Recently, Dima met with Sasha in a philatelic store, and since then they are collecting coins together. Their favorite occupation is to sort collections of coins. Sasha likes having things in order, that is why he wants his coins to be arranged in a row in such a way that firstly come coins out of circulation, and then come coins still in circulation. 

For arranging coins Dima uses the following algorithm. One step of his algorithm looks like the following:

  1. He looks through all the coins from left to right; 
  2. If he sees that the i-th coin is still in circulation, and (i + 1)-th coin is already out of circulation, he exchanges these two coins and continues watching coins from (i + 1)-th. 



Dima repeats the procedure above until it happens that no two coins were exchanged during this procedure. Dima calls hardness of ordering the number of steps required for him according to the algorithm above to sort the sequence, e.g. the number of times he looks through the coins from the very beginning. For example, for the ordered sequence hardness of ordering equals one.

Today Sasha invited Dima and proposed him a game. First he puts n coins in a row, all of them are out of circulation. Then Sasha chooses one of the coins out of circulation and replaces it with a coin in circulation for n times. During this process Sasha constantly asks Dima what is the hardness of ordering of the sequence. 

The task is more complicated because Dima should not touch the coins and he should determine hardness of ordering in his mind. Help Dima with this task. 

Input

The first line contains single integer n (1 ≤ n ≤ 300 000) — number of coins that Sasha puts behind Dima.

Second line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n) — positions that Sasha puts coins in circulation to. At first Sasha replaces coin located at position p1, then coin located at position p2 and so on. Coins are numbered from left to right.

Output

Print n + 1 numbers a0, a1, ..., an, where a0 is a hardness of ordering at the beginning, a1 is a hardness of ordering after the first replacement and so on. 

Examples

Input

4
1 3 4 2


Output

1 2 3 2 1


Input

8
6 8 3 4 7 2 1 5


Output

1 2 2 3 4 3 4 5 1

Note

Let's denote as O coin out of circulation, and as X — coin is circulation.

At the first sample, initially in row there are coins that are not in circulation, so Dima will look through them from left to right and won't make any exchanges.

After replacement of the first coin with a coin in circulation, Dima will exchange this coin with next three times and after that he will finally look through the coins and finish the process.

XOOO →  OOOX

After replacement of the third coin, Dima's actions look this way:

XOXO →  OXOX →  OOXX

After replacement of the fourth coin, Dima's actions look this way:

XOXX →  OXXX

Finally, after replacement of the second coin, row becomes consisting of coins that are in circulation and Dima will look through coins from left to right without any exchanges.
      import java.util.*; 
                                            import java.math.*;
                                            import java.io.*;
                                            import java.text.DecimalFormat;
                                            import java.math.BigInteger;
                                            public class Main{
                                                //static int d=20;
                                                static long mod=1000000007 ;
                                                
                                                static ArrayList<ArrayList<Integer>> arr;
                                               // static long[] dp1,dp2;
                                                static int[] a;
                                                static int[] vis,num;
                                                static long max;
                                                static HashSet<String> hs;
                                                //static int flag,ans;
                                                static long max1,max2,ans1;
                                                
                                                static int flag=0;
                                                static int[] tin,tout,parent,level;
                                                static HashMap<Long,Integer> hm;
                                                static long[] dp1,dp2,dp3,dp4;
                                                   
                                                public static void main(String[] args)  throws IOException {
                                                    ///long start=System.currentTimeMillis();
                                                    boolean online =false;
                                                    String fileName = "B-small-attempt0";
                                                    PrintWriter out; 
                                                    if (online) {
                                                        s.init(new FileInputStream(new File("Downloads/"+fileName + ".in")));
                                                         out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                                    }
                                                     else {
                                                        s.init(System.in);   
                                                    
                                                        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
                                                        //out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                                    }//r,b,y,g

                                                    int n=s.ni();
                                                    int[] a=new int[n];
                                                    int[] c=new int[n+1];
                                                    for(int i=0;i<n;i++)
                                                        a[i]=s.ni();
                                                    int prev=1;
                                                    int[] b=new int[n+1];
                                                    out.print("1 ");
                                                    for(int i=0;i<n;i++){
                                                        if(i==n-1){
                                                            out.print("1 ");
                                                        }
                                                        else{
                                                            int x=a[i];
                                                            c[x]++;
                                                            if(x==n || (b[x+1]==1)){
                                                                b[x] = 1;
                                                                int ct=0;
                                                                for(int j=x-1;j>=1;j--){
                                                                    if(c[j]==1)
                                                                        ct++;
                                                                    else
                                                                        break;
                                                                    b[j]=1;

                                                                }
                                                                out.print((prev-ct)+" ");
                                                                prev=prev-ct;
                                                            }
                                                            else{
                                                                prev++;
                                                                out.print(prev+" ");
                                                            }
                                                        }
                                                    }
                                                    out.println();
                                                    out.close();
                                                        
                                                      
                                                            
                                            
                                                }
                                               
                                                

                                                public static void union(int[] a,int x,int y){
                                                    int u=find(a,x);
                                                    int v=find(a,y);
                                                    a[v]=u;

                                                }
                                                public static int find(int[] a,int x){
                                                    if(a[x]!=x){
                                                        a[x]=find(a,a[x]);
                                                    }
                                                    return a[x];
                                                }
                                                public static int gcd(int a, int b){
                                                        if (a == 0) return b;
                                                        return gcd(b % a, a);
                                                }
                                                    
                                                public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
                                                    vis[c]=1;
                                                    if(g!=-1){
                                                        if(!arr.get(c).contains(g)){
                                                            flag=1;
                                                            return;
                                                        }
                                                    }
                                                    for(int x:arr.get(c)){
                                                        if(x!=p && x!=g && vis[x]==0 ){
                                                            cfs(arr,x,c,p,vis);
                                                        }
                                                    }
         
                                                }
                                                                      //   public static void dfs(int u,int p){
                 //                            //       if(p>=0)
                 //                            //           tin[u]=tout[u]=tt++;
                 //                            //       if(p>=0)
                 //                            //           level[u]=level[p]+1;
                 //                            //       parent[u]=p;
                 //                            //       for(int x:arr.get(u)){
                 //                            //           if(x!=p){
                 //                            //               dfs(x,u);
                 //                            //               tout[u]=Math.max(tout[u],tout[x]);
                 //                            //           }
                 //                            //       }
                 //                            //       
                 //
                 //
                                             //   }
                                                public static int lca(int[][] p,int a,int b){
                                                    if(level[a]<level[b]){
                                                        int x=a;
                                                        a=b;
                                                        b=x;
                                                    }
                                                    int log=p[0].length;
                                                    for(int i=log-1;i>=0;i--){
                                                        if(1<<i<=level[a]-level[b]){
                                                            a=p[a][i];
                                                        }
                                                    }
                                                    if(a==b)
                                                        return a;
                                                    for(int i=log-1;i>=0;i--){
                                                        if(p[a][i]!=p[b][i]){
                                                            a=p[a][i];
                                                            b=p[b][i];
                                                        }
                                                    }
                                                    return p[a][0];
                 
                                                }
                                                public static int[][] par(int[] parent){
                                                    int n=arr.size();
                                                    int[][] p=new int[n][17];
                                                    for(int i=0;i<n;i++)
                                                        p[i][0]=parent[i];
                                                    for(int k=1;k<17;k++){
                                                        for(int i=0;i<n;i++){
                                                            if(p[i][k-1]>-1)
                                                                p[i][k]=p[p[i][k-1]][k-1];
                                                            else
                                                                p[i][k]=-1;
                                                        }
                                                    }
                                                    return p;
                                                }
                                                static class Edge implements Comparable<Edge>{
                                                       int from;
                                                        int to;
                                                        long cost;
                                                
                                                       public Edge(int from, int to, long weight) {
                                                           this.from = from;
                                                           this.to = to;
                                                           this.cost= weight;
                                                       }
                                                       public int compareTo(Edge o){
                                                            return (int)Math.signum(cost-o.cost); 
                                                       }

                                                }                               
                                                static class Node {
                                                    int start;
                                                    int end;
                                
                                                    int cost;
                                                    int updated;
                                
                                                    Node[] nodes;
                                
                                                    public Node(int start, int end) {
                                                        this.start = start;
                                                        this.end = end;
                                
                                                        if (start < end) {
                                                            int[] pos = {start, (start + end) / 2, end};
                                                            nodes = new Node[2];
                                                            for (int i = 0; i < 2; i++) {
                                                                nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                                                            }
                                                        }
                                                    }
                                
                                                    public void update(int queryStart, int queryEnd, int value) {
                                                        if (queryEnd < start || end < queryStart) {
                                                            return;
                                                        }
                                
                                                        if (queryStart <= start && end <= queryEnd) {
                                                            cost += value;
                                                            updated += value;
                                                            return;
                                                        }
                                
                                                        propagate();
                                                        for (Node node: nodes) {
                                                            node.update(queryStart, queryEnd, value);
                                                        }
                                                    }
                                
                                                    public int query(int pos) {
                                                        if (pos < start || end < pos) {
                                                            return 0;
                                                        }
                                
                                                        if (start == end) {
                                                            return cost;
                                                        }
                                
                                                        propagate();
                                                        int ans = 0;
                                                        for (Node node: nodes) {
                                                            ans = Math.max(ans, node.query(pos));
                                                        }
                                                        return ans;
                                                    }
                                
                                                    public void propagate() {
                                                        if (updated != 0 && start < end) {
                                                            for (Node node: nodes) {
                                                                node.cost += updated;
                                                                node.updated += updated;
                                                            }
                                                            updated = 0;
                                                        }
                                                    }
                                                }
                                                public static double nthroot(int n, double A) {
                                                    return nthroot(n, A, 0.0000001);
                                                }
                                                public static double nthroot(int n, double A, double p) {
                                                    if(A < 0) {
                                                        System.err.println("A < 0");// we handle only real positive numbers
                                                        return -1;
                                                    } else if(A == 0) {
                                                        return 0;
                                                    }
                                                    double x_prev = A;
                                                    double x = A / n;  // starting "guessed" value...
                                                    while(Math.abs(x - x_prev) > p) {
                                                        x_prev = x;
                                                        x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
                                                    }
                                                    return x;
                                                }
                                                
                                                static class item implements Comparable<item> {
                                                    int from,to,cost;
                                                    public item(int x,int y){
                                                        from=x;
                                                        to=y;
                                                        
                                                    }
                                                    public int compareTo(item o){
                                                        
                                                        return  o.cost-cost;
                                                    }
                                                    
                                                }
                                               
                                                public static void dfs2(int c,int p,int[] a){
                                                    //System.out.println(c+" "+p);
                                                   
                                                    
                                                    
                         
                                                }
                //public static void dfs(int x,int[] vis,Stack<Integer> st){
                                                //    vis[x]=1;
                                                //    ArrayList<Integer> arr2=arr.get(x);
                                                //    Collections.sort(arr2);
                                                //    for(int i=arr2.size()-1;i>=0;i--){
                                                //        int z=arr2.get(i);
                                                //        if(vis[z]==0)
                                                //            dfs(z,vis,st);
                                                //    }
                                                //    st.push(x);
                         //
                                                //}
                                                public static long gcd(long a, long b){
                                                        if (a == 0) return b;
                                                        return gcd(b % a, a);
                                                }
                                                    
                                                public static boolean check(long x){
                                                    if(x%4==0 || x%7==0 || x%11==0)
                                                        return true;
                                                    if(x<4 || x<7 || x<11)
                                                        return false;
                                                    if(x%2==0){
                                                        return check(x/2);
                                                    }
                                                    else
                                                        return check(x/2) && check((x+1)/2);
                                                }
                                                public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
                                                    long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
                                                    if(val<0)
                                                        return 1;
                                                    else if(val>0)
                                                        return -1;
                                                    else
                                                        return 0;
                                                }
                                                
                                                static class BIT{
                                                
                                                    int N;
                                                    long tree[];
                                                    
                                                    BIT(int N){
                                                        this.N = N;
                                                        tree = new long[N + 1];
                                                    }
                                                    
                                                    void update(int idx,long val){
                                                        while(idx <= N){
                                                            tree[idx]+=val;
                                                            idx += (idx & -idx);
                                                        }
                                                    }
                                                    
                                                    long query(int l,int r){
                                                        if(l == 1)
                                                            return read(r);
                                                        else
                                                            return read(r) - read(l-1);
                                                    }
                                                    
                                                    long read(int idx){
                                                        long sum = 0;
                                                        while(idx > 0){
                                                            sum += tree[idx];
                                                            idx -= (idx & -idx);
                                                        }
                                                        return sum;
                                                    }
                                                }
                                                public static boolean pal(String a){
                                                    int i=0;
                                                    int j=a.length()-1;
                                                    while(i<j){
                                                        if(a.charAt(i)!=a.charAt(j)){
                                                            return false;
                                                        }
                                                        i++;
                                                        j--;
                                                    }
                                                    return true;
                                                        
                                                }
                                                public static long find(long n,long k){
                                                    if(n==2){
                                                        if(k==1 || k==3)
                                                            return 1;
                                                        else
                                                            return 2;
                                                    }
                                                    long t=pow2(2,n,mod)-1;
                                                    long z=(t+1)/2;
                                                    if(k==z)
                                                        return n;
                                                    if(k<z)
                                                        return find(n-1,k);
                                                    else
                                                        return find(n-1,k-z);
                                                }
                                                public static long pow2(long a,long b,long mod){
                                                        
                                                        long ans=1;
                                                       // long z=b;
                                                        while(b>0){
                                                           
                                                            if(b%2==1)
                                                                ans=(a*ans)%mod;
                                                            a=(a*a)%mod;
                                                            b/=2;
                                                        }
                                                      
                                                        return  ans;
                                                }
                                                 public static long pow3(long a,long b){
                                                        
                                                        long ans=1;
                                                       // long z=b;
                                                        while(b>0){
                                                           
                                                            if(b%2==1)
                                                                ans=(a*ans);
                                                            a=(a*a);
                                                            b/=2;
                                                        }
                                                      
                                                        return  ans;
                                                }
                                                public static long fib(long n){
                                                    long[][]    f=new long[][]{{1L,1L},{1L,0}};
                                                    if(n==0)
                                                        return 0;
                                                    f=arrpow(f,n-1);
                                                    return f[0][0];
                                                }
                                                public static long[][] arrpow(long[][] a,long b){
                                                   
                                                        int n=a.length;
                                                      //  long z=b;
                                                        long[][] ans=new long[n][n];
                                                        for(int i=0;i<n;i++)
                                                            ans[i][i]=1L;
                                                        while(b>0){
                                                            
                                                            if(b%2==1)
                                                                ans=mul(a,ans);
                                                            a=mul(a,a);
                                                            b/=2;
                                                        }
                                                        
                                                        return  ans;
                                                }
                                                public static long[][] mul(long[][] a,long[][] b){
                                                    int n=a.length;
                                                    int m=b[0].length;
                                                    long[][] ans=new long[n][m];
                                                    if(n==2 && m==2 && b.length==2){
                                                        ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
                                                        ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
                                                        ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
                                                        ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
                                                        return ans;
                     
                                                    }
                                                    for(int i=0;i<n;i++){
                                                        for(int j=0;j<m;j++){
                                                            for(int k=0;k<b.length;k++){
                                                                ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                                                            }
                                                        }
                                                    }
                                                    return ans; 
                                                }
                                                 static class name implements Comparable<name> {
                                                    long l,b,h;
                                                    public name(long   x,long y,long z){
                                                        {
                                                            l=x;
                                                            b=y;        
                                                        }
                                                        
                                                        
                                                        h=z;
                                                    }
                                                    public int compareTo(name o){
                                                        return -(int)(l*b-o.l*o.b);
                                                    }
                                                    
                                                }
                                                public static class s {
                                                    static BufferedReader reader;
                                                    static StringTokenizer tokenizer;
                                                
                                                    /** call this method to initialize reader for InputStream */
                                                    static void init(InputStream input) {
                                                        reader = new BufferedReader(
                                                                    new InputStreamReader(input) );
                                                        tokenizer = new StringTokenizer("");
                                                    }   
                                                
                                                    /** get next word */
                                                    static String ns() throws IOException {
                                                        while ( ! tokenizer.hasMoreTokens() ) {
                                                            //TODO add check for eof if necessary
                                                            tokenizer = new StringTokenizer(
                                                                reader.readLine() );
                                                        }
                                                        return tokenizer.nextToken();
                                                    }
                                                
                                                    static int ni() throws IOException {
                                                        return Integer.parseInt( ns() );
                                                    }
                                                
                                                    static double nd() throws IOException {
                                                        return Double.parseDouble( ns() );
                                                    }
                                                    static long nl() throws IOException {
                                                        return Long.parseLong( ns() );
                                                    }
                                                }
                                            }   
