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++ (GCC 9.2.1) (judge verdict: Accepted)

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

const long double PI = 4*atan(1);

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define f1r(i,a,b) for (int i = (a); i < (b); ++i)
#define f0r(i,a) f1r(i,0,a)
#define trav(a, x) for (auto& a : x)
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)(x).size()
#define all(x) x.begin(), x.end()
#define rall(x) rbegin(x), rend(x)
#define resz resize
#define ins insert

template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
  cout << "["; for(int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]"; }

template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }

namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1, T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T, SZ>& a);
    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class T, class... Ts> void re(T& t, Ts&... ts) {
        re(t); re(ts...); }
    template<class T> void re(complex<T>& x) { T a,b; re(a, b); x = cd(a, b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f, p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
    void pr(int x) { cout << x; }
    void pr(long x) { cout << x; }
    void pr(ll x) { cout << x; }
    void pr(unsigned x) { cout << x; }
    void pr(unsigned long x) { cout << x; }
    void pr(unsigned long long x) { cout << x; }
    void pr(float x) { cout << x; }
    void pr(double x) { cout << x; }
    void pr(ld x) { cout << x; }
    void pr(char x) { cout << x; }
    void pr(const char* x) { cout << x; }
    void pr(const string& x) { cout << x; }
    void pr(bool x) { pr(x ? "true" : "false"); }
    template<class T> void pr(const complex<T>& x) { cout << x; }
    template<class T1, class T2> void pr(const pair<T1, T2>& x);
    template<class T> void pr(const T& x);
    template<class T, class... Ts> void pr(const T& t, const Ts&... ts) {
        pr(t); pr(ts...); }
    template<class T1, class T2> void pr(const pair<T1, T2>& x) {
        pr("{",x.f,", ",x.s,"}"); }
    template<class T> void pr(const T& x) {
        pr("{");
        bool fst = 1; for (const auto& a: x) pr(!fst ? ", " : "", a), fst = 0;
        pr("}"); }
    void ps() { pr("\n"); }
    template<class T, class... Ts> void ps(const T& t, const Ts&... ts) {
        pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); }
    void pc() { pr("]\n"); }
    template<class T, class... Ts> void pc(const T& t, const Ts&... ts) {
        pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); }
}

using namespace output;

namespace io {
    void setIn(string s) { freopen(s.c_str(), "r", stdin); }
    void setOut(string s) { freopen(s.c_str(), "w", stdout); }
    void setIO(string s = "") {
        cin.sync_with_stdio(0); cin.tie(0);
        if (sz(s)) { setIn(s + ".in"), setOut(s + ".out"); }
    }
}

using namespace io;
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

const int MOD = 1e9 + 7;

typedef decay<decltype(MOD)>::type T;
struct mi {
    T val;
    explicit operator T() const { return val; }
    mi() { val = 0; }
    mi(const ll& v) {
        val = (-MOD <= v && v <= MOD) ? v : v % MOD;
        if (val < 0) val += MOD; }
    friend ostream& operator<<(ostream& os, const mi& a) { return os << a.val; }
    friend void pr(const mi& a) { pr(a.val); }
    friend void re(mi& a) { ll x; re(x); a = mi(x); }
    friend bool operator==(const mi& a, const mi& b) { return a.val == b.val; }
    friend bool operator!=(const mi& a, const mi& b) { return !(a == b); }
    friend bool operator<(const mi& a, const mi& b) { return a.val < b.val; }
    mi operator-() const { return mi(-val); }
    mi& operator+=(const mi& m) {
        if ((val += m.val) >= MOD) val -= MOD;
        return *this; }
    mi& operator-=(const mi& m) {
        if ((val -= m.val) < 0) val += MOD;
        return *this; }
    mi& operator*=(const mi& m) { val = (ll) val * m.val % MOD;
        return *this; }
    friend mi pow(mi a, ll p) {
        mi ans = 1; assert(p >= 0);
        for (; p; p /= 2, a *= a) if (p & 1) ans *= a;
        return ans; }
    friend mi inv(const mi& a) { assert(a != 0); return pow(a, MOD-2); }
    mi& operator/=(const mi& m) { return (*this) *= inv(m); }
    friend mi operator+(mi a, const mi& b) { return a += b; }
    friend mi operator-(mi a, const mi& b) { return a -= b; }
    friend mi operator*(mi a, const mi& b) { return a *= b; }
    friend mi operator/(mi a, const mi& b) { return a /= b; }
};

typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
const int MAX = 1e5 + 5;
int cnt[MAX];
int a[MAX];
set<pi, greater<pi>> use;
set<int> rem;
vi ans;
void process(int id){ // remove id
    rem.erase(id);
    use.erase(mp(cnt[id], id));
    int v = a[id];
    if(rem.count(v) == 0) return;
    use.erase(mp(cnt[v], v));
    cnt[v]--;
    use.insert(mp(cnt[v], v));
}

int last(){
    if(sz(ans)) return a[ans.back()];
    return -1;
}
bool each_other(int x, int y){
    if(a[x] == y && a[y] == x) return true;
    return false;
}
bool check_bad(int id){ // if i remove id will i be bad
    if(last() == id) return true;
    int v = a[id];
    if(rem.count(v) && cnt[v] == sz(rem)-1){
        return true;
    }
    if(sz(rem) == 3){
        int x = *rem.begin();
        int y = *rem.rbegin();
        int z = *next(rem.begin());
        if(y == id) swap(y, z);
        if(x == id) swap(x, z);
        if(each_other(x, y)){
            return true;
        }
    }
    if(sz(rem) == 2){
        int x = *rem.begin();
        int y = *rem.end();
        if(last() == x){
            if(a[x] == y) return true;
        }
        else if(last() == y){
            if(a[y] == x) return true;
        }
        else{
            if(a[y] == x && a[x] == y) return true;
        }
    }
    return false;

}
int main(){
    setIO("");
    int n; re(n);
    f0r(i, n) re(a[i]);
    f0r(i, n) a[i]--;
    if(n == 2){
        ps(-1);
        return 0;
    }    f0r(i, n) rem.insert(i);
    f0r(i, n) cnt[a[i]]++;
    f0r(i, n) use.insert(mp(cnt[i], i));
    while(sz(rem)){
        if(sz(rem) == 2){
            int x = *rem.begin();
            int y = *rem.rbegin();
            if(last() == x) ans.eb(y), ans.eb(x);
            else if(last() == y) ans.eb(x), ans.eb(y);
            else if(a[x] == y) ans.eb(y), ans.eb(x);
            else if(a[y] == x) ans.eb(x), ans.eb(y);
            else{
                ans.eb(min(x, y)); ans.eb(max(x, y));
            }
            rem.clear();
            break;
        }
        auto beg = *use.begin();
        if(beg.f == sz(rem)-1){
            ans.eb(beg.s);
            process(beg.s);
        }
        else{
            int small = *rem.begin();
            if(sz(rem) == 3){
                for(auto x: rem){
                    if(!check_bad(x)){
                        ans.eb(x);
                        process(x);
                        break;
                    }
                }
            }
            else{
                for(auto x: rem){
                    if(!check_bad(x)){
                        ans.eb(x);
                        process(x);
                        break;
                    }
                }
            }
        }
    }
    for(int x: ans) pr(x+1, " ");
    ps();
    return 0;
}