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


public class Main
{
	private InputStream is;
	private PrintWriter out;
	int time = 0, freq[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7), arr[], weight[][], x[], y[], parent[];
	int MAX = 1000001, N, K;
	long red[], ans = Long.MAX_VALUE;

	ArrayList<Integer>[] amp;
	ArrayList<Pair>[] pmp;
	boolean b[];
	boolean boo[][], b1[];
	Pair prr[];
	HashMap<Pair, Integer> hm = new HashMap();
	int Dp[][] = new int[1100][1100];

	void soln() 
	{
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();

		// out.close();
		out.flush();
		// tr(System.currentTimeMillis() - s + "ms");
	}

	static class ST1 // min ST
	{
		long arr[], st[];
		int size;

		ST1(long a[]) {
			arr = a.clone();
			size = 10 * arr.length;
			st = new long[size];
			build(0, arr.length - 1, 1);
		}

		void build(int ss, int se, int si) {
			if (ss == se) {
				st[si] = arr[ss];
				return;
			}
			int mid = (ss + se) / 2;
			int val = 2 * si;
			build(ss, mid, val);
			build(mid + 1, se, val + 1);
			st[si] = Math.min(st[val], st[val + 1]);
		}

		void update(int ss, int se, int idx, long val, int si) {
			if (ss == se) {
				// if(si==idx+1)
				st[si] = val;
				return;
			}
			int mid = (ss + se) / 2;
			if (ss <= idx && idx <= mid) {
				update(ss, mid, idx, val, 2 * si);
			} else {
				update(mid + 1, se, idx, val, 2 * si + 1);
			}
			int v = 2 * si;
			st[si] = Math.min(st[v], st[v + 1]);
		}

		long get(int ss, int se, int l, int r, int si) {
			if (l > se || r < ss || l > r)
				return Long.MAX_VALUE / 1000;
			if (l <= ss && r >= se)
				return st[si];
			int mid = (ss + se) / 2;
			int val = 2 * si;
			return Math.min(get(ss, mid, l, r, val), get(mid + 1, se, l, r, val + 1));
		}
	}

	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable() 
		{
			public void run() 
			{
				try 
				{
					// new CODEFORCES().soln();
				} catch (Exception e) 
				{
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
		new Main().soln();
	}

	int D[][];
	char ch[][], ch1[];
	int hash = 29;
	int x2, y2;
	HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
	cell[] c;
	Pair[] p = new Pair[4];
	void solve() 
	{
		int n = ni();
		int arr[] = new int[n+1];
		for(int i = 1; i<=n; i++) arr[i] = ni();
		int last = n;
		int ans = 0;
		out.print(1+" ");
		boolean b[] = new boolean[n+1];
		for(int i = 1; i<=n; i++) {
			b[arr[i]] = true;
			while(last>0 && b[last]) {
				ans++;
				last--;
			}
			out.print(i+1-ans+" ");
		}
	}
	void bfs(int s, int n) {
		b = new boolean[n];
		dist = new int[n];
		Arrays.fill(dist, 1000000);
		dist[s] = 0;
		b[s] = true;
		Queue<Integer> q = new LinkedList<>();
		q.add(s);
		while(!q.isEmpty()) {
			int y = q.poll();
			for(int i : amp[y]) {
				dist[i] = min(dist[i],dist[y]+1);
				if(!b[i]) {
					b[i] = true;
					q.add(i);
				}
			}
		}
	}
	boolean check(String s, String s1) {
		char ch1[] = s.toCharArray(), ch2[] = s1.toCharArray();
		int arr[] = new int[10];
		for(char c : ch1) {
			arr[c-'0']++;
		}
		int ans = 0;
		for(char c:ch2) {
			arr[c-'0']--;
		}
		
		for(int i:arr) ans += ((i>0)?i:0);
		return ans==3;
	}
	void seive(int n)
	{
		start = new int[n];
		for(int i = 2;i<n;i++) {
			if(start[i]==0) {
				for(int j = 2*i;j<n;j+=i) {
					start[j] = i;
				}
			}
		}
	}
	void print(int[][] arr) 
	{
		int seed = 110, n = arr.length - 220;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				System.out.print(arr[i + seed][j + seed] + " ");
			}
			System.out.println();
		}
		System.out.println();
	}

	 class cell implements Comparable<cell>
	 {
		int s, d, p, i;

		cell(int t, int d, int p, int i) {
			this.s = t;
			this.p = p;
			this.d = d;
			this.i = i;
		}

		public int compareTo(cell other) {
			// return Integer.compare(val, other.val);
			return Long.compare(d, other.d) != 0 ? (Long.compare(d, other.d)): (Long.compare(i,other.i));
											// other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)):
											// (Long.compare(v, other.v)))
			// &(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)):
			// (Long.compare(v, other.u))));
		}

		public String toString() {
			return this.d + " " + this.s +" "+this.p+" "+this.i;
		}
	}

	long abs(long x)
	{
		return ((x > 0) ? x : -x);
	}

	long ret(int p) 
	{
		if (p >= 0)
			return 0;
		else
			return 1;
	}

	long val(int p, int a, int b) 
	{
		if (p >= 0) {
			return (a * 1l * p);
		}
		return (b * 1l * p);
	}

	void ternary_search(int l, int r) 
	{
		// System.out.println(l+" "+r+" "+ans);
		// for(int i : arr) System.out.print(i+" ");
		// System.out.println();
		if (r >= l) {
			int mid1 = l + (r - l) / 3;
			int mid2 = r - (r - l) / 3;
			long cnt1 = 0, cnt2 = 0;
			cnt1 = compute(mid1);
			cnt2 = compute(mid2);
			// System.out.println(mid1+" "+ cnt1+" "+mid2+" "+cnt2);
			ans = Math.min(cnt1, cnt2);
			if (cnt1 < cnt2) {
				ternary_search(l, mid2 - 1);
			} else {
				ternary_search(mid1 + 1, r);
			}
		}
		return;
	}

	long compute(int x) 
	{
		long ans = 0;
		int c = arr[0];
		for (int i = 1; i <= x; i++) {
			ans += max(c + 1 - arr[i], 0);
			c = max(c + 1, arr[i]);
		}
		int temp = arr[x];
		arr[x] = max(c + 1, arr[x]);
		// SSystem.out.println(arr[x]+" "+ans);
		c = arr[arr.length - 1];
		for (int i = arr.length - 1; i > x; i--) {
			ans += max(c + 1 - arr[i - 1], 0);
			c = max(c + 1, arr[i - 1]);
		}
		arr[x] = temp;
		return ans;
	}

	public int getParent(int x) 
	{
		while (parent[x] != x) {
			parent[x] = parent[parent[x]];
			x = parent[x];
		}
		return x;
	}

	void getFactors(int n, int x)
	{
		for (int i = 1; i * i <= n; i++) {
			if (n % i == 0) {
				hs[x].add(i);
				hs[x].add(n / i);
			}
		}
	}

	void recur(int a, int b, int k) 
	{
		if (k == 0) {
			if (a == x2 && b == y2)
				ans++;
			return;
		}
		recur(a, b + 1, k - 1);
		recur(a, b - 1, k - 1);
		recur(a + 1, b, k - 1);
		recur(a - 1, b, k - 1);
	}

	int min(int a, int b) 
	{
		return (a < b) ? a : b;
	}

	/*private class Cell implements Comparable<Cell> {
		int u, v, s;

		public Cell(int u, int v, int s) {
			this.u = u;
			this.v = v;
			this.s = s;
		}

		public int hashCode() {
			return Objects.hash();
		}

		public int compareTo(Cell other) {
			return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
					: (Long.compare(v, other.v) != 0 ? Long.compare(v, other.v) : Long.compare(u, other.u)))
					& ((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
							: (Long.compare(u, other.v) != 0 ? Long.compare(u, other.v) : Long.compare(v, other.u))));
		}

		public String toString() {
			return this.u + " " + this.v;
		}
	}*/

	class Pair implements Comparable<Pair>
	{
		int u ,v,i;

		Pair(int u, int v) {
			this.u = u;
			this.i = v;
		}

		Pair(int u, int v, int i) {
			this.u = u;
			this.v = v;
			this.i = i;
		}

		public int hashCode() {
			return Objects.hash();
		}

		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));
		}

		public int compareTo(Pair other) {
			// return Integer.compare(val, other.val);
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(i, other.i));// ((Long.compare(u,
		
		}									
		public String toString() {
			return this.u + " " + this.v +" "+this.i;
		}
	}

	int max(int a, int b) 
	{
		if (a > b)
			return a;
		return b;
	}

	static class FenwickTree 
	{

		int[] array; // 1-indexed array, In this array We save cumulative
						// information to perform efficient range queries and
						// updates

		public FenwickTree(int size) {
			array = new int[size + 1];
		}

		public int rsq(int ind) {
			assert ind > 0;
			int sum = 0;
			while (ind > 0) {
				sum += array[ind];
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and decrementing ind by that
				// number
				ind -= ind & (-ind);
			}
			return sum;
		}

		public int rsq(int a, int b) {
			assert b >= a && a > 0 && b > 0;
			return rsq(b) - rsq(a - 1);
		}

		public void update(int ind, int value) {
			assert ind > 0;
			while (ind < array.length) {
				array[ind] += value;
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and incrementing ind by that
				// number
				ind += ind & (-ind);
			}
		}

		public int size() {
			return array.length - 1;
		}
	}

	void buildGraph(int n)
	{
		for (int i = 0; i < n; i++) {
			int x1 = ni(), y1 = ni(), z = ni();
			//pmp[x1].add(new Pair(y1, z));
		}
	}

	long modInverse(long a, long mOD2)
	{
		return power(a, mOD2 - 2, mOD2);
	}

	long power(long x, long y, long m) 
	{
		if (y == 0)
			return 1;
		long p = power(x, y / 2, m) % m;
		p = (p * p) % m;

		return (y % 2 == 0) ? p : (x * p) % m;
	}

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

	static class ST 
	{
		int arr[], lazy[], n;

		ST(int a) {
			n = a;
			arr = new int[10 * n];
			lazy = new int[10 * n];
		}

		void up(int l, int r, int val) {
			update(0, n - 1, 0, l, r, val);
		}

		void update(int l, int r, int c, int x, int y, int val) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l > r || x > y || l > y || x > r)
				return;
			if (x <= l && y >= r)

			{
				lazy[c] += val;
				return;
			}
			int mid = l + r >> 1;
			update(l, mid, 2 * c + 1, x, y, val);
			update(mid + 1, r, 2 * c + 2, x, y, val);
			arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
		}

		int an(int ind) {
			return ans(0, n - 1, 0, ind);
		}

		int ans(int l, int r, int c, int ind) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l == r)
				return arr[c];
			int mid = l + r >> 1;
			if (mid >= ind)
				return ans(l, mid, 2 * c + 1, ind);
			return ans(mid + 1, r, 2 * c + 2, ind);
		}
	}

	public static int[] shuffle(int[] a, Random gen)
	{
		for (int i = 0, n = a.length; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int d = a[i];
			a[i] = a[ind];
			a[ind] = d;
		}
		return a;
	}

	long power(long x, long y, int mod)
	{
		long ans = 1;
		while (y > 0) {
			if (y % 2 == 0) {
				x = (x * x) % mod;
				y /= 2;
			} else {
				ans = (x * ans) % mod;
				y--;
			}
		}
		return ans;
	}

	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() 
	{
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}