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.

Examples

Input

4
2 3 4 1


Output

1 3 2 4


Input

2
2 1


Output

-1


Input

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


Output

1 3 2 4 6 5 7 9 8 10 12 11 13
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		int[] ng = na(n);
		for(int i= 0;i <n;i++)ng[i]--;
		if(n == 2){
			out.println(-1);
			return;
		}
		
		// 先頭hとして、hのあとが未登場のやつ1個に向いてたらアウト
		int[] f = new int[n];
		for(int i = 0;i < n;i++){
			f[ng[i]]++;
		}
		
		LST lst = new LST(n);
		lst.setRange(n);
		int[] ans = new int[n];
		outer:
		for(int i = 0;i < n-1;i++){
			for(int j = lst.next(0);j != -1;j = lst.next(j+1)){
				if(i > 0 && ng[ans[i-1]] == j)continue;
				lst.unset(j);
				if(i == n-3){
					int k = lst.next(0), l = lst.next(k+1);
					if(ng[k] == l && ng[l] == k){
						lst.set(j);
						continue;
					}
				}
				f[ng[j]]--;
//				tr(i, j, f, ng, f[ng[j]], n-2-i);
				if(f[ng[j]] == n-2-i && lst.get(ng[j])){
					f[ng[j]]++;
					lst.set(j);
					continue;
				}
				ans[i] = j;
				continue outer;
			}
			throw new RuntimeException();
		}
		ans[n-1] = lst.next(0);
		
		for(int i = 0;i < n;i++){
			out.print(ans[i]+1 + " ");
		}
		out.println();
	}
	
	public static class LST {
		public long[][] set;
		public int n;
//		public int size;
		
		public LST(int n) {
			this.n = n;
			int d = 1;
			for(int m = n;m > 1;m>>>=6, d++);
			
			set = new long[d][];
			for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){
				set[i] = new long[m+1];
			}
//			size = 0;
		}
		
		// [0,r)
		public LST setRange(int r)
		{
			for(int i = 0;i < set.length;i++, r=r+63>>>6){
				for(int j = 0;j < r>>>6;j++){
					set[i][j] = -1L;
				}
				if((r&63) != 0)set[i][r>>>6] |= (1L<<r)-1;
			}
			return this;
		}
		
		// [0,r)
		public LST unsetRange(int r)
		{
			if(r >= 0){
				for(int i = 0;i < set.length;i++, r=r+63>>>6){
					for(int j = 0;j < r+63>>>6;j++){
						set[i][j] = 0;
					}
					if((r&63) != 0)set[i][r>>>6] &= ~((1L<<r)-1);
				}
			}
			return this;
		}
		
		public LST set(int pos)
		{
			if(pos >= 0 && pos < n){
//				if(!get(pos))size++;
				for(int i = 0;i < set.length;i++, pos>>>=6){
					set[i][pos>>>6] |= 1L<<pos;
				}
			}
			return this;
		}
		
		public LST unset(int pos)
		{
			if(pos >= 0 && pos < n){
//				if(get(pos))size--;
				for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){
					set[i][pos>>>6] &= ~(1L<<pos);
				}
			}
			return this;
		}
		
		public boolean get(int pos)
		{
			return pos >= 0 && pos < n && set[0][pos>>>6]<<~pos<0;
		}
		
		public LST toggle(int pos)
		{
			return get(pos) ? unset(pos) : set(pos);
		}
		
		public int prev(int pos)
		{
			for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){
				int pre = prev(set[i][pos>>>6], pos&63);
				if(pre != -1){
					pos = pos>>>6<<6|pre;
					while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}
		
		public int next(int pos)
		{
			for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){
				int nex = next(set[i][pos>>>6], pos&63);
				if(nex != -1){
					pos = pos>>>6<<6|nex;
					while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}
		
		private static int prev(long set, int n)
		{
			long h = set<<~n;
			if(h == 0L)return -1;
			return -Long.numberOfLeadingZeros(h)+n;
		}
		
		private static int next(long set, int n)
		{
			long h = set>>>n;
			if(h == 0L)return -1;
			return Long.numberOfTrailingZeros(h)+n;
		}
		
		@Override
		public String toString()
		{
			List<Integer> list = new ArrayList<Integer>();
			for(int pos = next(0);pos != -1;pos = next(pos+1)){
				list.add(pos);
			}
			return list.toString();
		}
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
