rep (i,n) {
        assert(sz(s) == n-sz(ans));
        const int NN = 5;
        if (sz(s) <= NN) {
            vector<int> v;
            for (int x : s) v.eb(x);
            sort(all(v));
            dump(v);
            do {
                bool flag = false;
                rep (i,sz(v)-1) if (a[v[i]] == v[i+1]) flag = true;
                if (!ans.empty() && a[ans.back()] == v[0]) flag = true;
                if (!flag) {
                    for (int x : v) ans.eb(x);
                    rep (i,sz(ans)) cout << (i ? " " : "") << ans[i]+1;
//                    for (int x : ans) cout << x+1 << " ";
                    cout << endl;
                    exit(0);
                }
            } while (next_permutation(all(v)));
            assert(0);
        } else {
            auto p = seg.get(0,n);
            assert(p.snd != -1);
            if (p.fst == sz(s)-1) {
                add(p.snd);
            } else {
                int x = *s.begin();
                if (!ans.empty() && a[ans.back()] == x) {
                    assert(sz(s) >= 2);
                    x = *++s.begin();
                }
                add(x);
            }
        }
    }
    assert(0);

}