Problem: There are n friends who want to give gifts for the New Year to each other. Each friend should give exactly one gift and receive exactly one gift. The friend cannot give the gift to himself.

For each friend the value f_i is known: it is either f_i = 0 if the i-th friend doesn't know whom he wants to give the gift to or 1 ≤ f_i ≤ n if the i-th friend wants to give the gift to the friend f_i.

You want to fill in the unknown values (f_i = 0) in such a way that each friend gives exactly one gift and receives exactly one gift and there is no friend who gives the gift to himself. It is guaranteed that the initial information isn't contradictory.

If there are several answers, you can print any.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of friends.

The second line of the input contains n integers f_1, f_2, ..., f_n (0 ≤ f_i ≤ n, f_i ≠ i, all f_i ≠ 0 are distinct), where f_i is the either f_i = 0 if the i-th friend doesn't know whom he wants to give the gift to or 1 ≤ f_i ≤ n if the i-th friend wants to give the gift to the friend f_i. It is also guaranteed that there is at least two values f_i = 0.

Output

Print n integers nf_1, nf_2, ..., nf_n, where nf_i should be equal to f_i if f_i ≠ 0 or the number of friend whom the i-th friend wants to give the gift to. All values nf_i should be distinct, nf_i cannot be equal to i. Each friend gives exactly one gift and receives exactly one gift and there is no friend who gives the gift to himself.

If there are several answers, you can print any.

Examples

Input


5
5 0 0 2 4


Output


5 3 1 2 4 


Input


7
7 0 0 1 4 0 6


Output


7 3 2 1 4 5 6 


Input


7
7 4 0 3 0 5 1


Output


7 4 2 3 6 5 1 


Input


5
2 1 0 0 0


Output


2 1 4 5 3 

Solution (in JAVA):

Solution:


import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.net.StandardSocketOptions;
import java.security.cert.CollectionCertStoreParameters;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

import javax.script.ScriptEngine;
import javax.script.ScriptEngineManager;
import javax.script.ScriptException;

public class Main {

	public static int lowerBound(ArrayList<Integer> array, int length, long value) {
		int low = 0;
		int high = length;
		while (low < high) {
			final int mid = (low + high) / 2;
			if (value <= array.get(mid)) {
				high = mid;
			} else {
				low = mid + 1;
			}
		}
		return low;
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static void sortbyColumn(int arr[][], int col) {
		// Using built-in sort function Arrays.sort
		Arrays.sort(arr, new Comparator<int[]>() {

			@Override
			// Compare values according to columns
			public int compare(final int[] entry1, final int[] entry2) {

				// To sort in descending order revert
				// the '>' Operator
				// if (entry1[col] > entry2[col])
				// return 1;
				// else //(entry1[col] >= entry2[col])
				// return -1;
				return new Integer(entry1[col]).compareTo(entry2[col]);
				// return entry1[col].
			}
		}); // End of function call sort().
	}

	class pair<X, Y> { // utilizing Java "Generics"
		X _first;
		Y _second;

		public pair(X f, Y s) {
			_first = f;
			_second = s;
		}

		X first() {
			return _first;
		}

		Y second() {
			return _second;
		}

		void setFirst(X f) {
			_first = f;
		}

		void setSecond(Y s) {
			_second = s;
		}
	}

	public static int[] swap(int data[], int left, int right) {
		int temp = data[left];
		data[left] = data[right];
		data[right] = temp;
		return data;
	}

	public static int[] reverse(int data[], int left, int right) {
		while (left < right) {
			int temp = data[left];
			data[left++] = data[right];
			data[right--] = temp;
		}
		return data;
	}

	public static boolean findNextPermutation(int data[]) {
		if (data.length <= 1)
			return false;

		int last = data.length - 2;
		while (last >= 0) {
			if (data[last] < data[last + 1]) {
				break;
			}
			last--;
		}
		if (last < 0)
			return false;

		int nextGreater = data.length - 1;
		for (int i = data.length - 1; i > last; i--) {
			if (data[i] > data[last]) {
				nextGreater = i;
				break;
			}
		}
		data = swap(data, nextGreater, last);
		data = reverse(data, last + 1, data.length - 1);
		return true;
	}

	static long nCr(long n, long r) {
		long x = 1;
		long yu = n - r;
		while (n > r) {
			x = x * n;
			n--;
		}
		while (yu > 0) {
			x /= yu;
			yu--;
		}
		return x;
	}

	/*
	 * static boolean prime[] = new boolean[1000007];
	 * 
	 * public static void sieveOfEratosthenes(int n) {
	 * 
	 * for (int i = 0; i < n; i++) prime[i] = true; * for (int p = 2; p * p <=
	 * n; p++) { // If prime[p] is not changed, then it is a prime if (prime[p]
	 * == true) { // Update all multiples of p for (int i = p * p; i <= n; i +=
	 * p) prime[i] = false; } }
	 * 
	 * // Print all prime numbers // for(int i = 2; i <= n; i++) // { //
	 * if(prime[i] == true) // System.out.print(i + " "); // } }
	 */

	static long power(long fac2, int y, int p) {

		// Initialize result
		long res = 1;

		// Update x if it is more than or
		// equal to p
		fac2 = fac2 % p;

		while (y > 0) {

			// If y is odd, multiply x
			// with result
			if (y % 2 == 1)
				res = (res * fac2) % p;

			// y must be even now
			y = y >> 1; // y = y/2
			fac2 = (fac2 * fac2) % p;
		}

		return res;
	}

	// Returns n^(-1) mod p
	static long modInverse(long fac2, int p) {
		return power(fac2, p - 2, p);
	}

	// Returns nCr % p using Fermat's
	// little theorem.
	static long nCrModPFermat(int n, int r, int p) {

		// Base case
		if (r == 0)
			return 1;

		return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p;
	}

	static long[] fac;

	public static void main(String[] args) throws NumberFormatException, IOException, ScriptException {
		FastReader sc = new FastReader();
		PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		// Scanner scn = new Scanner(System.in);
		//
		int n = sc.nextInt();
		int arr[] = new int[n];
		HashSet<Integer> h = new HashSet<>();

		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
			if (arr[i] != 0) {
				h.add(arr[i]);
			}
		}
		int c = 1;
		// System.out.println("h");
		ArrayList<Integer> an = new ArrayList<>();
		for (int i = 0; i < n; i++) {

			if (arr[i] == 0) {
				while (h.contains(c) == true) {
					c++;
				}
				an.add(c);
				c++;
			}
		}
		// ArrayList<Integer> ans = new ArrayList<>();
		c = -1;
		int j=0;
	//	System.out.println(an);
		for (int i = 0; i < n; i++) {
			if (arr[i] == 0) {
			//	System.out.println((i+1)+" "+(an.get(j))+" "+c);
				if ((i + 1) != an.get(j))
					arr[i] = an.get(j);
				else {
					if (c == -1) {
						arr[i] = an.get(j + 1);
						an.add(0, an.remove(j + 1));

					} else {
						
						int t = arr[c];
						arr[c] = an.get(j);
						arr[i] = t;
					//	System.out.println(t+" "+c);
					}
				}
				j++;
				c = i;
				//System.out.println(c);
			}
		}
		for(int i=0;i<n;i++)
			pr.print(arr[i]+" ");
		//
		// coded to perfection by Rohan Mukhija
		pr.flush();
		pr.close();
	}

	private static boolean possible(long[] arr, int[] f, long mid, long k) {
		long c = 0;

		for (int i = 0; i < arr.length; i++) {
			if ((arr[i] * f[f.length - i - 1]) > mid) {
				c += (arr[i] - (mid / f[f.length - i - 1]));
			}
		}
		// System.out.println(mid+" "+c);
		if (c <= k)
			return true;
		return false;
	}

}