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.*;
import java.util.*;

public class Main2 implements Runnable {


    long m = (int)1e9+7;
    PrintWriter rw;
    ArrayList<Integer> prime;
    ArrayList<Integer> factors;
    boolean is_prime[];
    InputReader sc;
    public void run() {
        sc = new InputReader(System.in);
        rw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[] a = new int[n];
        ArrayList<Integer> index = new ArrayList<>();
        ArrayList<Integer> notUsed = new ArrayList<>();
        boolean[] visited = new boolean[n];
        for(int i = 0; i < n; i++){
            int friend = sc.nextInt() - 1;
            a[i] = friend;
            if(friend == -1){
                index.add(i);
            } else {
                visited[friend] = true;
            }
        }

        for(int i = n-1; i >= 0; i--){
            if(!visited[i]){
                notUsed.add(i);
            }
        }

        for(int i = 0; i < notUsed.size(); i++){
            int x = index.get(i);
            int y = notUsed.get(i);
            a[x] = y;
        }

        for(int i = 0; i < notUsed.size(); i++){
            int x = index.get(i);
            int y = notUsed.get(i);
            if(x == y){
                if(i > 0){
                    i--;
                } else {
                    i++;
                }
                int x1 = index.get(i);
                int y1 = notUsed.get(i);
                a[x] = y1;
                a[x1] = y;
                break;
            }
        }
        for(int i = 0; i < n; i++){
            rw.print(a[i] + 1 + " ");
        }


        rw.close();
    }



    private static int maxIndex(List<Integer> list) {
        Integer i=0, maxIndex=-1, max=null;
        for (Integer x : list) {
            if ((x!=null) && ((max==null) || (x>max))) {
                max = x;
                maxIndex = i;
            }
            i++;
        }
        return maxIndex;
    }

    public void factor(int n){
        factors = new ArrayList<>();
        for(int i = 1; i <= n; i++){
            if(n % i == 0){
                factors.add(i);
            }
        }
    }

    public void merge(int[] left, int[] right, int[] a){
        int nLeft = left.length;
        int nRight = right.length;
        int i = 0, j = 0, k = 0;
        while(i < nLeft && j < nRight) {
            if (left[i] <= right[j]) {
                a[k] = left[i];
                k++;
                i++;
            } else {
                a[k] = right[j];
                k++;
                j++;
            }
        }
        while (i < nLeft) {
            a[k] = left[i];
            i++;
            k++;
        }
        while (j < nRight) {
            a[k] = right[j];
            j++;
            k++;
        }
    }

    public void mergeSort(int[] a){
        int n = a.length;
        if(n < 2){
            return;
        }
        int mid = n/2;
        int[] left = new int[mid];
        int[] right = new int[n-mid];
        for(int i = 0; i < mid; i++){
            left[i] = a[i];
        }
        for(int i = mid; i < n; i++){
            right[i-mid] = a[i];
        }
        mergeSort(left);
        mergeSort(right);
        merge(left,right,a);
    }

    static int smallest(int[] arr){
        int min = arr[0];
        for(int i = 1; i < arr.length; i++){
            if(arr[i] < min){
                min = arr[i];
            }
        }
        return min;
    }

    static int largest(int[] arr) {
        int i;
        int max = arr[0];
        for (i = 1; i < arr.length; i++)
            if (arr[i] > max)
                max = arr[i];
        return max;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    void sieve(int n) {
        is_prime = new boolean[n+10];
        prime = new ArrayList<>();
        for(int i=2;i<=n;i++)
            is_prime[i] = true;

        for (int i = 2; i <= n; ++i) {
            if (is_prime[i]) prime.add(i);
            for (int j = 0; j < prime.size () && i * prime.get(j) < n; ++j) {
                is_prime[i * prime.get(j)] = false;
                if (i % prime.get(j) == 0) break;
            }
        }
    }
    public static void sortbyColumn(int arr[][], int col){
        Arrays.sort(arr, new Comparator<int[]>()
        {
            public int compare(int[] o1, int[] o2){
                return(Integer.valueOf(o1[col]).compareTo(o2[col]));
            }
        });

    }
    public static class DJSet {
        public int[] upper;

        public DJSet(int n) {
            upper = new int[n];
            Arrays.fill(upper, -1);
        }

        public int root(int x) {
            return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
        }

        public boolean equiv(int x, int y) {
            return root(x) == root(y);
        }

        public boolean union(int x, int y) {
            x = root(x);
            y = root(y);
            if (x != y) {
                if (upper[y] < upper[x]) {
                    int d = x;
                    x = y;
                    y = d;
                }
                upper[x] += upper[y];
                upper[y] = x;
            }
            return x == y;
        }
    }
    public static int[] radixSort(int[] f)    {
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        return f;
    }


    public void printArray(int[] a){
        for(int i=0;i<a.length;i++)
            rw.print(a[i]+" ");
        rw.println();
    }
    public int[] scanArrayI(int n){
        int[] a = new int[n];
        for(int i=0;i<n;i++)
            a[i] = sc.nextInt();
        return a;
    }

    public int[][] scan2dArrayI(int n, int m){
        int [][] a = new int[n][m];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                a[i][j] = sc.nextInt();
            }
        }
        return  a;
    }
    public void print2dArrayI(int[][] a){
        for(int i = 0; i < a.length; i++){
            for(int j = 0; j < a.length; j++){
                rw.print(a[i][j] + " ");
            }
            rw.println();
        }
    }
    public long[] scanArrayL(int n){
        long[] a = new long[n];
        for(int i=0;i<n;i++)
            a[i] = sc.nextLong();
        return a;
    }
    public void printArray(long[] a){
        for(int i=0;i<a.length;i++)
            rw.print(a[i]+" ");
        rw.println();
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main2(),"Main",1<<26).start();
    }
}