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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {

    static double Phi = (1 + Math.sqrt(5)) / 2.0;
    static int MAX = -1 >>> 1;
    static long MODL = 1_000_000_007L;
    static int MOD = 1_000_000_007;
    static void no() throws IOException {println("NO");}
    static void yes() throws IOException {println("YES");}

    static boolean testCases = false;
    static boolean DEBUG = true;

    static void main() throws Exception {
        int n = ni();
        int[] f = new int[n];
        int[] rcvFrom = new int[n];
        int[] givenTo = new int[n];
        Arrays.fill(rcvFrom, -1);
        Arrays.fill(givenTo, -1);
        for (int i = 0; i < n; ++i) {
            f[i] = ni() - 1;
            if (f[i] != -1) {
                givenTo[i] = f[i];
                rcvFrom[f[i]] = i;
            }
        }
        debug(Arrays.toString(rcvFrom));
        debug(Arrays.toString(givenTo));
        // 3 types
        // 00
        // x0
        // 0x

        Deque<Integer> type1 = new ArrayDeque<>();
        Queue<Integer> type2 = new LinkedList<>();
        Queue<Integer> type3 = new LinkedList<>();

        for (int i = 0; i < n; ++i) {
            if (rcvFrom[i] == -1 && givenTo[i] == -1) {
                type1.add(i);
            } else if (rcvFrom[i] == -1) {
                type2.add(i);
            } else if (givenTo[i] == -1) {
                type3.add(i);
            }
        }
        debug(type1);
        debug(type2);
        debug(type3);
        //handles even case..1 remains in odd case
        //what if type2 and type3 are zero but this is odd??
        if(type2.size() == 0 && type3.size() == 0 && type1.size() % 2 != 0) {
            //00 00 00
            int first = type1.peek();
            while(!type1.isEmpty()) {
                int head = type1.poll();
                givenTo[head] = type1.isEmpty() ? first : type1.peek();
                rcvFrom[type1.isEmpty() ? first : type1.peek()] = head;
            }
        }
        while (type1.size() > 1) {
            int p1 = type1.poll();
            int p2 = type1.poll();
            rcvFrom[p1] = p2;
            rcvFrom[p2] = p1;
            givenTo[p1] = p2;
            givenTo[p2] = p1;
        }
        debug(type1);
        if(!type1.isEmpty()) {
            //one remains 
            int p1 = type1.poll();
            //there must be 1 of each type2 and type3
            int p2 = type2.poll();
            int p3 = type3.poll();
            rcvFrom[p1] = p3;
            givenTo[p1] = p2;

            rcvFrom[p2] = p1;
            givenTo[p3] = p1;
        }
        //can also handle case when type1 is always zero
        while (!type2.isEmpty() && !type3.isEmpty()) {
            int p1 = type2.poll();
            int p2 = type3.poll();
            rcvFrom[p1] = p2;
            givenTo[p2] = p1;
        }
        assert type2.isEmpty() && type3.isEmpty();
        for(int ele : givenTo) {
            print(ele + 1 + " ");
        }
        println();
    }

    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (DEBUG && System.getProperty("ONLINE_JUDGE") == null) {
            HABLA = true;
            debug("Debugging enabled");
        }

        int t = testCases ? ni() : 1;
        int to = t;
        while (t-- > 0) {
            debug("Case #" + (to - t) + " ---------------- ");
            main();
        }
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (HABLA)
            debug("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
    }

//IO Stuff
    private static boolean HABLA = false;
    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T str) throws IOException {
        printerBW.append(str.toString());
        if (HABLA) flush();
    }

    static <T> void println() throws IOException {
        printerBW.append('\n');
        if (HABLA) flush();
    }

    static <T> void println(T str) throws IOException {
        if (str == null) {
            printerBW.append("null\n");
        } else {
            printerBW.append(str.toString());
            printerBW.append('\n');
            if (HABLA) flush();
        }
    }

    public static final String ANSI_RESET = "\u001B[0m";
    public static final String ANSI_DEBUG = "\u001B[33m";
    static <T> void debugl(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
        }
        flush();
    }

    static void debug() throws IOException {
        if (!HABLA) return;
        printerBW.append('\n');
        flush();
    }
    static <T> void debug(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null\n");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
            printerBW.append('\n');
        }
        flush();
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }
}