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.IOException; 
import java.io.InputStreamReader; 
import java.util.*; 
import java.util.StringTokenizer; 
import java.io.PrintWriter;
import java.io.*;
import java.util.stream.Collectors.*;
import java.lang.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;
public class Ideo
{ 
    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 int power(int x,int y) 
{ 
    int res = 1;      // Initialize result 
  
      // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y%2==1) 
            res = (res*x); 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x);   
    } 
    return res; 
} 
 
 static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
 
 
  static boolean compareSeq(char[] S, int x, int y, int n) 
    { 
        for (int i = 0; i < n; i++)
         {
 
            if (S[x] < S[y]) 
               return true;
            else if (S[x] > S[y]) 
                return false; 
            x = (x + 1) % n; 
            y = (y + 1) % n; 
        } 
        return true; 
    } 
 
    static void build(long[] sum,int[] arr,int n)
    {
      for(int i=0;i<(1<<n);i++)
      {
        long total=0;
        for(int j=0;j<n;j++)
        {
          if((i & (1 << j)) > 0)
            total+=arr[j];
        }
 
        sum[i]=total;
      }
    }
 
 
     static int count(long arr[], long x, int n) 
       {
 
        int l=0;
        int h=n-1;
 
        int res=-1;
        int mid=-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res=mid;
            h=mid-1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }
 
        if(res==-1)
          return 0;
 
        //res is first index and res1 is last index of an element in a sorted array total number of occurences is (res1-res+1)
 
        int res1=-1;
        l=0;
        h=n-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res1=mid;
            l=mid+1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }
 
 
 
        if(res1==-1)
          return 0;
        if(res!=-1 && res1!=-1)
          return (res1-res+1);
 
        return 0;
 
       } 
 
       static int parity(int a)
       {
    a^=a>>16;
    a^=a>>8;
    a^=a>>4;
    a^=a>>2;
    a^=a>>1;
    return a&1;
  }
/*
  PriorityQueue<aksh> pq = new PriorityQueue<>((o1, o2) -> {
            if (o1.p < o2.p)
                return 1;
            else if (o1.p > o2.p)
                return -1;
            else
                return 0;
 
        });//decreasing order acc to p*/
static int power(int x, int y, int m)  
    { 
        if (y == 0) 
            return 1; 
          
        int p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
static int modinv(int a, int m) 
    { 
        int g = gcd(a, m); 
        if (g != 1) 
            return 0;
        else 
        { 
           return power(a, m - 2, m); 
        } 
        //return 0;
    } 
 
static int[] product(int[] nums) {
    int[] result = new int[nums.length];
 
    int[] t1 = new int[nums.length];
    int[] t2 = new int[nums.length];
 
    t1[0]=1;
    t2[nums.length-1]=1;
 
    //scan from left to right
    for(int i=0; i<nums.length-1; i++){
        t1[i+1] = nums[i] * t1[i];
    }
 
    //scan from right to left
    for(int i=nums.length-1; i>0; i--){
        t2[i-1] = t2[i] * nums[i];
    }
 
    for(int i=0;i<nums.length;i++)
      {
        System.out.print(t1[i]+" "+t2[i]);
        System.out.println();
      }
 
    //multiply
    for(int i=0; i<nums.length; i++){
        result[i] = t1[i] * t2[i];
    }
 
    return result;
}
 
static int getsum(int[] bit,int ind)
{
  int sum=0;
  while(ind>0)
  {
    sum+=bit[ind];
    ind-= ind & (-ind);
  }
 
  return sum;
}
 
static void update(int[] bit,int max,int ind,int val)
{
  while(ind<=max)
  {
    bit[ind]+=val;
    ind+= ind & (-ind);
  }
}
 
    //static ArrayList<Integer>[] adj;
    static int[] bfs(ArrayList<Integer>[] adj,int n,ArrayList<Integer> arr)
    {
      int[] vis=new int[n];
      int[] dis=new int[n];
      int[] par=new int[n];
      Queue<Integer> q=new LinkedList<>();
 
      Arrays.fill(dis,-1);
 
      for(int i=0;i<arr.size();i++)
      {
        vis[arr.get(i)]=1;
        dis[arr.get(i)]=0;
        par[arr.get(i)]=-1;
        q.add(arr.get(i));
      }
 
      while(!q.isEmpty())
      {
        int x=q.remove();
        for(int u:adj[x])
        {
          if(vis[u]==0)
          {
            vis[u]=1;
            dis[u]=dis[x]+1;
            par[u]=x;
            q.add(u);
          }
        }
      }
 
      return dis;
    }
 
    static boolean check(long mid,long a,long b)
    {
      long count=1;
      while(count<=mid)
      {
        count++;
        if(a<b)
          a+=count;
        else
          b+=count;
 
        if(a==b)
          return true;
      }
        return false;
    }
 
    static class a1 implements Comparable<a1>
    {
      int p;
      int q;
 
      public a1(int p,int q)
      {
        this.p=p;
        this.q=q;
      }
 
      public int compareTo(a1 o)
      {
        return p-o.p;
      }
    }
    static int get(int arr[], int n) 
    { 
        int result = 0; 
        int x, sum; 
          
        // Iterate through every bit 
        for(int i=0; i<32; i++) 
        { 
            // Find sum of set bits at ith position in all  
            // array elements 
            sum = 0; 
            x = (1 << i); 
            for(int j=0; j<n; j++) 
            { 
                if((arr[j] & x)!=0) 
                sum++; 
            } 
            // The bits with sum not multiple of 3, are the 
            // bits of element with single occurrence. 
            if ((sum % 3)!=0) 
            result |= x; 
        } 
        return result; 
    } 
    /*        Collections.sort(orders, new Comparator<Point>() {
            @Override
            public int compare(Point o1, Point o2) {
                if (o1.diff < o2.diff) {
                    return -1;
                } else if (o1.diff > o2.diff) {
                    return 1;
                } else {
                    return 0;
                }
            }
        });  */
 
 
    static boolean isPrime(int n)  
    {  
        // Corner cases  
        if (n <= 1) return false;  
        if (n <= 3) return true;  
          
        // This is checked so that we can skip  
        // middle five numbers in below loop  
        if (n % 2 == 0 || n % 3 == 0) return false;  
          
        for (int i = 5; i * i <= n; i = i + 6)  
            if (n % i == 0 || n % (i + 2) == 0)  
            return false;  
          
        return true;  
    }  
      
    static int nextPrime(int N)  
    {  
      
        // Base case  
        if (N <= 1)  
            return (2-N);  
      
        int prime = N;  
        boolean found = false;  
      
        // Loop continuously until isPrime returns  
        // true for a number greater than n  
        while (!found)  
        {  
            if (isPrime(prime))  
                {
                  found = true;
                  break;
                }  
 
            prime++;
        }  
      
        return (prime-N);  
    }  
 
 
    static long product(long x) 
{ 
    long prod = 1; 
    while (x > 0)  
    { 
        prod *= (x % 10); 
        x /= 10; 
    } 
    return prod; 
} 
  
// This function returns the number having 
// maximum product of the digits 
static long findNumber(long l, long r) 
{ 
    // Converting both integers to strings 
    //string a = l.ToString(); 
    String b = Long.toString(r); 
  
    // Let the current answer be r 
    long ans = r; 
    for (int i = 0; i < b.length(); i++)  
    { 
        if (b.charAt(i) == '0') 
            continue; 
  
        // Stores the current number having 
        // current digit one less than current 
        // digit in b 
        char[] curr = b.toCharArray(); 
        curr[i] = (char)(((int)(curr[i] -  
                    (int)'0') - 1) + (int)('0')); 
  
        // Replace all following digits with 9 
        // to maximise the product 
        for (int j = i + 1; j < curr.length; j++) 
            curr[j] = '9'; 
  
        // Convert string to number 
        int num = 0; 
        for (int j = 0; j < curr.length; j++) 
            num = num * 10 + (curr[j] - '0'); 
  
        // Check if it lies in range and its product 
        // is greater than max product 
        if (num >= l && product(ans) < product(num)) 
            ans = num; 
    } 
  
    return product(ans); 
} 
 
static long mod=998244353;
 
static long pow(long in, long pow) {
    if(pow == 0) return 1;
    long out = pow(in, pow / 2);
    out = (out * out) % mod;
    if(pow % 2 == 1) out = (out * in) % mod;
    return out;
  }
  static long inv(long in) {
    return pow(in, mod - 2);
  }
 
  static void swap(int x,int y)
  {
    int temp=x;
    x=y;
    y=temp;
  }
 
  static int[] par;
  static int[] size;
  static int find(int i) 
  {
     if (par[i] == i)
      return i;
 
    return par[i] = find(par[par[i]]);
  }
 
  static void union(int x, int y) 
  {
      x = find(x);
      y = find(y);
      if (x == y)
        return;
      if (size[x] < size[y])
        swap(x, y);
 
      par[y] = x;
      size[x] += size[y];
    }
 
    static final long INF = Long.MAX_VALUE/5;
    static ArrayList<Integer>[] adj;
    public static void main(String args[] ) throws Exception 
    {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT */
 
        FastReader sc=new FastReader();
        int n=sc.nextInt();
        int[] a=new int[n+1];
        ArrayList<Integer> give=new ArrayList<>();
        ArrayList<Integer> take=new ArrayList<>();
        HashSet<Integer> h=new HashSet<>();
 
        for(int i=1;i<=n;i++)
          {
            a[i]=sc.nextInt();
            if(a[i]==0)
              give.add(i);
            h.add(a[i]);
          }
 
        for(int i=1;i<=n;i++)
        {
          if(!h.contains(i))
            take.add(i);
        }

        for (int i=0;i<take.size();i++)
        {
          a[give.get(i)]=take.get(i);
          if ((int)take.get(i) == (int)give.get(i))
          {
            if(i>0)
              {
                int temp=a[give.get(i-1)];
                a[give.get(i-1)]=a[give.get(i)];
                a[give.get(i)]=temp;
              }
            else
              {
                Integer temp=take.get(i+1);
                take.set(i+1,take.get(i));
                take.set(i,temp);
                a[give.get(i)] = take.get(i);
              }
          }
        }

        for(int i=1;i<=n;i++)
          System.out.print(a[i]+" ");

      }
 
    }