Recently, Mike was very busy with studying for exams and contests. Now he is going to chill a bit by doing some sight seeing in the city.

City consists of n intersections numbered from 1 to n. Mike starts walking from his house located at the intersection number 1 and goes along some sequence of intersections. Walking from intersection number i to intersection j requires |i - j| units of energy. The total energy spent by Mike to visit a sequence of intersections p1 = 1, p2, ..., pk is equal to <image> units of energy.

Of course, walking would be boring if there were no shortcuts. A shortcut is a special path that allows Mike walking from one intersection to another requiring only 1 unit of energy. There are exactly n shortcuts in Mike's city, the ith of them allows walking from intersection i to intersection ai (i ≤ ai ≤ ai + 1) (but not in the opposite direction), thus there is exactly one shortcut starting at each intersection. Formally, if Mike chooses a sequence p1 = 1, p2, ..., pk then for each 1 ≤ i < k satisfying pi + 1 = api and api ≠ pi Mike will spend only 1 unit of energy instead of |pi - pi + 1| walking from the intersection pi to intersection pi + 1. For example, if Mike chooses a sequence p1 = 1, p2 = ap1, p3 = ap2, ..., pk = apk - 1, he spends exactly k - 1 units of total energy walking around them.

Before going on his adventure, Mike asks you to find the minimum amount of energy required to reach each of the intersections from his home. Formally, for each 1 ≤ i ≤ n Mike is interested in finding minimum possible total energy of some sequence p1 = 1, p2, ..., pk = i.

Input

The first line contains an integer n (1 ≤ n ≤ 200 000) — the number of Mike's city intersection.

The second line contains n integers a1, a2, ..., an (i ≤ ai ≤ n , <image>, describing shortcuts of Mike's city, allowing to walk from intersection i to intersection ai using only 1 unit of energy. Please note that the shortcuts don't allow walking in opposite directions (from ai to i).

Output

In the only line print n integers m1, m2, ..., mn, where mi denotes the least amount of total energy required to walk from intersection 1 to intersection i.

Examples

Input

3
2 2 3


Output

0 1 2 


Input

5
1 2 3 4 5


Output

0 1 2 3 4 


Input

7
4 4 4 4 7 7 7


Output

0 1 2 1 2 3 3 

Note

In the first sample case desired sequences are:

1: 1; m1 = 0;

2: 1, 2; m2 = 1;

3: 1, 3; m3 = |3 - 1| = 2.

In the second sample case the sequence for any intersection 1 < i is always 1, i and mi = |1 - i|.

In the third sample case — consider the following intersection sequences:

1: 1; m1 = 0;

2: 1, 2; m2 = |2 - 1| = 1;

3: 1, 4, 3; m3 = 1 + |4 - 3| = 2;

4: 1, 4; m4 = 1;

5: 1, 4, 5; m5 = 1 + |4 - 5| = 2;

6: 1, 4, 6; m6 = 1 + |4 - 6| = 3;

7: 1, 4, 5, 7; m7 = 1 + |4 - 5| + 1 = 3.

	
	    /*
	     * Author- Priyam Vora
	     * BTech 2nd Year DAIICT
	     */
	     
	            
	    import java.io.*;
	    import java.math.*;
	    import java.util.*;
	    import javax.print.attribute.SetOfIntegerSyntax;
	     
	    public class Graph1 {
	    	private static InputStream stream;
	    	private static byte[] buf = new byte[1024];
	    	private static int curChar;
	    	private static int numChars;
	    	private static SpaceCharFilter filter;
	    	private static PrintWriter pw;
	    	private static long count = 0,mod=1000000007;
	    	private static TreeSet<Integer>ts[]=new TreeSet[200000];
	    	private static HashSet hs=new HashSet();
	     
	    	public static void main(String args[]) throws Exception {
	    		InputReader(System.in);
	    		pw = new PrintWriter(System.out);
	    		//ans();
	    		soln();
	    		pw.close();
	    	}
	     
	    	public static long gcd(long x, long y) {
	    		if (x == 0)
	    			return y;
	    		else
	    			return gcd( y % x,x);
	    	}
	    	
	    	private static int BinarySearch(int a[], int low, int high, int target) {
	    		if (low > high)
	    			return -1;
	    		int mid = low + (high - low) / 2;
	    		if (a[mid] == target)
	    			return mid;
	    		if (a[mid] > target)
	    			high = mid - 1;
	    		if (a[mid] < target)
	    			low = mid + 1;
	    		return BinarySearch(a, low, high, target);
	    	}
	    	
	    	public static String reverseString(String s) {
	    		StringBuilder sb = new StringBuilder(s);
	    		sb.reverse();
	    		return (sb.toString());
	    	}
	    	
	    	public static long pow(long n, long p) {
	    		if(p==0)
	    			return 1;
	    		if(p==1)
	    			return n%mod;
	    		if(p%2==0){
	    			long temp=pow(n, p/2);
	    		return (temp*temp)%mod;
	    		}else{
	    			 	long temp=pow(n,p/2);
	    			 	temp=(temp*temp)%mod;
	    			 	return(temp*n)%mod;
	    			 	
	    		}
	    	}
	     
	    		
	     
	    	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 static int nextPowerOf2(final int a) {
	    		int b = 1;
	    		while (b < a) {
	    			b = b << 1;
	    		}
	    		return b;
	    	}
	     
	    	public static boolean PointInTriangle(int p1, int p2, int p3, int p4, int p5, int p6, int p7, int p8) {
	    		int s = p2 * p5 - p1 * p6 + (p6 - p2) * p7 + (p1 - p5) * p8;
	    		int t = p1 * p4 - p2 * p3 + (p2 - p4) * p7 + (p3 - p1) * p8;
	     
	    		if ((s < 0) != (t < 0))
	    			return false;
	     
	    		int A = -p4 * p5 + p2 * (p5 - p3) + p1 * (p4 - p6) + p3 * p6;
	    		if (A < 0.0) {
	    			s = -s;
	    			t = -t;
	    			A = -A;
	    		}
	    		return s > 0 && t > 0 && (s + t) <= A;
	    	}
	     
	    	public static float area(int x1, int y1, int x2, int y2, int x3, int y3) {
	    		return (float) Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
	    	}
	     
	    	public 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;
	    	}
	     
	    	//merge Sort
	     
	    	static long sort(int a[])
	    	{  int n=a.length;
	    		int b[]=new int[n];	
	    		return mergeSort(a,b,0,n-1);}
	    	static long mergeSort(int a[],int b[],long left,long right)
	    	{ long c=0;if(left<right)
	    	 {   long mid=left+(right-left)/2;
	    		 c= mergeSort(a,b,left,mid);
	    		 c+=mergeSort(a,b,mid+1,right);
	    		 c+=merge(a,b,left,mid+1,right); }	
	    		return c;	 }
	    	static long merge(int a[],int  b[],long left,long mid,long right)
	    	{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
	    	while(i<=(int)mid-1&&j<=(int)right)
	    	{ if(a[i]>a[j]) {b[k++]=a[i++]; }
	    	else	{ b[k++]=a[j++];c+=mid-i;}}
	    	while (i <= (int)mid - 1)   b[k++] = a[i++]; 
	    	while (j <= (int)right) b[k++] = a[j++];
	    	for (i=(int)left; i <= (int)right; i++) 
	    		a[i] = b[i];  return c;  }
	    	public static boolean isSubSequence(String large, String small, int largeLen, int smallLen) {
	    		//base cases
	    		if (largeLen == 0)
	    			return false;
	    		if (smallLen == 0)
	    			return true;
	    		// If last characters of two strings are matching
	    		if (large.charAt(largeLen - 1) == small.charAt(smallLen - 1))
	    			isSubSequence(large, small, largeLen - 1, smallLen - 1);
	    		// If last characters are not matching
	    		return isSubSequence(large, small, largeLen - 1, smallLen);
	    	}
	     
	    	// To Get Input
	    	// Some Buffer Methods
	     
	    	public static void InputReader(InputStream stream1) {
	    		stream = stream1;
	    	}
	     
	    	private static boolean isWhitespace(int c) {
	    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    	}
	     
	    	private static boolean isEndOfLine(int c) {
	    		return c == '\n' || c == '\r' || c == -1;
	    	}
	     
	    	private static 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++];
	    	}
	     
	    	private static 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;
	    	}
	     
	    	private static 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;
	    	}
	     
	    	private static String nextToken() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		StringBuilder res = new StringBuilder();
	    		do {
	    			res.appendCodePoint(c);
	    			c = read();
	    		} while (!isSpaceChar(c));
	    		return res.toString();
	    	}
	     
	    	private static String nextLine() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		StringBuilder res = new StringBuilder();
	    		do {
	    			res.appendCodePoint(c);
	    			c = read();
	    		} while (!isEndOfLine(c));
	    		return res.toString();
	    	}
	     
	    	private static int[] nextIntArray(int n) {
	    		int[] arr = new int[n];
	    		for (int i = 0; i < n; i++) {
	    			arr[i] = nextInt();
	    		}
	    		return arr;
	    	}
	     
	    	private static int[][] next2dArray(int n, int m) {
	    		int[][] arr = new int[n][m];
	    		for (int i = 0; i < n; i++) {
	    			for (int j = 0; j < m; j++) {
	    				arr[i][j] = nextInt();
	    			}
	    		}
	    		return arr;
	    	}
	    	private static char[][] nextCharArray(int n,int m){
	    		char [][]c=new char[n][m];
	    		for(int i=0;i<n;i++){
	    			String s=nextLine();
	    			for(int j=0;j<s.length();j++){
	    				c[i][j]=s.charAt(j);
	    			}
	    		}
	    		return c;
	    	}
	     
	    	private static long[] nextLongArray(int n) {
	    		long[] arr = new long[n];
	    		for (int i = 0; i < n; i++) {
	    			arr[i] = nextLong();
	    		}
	    		return arr;
	    	}
	     
	    	private static void pArray(int[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static void pArray(long[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static void pArray(boolean[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static boolean isSpaceChar(int c) {
	    		if (filter != null)
	    			return filter.isSpaceChar(c);
	    		return isWhitespace(c);
	    	}
	     
	    	private interface SpaceCharFilter {
	    		public boolean isSpaceChar(int ch);
	    	}
	
	    	//----------------------------------------My Code------------------------------------------------//
	    	private static void soln() {
	    		//-1 west 1 east 2 north -2 south
	
	    		int n=nextInt();
	    		int a[]=new int [n+1];
	    		for(int i=1;i<=n;i++){
	    			a[i]=nextInt();
	    		}
	    		HashSet hs[]=new HashSet[n+1];
	    		for(int i=1;i<=n;i++)
	    			hs[i]=new HashSet();
	    	Graph g=new Graph(n);
	    		for(int i=1;i<=n;i++){
	   
	    			if(!hs[i].contains(a[i]) && i!=a[i]){
	    				g.addEdge(i, a[i]);
	    			}
	    			if(i<n && !hs[i].contains(i+1)){
	    				g.addEdge(i, i+1);
	    			}
	    			if(i>1 && !hs[i].contains(i-1)){
	    				g.addEdge(i, i-1);
	    			}
	    		}
	    		g.BFS2(1);
	    		pw.print(0+" ");
	    		for(int i=2;i<=n;i++){
	    			pw.print(g.getAn(i)+" ");
	    		}
	    		
	    	}
	    
	    	
	    	
	    	
	    		//-----------------------------------------The End--------------------------------------------------------------------------//
	    	
	    
	    
	    
	 }
	    	
	   
	    
		class Pair implements Comparable<Pair>{
		   
			int ind;
			int len;
			Pair(int ind,int len){
				this.ind=ind;
				this.len=len;
			}
			@Override
			public int compareTo(Pair o) {
				// TODO Auto-generated method stub
			//	Sort in increasing order
return len-o.len;
			}
		
		}
	        class Graph{
	        	private static int V,level[][],count=-1,lev_dfs[],degree=0,no_vert_conn_comp=0;
	        	private Stack <Integer>st=new Stack();
	        	private static LinkedList<Integer > adj[];
	        	private boolean[][] Visite;
	        	private static boolean [] Visited;
	        	private static HashSet<Integer> Vis=new HashSet();
	        	private static Stack<Integer> topo_sort=new Stack<>();
	        	private static HashMap<String,Integer> hm=new HashMap<>();
	  
		    
		    	
	    Graph(int V){
	    V++;
	    this.V=(V);
	    adj=new LinkedList[V];
	    Visite=new boolean[100][100];
	    
 	    Visited=new boolean[V];
	    level=new int[100][100];
	    lev_dfs=new int[V]; 
	   for(int i=0;i<V;i++)
		   adj[i]=new LinkedList<Integer>();
	
	    }
	    void setup(int n,int m){
	    	//HashMap<String,Integer> hm=new HashMap<>();
    		int co=1;
	    	for(int i=0;i<n;i++){
    			for(int j=0;j<m;j++){
    				String s="";
    				s+=(i)+" "+(j);
    				hm.put(s, co);
    			co++;
    			}
    		}
	    }
	   void addEdge(int v,int w){
	    	
	    	if(adj[v]==null){
	    		adj[v]=new LinkedList();
	    	}
	    	adj[v].add(w);
	     
	    	
	    }
	  
	 public static void top_ans(){
	while(topo_sort.size()!=0)
{
	System.out.print(hm.get(topo_sort.peek()));
topo_sort.pop();
}
	
	 }
	 public static void topoSort(int startVert){
		 if(!Vis.contains(startVert)){
			 topoSortUtil(startVert);
		 }
	 }
	    public static void topoSortUtil(int curr_Vert){
	    	Vis.add(curr_Vert);
	    	Iterator<Integer> it=adj[curr_Vert].listIterator();
	    	
	    	while(it.hasNext()){
	    		int n=it.next();
	   // 		System.out.println(n);
	    		if(!Vis.contains(n)){
	    			topoSortUtil(n);
	    		}
	    		
	    	}
	    	topo_sort.push(curr_Vert);
	    }
	    
	    public static int BFS2(int startVert){
	    	Visited=new boolean[V];
	    	for(int i=1;i<V;i++){
	    		lev_dfs[i]=-1;
	    	}
	    //	System.out.println(startVert);
	    	Queue<Integer> q=new LinkedList<Integer>();
	    	q.add(startVert);
	    	
	    	lev_dfs[startVert]=0;
	    	while(!q.isEmpty()){
	    		int top=q.poll();
	    		
	    		Iterator<Integer> i= adj[top].listIterator();
	    		while(i.hasNext()){
	    			int n=i.next();
	    	//		System.out.println(top+" "+n);
	    			if(!Visited[n]){
	    				q.add(n);
	    				Visited[n]=true;
	    				lev_dfs[n]=lev_dfs[top]+1;
	    			
	    			}
	    		}
	    	}
	    
	    //	q.clear();
	    	return -1;
	    }
	    public static int getAn(int end){
	    	return lev_dfs[end];
	    }
	    public int getEd(){
	    	return degree/2;
	    }
	    public void get(int from,int to){
	    	int h=lev_dfs[from]-lev_dfs[to];
	    	if(h<=0){
	    		System.out.println(-1);
	    	}else{
	    		System.out.println(h-1);
	    	}
	    }
	    private static boolean check(int x,int y,char c[][]){
		
			if((x>=0 && y>=0) && (x<c.length && y<c[0].length) && c[x][y]!='#'){
				
				return true;
			}
			return false;
		}
	    public int BFS(int x,int y,int k,char[][] c)
	    {
	    	 LinkedList<Pair> queue = new LinkedList<Pair>();
	        //Visited[s]=true;
	   //     queue.add(new Pair(x,y));
	       int count=0;
	   level[x][y]=-1;
	   c[x][y]='M';
	        while (!queue.isEmpty())
	        {
	            Pair temp = queue.poll();
	        
	            
	        }
	        return V;
	    }
	    
	   
	    
	     public long dfs(int startVertex,int end){
	    //	 getAns(startVertex);
	    	 Visited=new boolean[V];
	    	 if(!Visited[startVertex])  {
	    
	   return dfsUtil(startVertex,end);
	    	//return getAns();
	    	}
	    	 
	    
	     
	    return 0;
	    	}
	 private long dfsUtil(int startVertex,int end) {//0-Blue 1-Pink
		 int c=1;
	
		 long cout=0;
	      degree=0;
	    	Visited[startVertex]=true;
	    	lev_dfs[startVertex]=0;
	      st.push(startVertex);
	      int temp=-1;
	      
	    while(!st.isEmpty()){
	    	
	    	int top=st.pop();
	    temp=Math.max(temp, top);
	    //	ts.add(top);
	    	Iterator<Integer> i=adj[top].listIterator();
	     
	    while(i.hasNext()){
	    //	System.out.println(top);
	    	int n=i.next();
	     if( !Visited[n]){
	    				Visited[n]=true;
	    				
	    			//	col_freq[col[n-1]]++;
	    				c++;
	    				st.push(n);
	    					lev_dfs[n]=lev_dfs[top]+1;
	    					if(n==end){
	    	    				return lev_dfs[n];	
	    	    				}
	    		 }
	         }
	 }
	 //   System.out.println(temp);
	    if(lev_dfs[temp]+(end-temp)<=0){
	    	return end-startVertex;
	    }
	    return Math.min(end-startVertex, lev_dfs[temp]+(end-temp));
	    	
	    }
	        
	        }     
	       	        
	    class Dsu{
	    	private int rank[], parent[] ,n;
	    	
	    	Dsu(int size){
	    		this.n=size+1;
	    		rank=new int[n];
	    		parent=new int[n];
	    	makeSet();
	    	}
	    	
	    	void makeSet(){
	    		for(int i=0;i<n;i++){
	    			parent[i]=i;
	    		}
	    	}
	    	
	    	int find(int x){
	    		if(parent[x]!=x){
	    			
	    			parent[x]=find(parent[x]);
	    		}
	    		return parent[x];
	    	}	
	    	
	    	void union(int x,int y){
	    		int xRoot=find(x);
	    		int yRoot=find(y);
	    		
	    		if(xRoot==yRoot)
	    			return;
	    		if(rank[xRoot]<rank[yRoot]){
	    		parent[xRoot]=yRoot;	
	    		}else if(rank[yRoot]<rank[xRoot]){
	    			parent[yRoot]=xRoot;
	    		}else{
	    			parent[yRoot]=xRoot;
	    			rank[xRoot]++;
	    		}
	    		
	    	}
	     
	    }
	    class Heap{
	    	
	    	public static void build_max_heap(long []a,int size){
	    		
	    		for(int i=size/2;i>0;i--){
	    			max_heapify(a, i,size);
	    		}
	    		
	    			}
	    	private static void max_heapify(long[] a,int i,int size){
	    		int left_child=2*i;
	    		int right_child=(2*i+1);
	    		int largest=0;
	    		
	    		if(left_child<size && a[left_child]>a[i]){
	    			largest=left_child;
	    		}else{
	    			largest=i;
	    		}
	    		
	    		if(right_child<size && a[right_child]>a[largest]){
	    			largest=right_child;
	    		}
	    		if(largest!=i){
	    			long temp=a[largest];
	    			a[largest]=a[i];
	    			a[i]=temp;
	    			max_heapify(a, largest,size);
	    		}
	    	}
	    	private static void min_heapify(int[] a,int i){
	    		int left_child=2*i;
	    		int right_child=(2*i+1);
	    		int largest=0;
	    		
	    		if(left_child<a.length && a[left_child]<a[i]){
	    			largest=left_child;
	    		}else{
	    			largest=i;
	    		}
	    		
	    		if(right_child<a.length && a[right_child]<a[largest]){
	    			largest=right_child;
	    		}
	    		if(largest!=i){
	    			int temp=a[largest];
	    			a[largest]=a[i];
	    			a[i]=temp;
	    			min_heapify(a, largest);
	    		}
	    	}
	    	public static void extract_max(int size,long a[]){
	    		if(a.length>1){
	    			long max=a[1];
	    			a[1]=a[a.length-1];
	    			size--;
	    			max_heapify(a, 1,a.length-1);
	    		}
	    	}
	    }
	    
	    class MyComp implements Comparator<Long>{
	        
			@Override
			public int compare(Long o1, Long o2) {
				if(o1<o2){
					return 1;
				}else if(o1>o2){
					return -1;
				}
				return 0;
				
			}
	    }