Vasya commutes by train every day. There are n train stations in the city, and at the i-th station it's possible to buy only tickets to stations from i + 1 to ai inclusive. No tickets are sold at the last station.

Let ρi, j be the minimum number of tickets one needs to buy in order to get from stations i to station j. As Vasya is fond of different useless statistic he asks you to compute the sum of all values ρi, j among all pairs 1 ≤ i < j ≤ n.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of stations.

The second line contains n - 1 integer ai (i + 1 ≤ ai ≤ n), the i-th of them means that at the i-th station one may buy tickets to each station from i + 1 to ai inclusive.

Output

Print the sum of ρi, j among all pairs of 1 ≤ i < j ≤ n.

Examples

Input

4
4 4 4


Output

6


Input

5
2 3 5 5


Output

17

Note

In the first sample it's possible to get from any station to any other (with greater index) using only one ticket. The total number of pairs is 6, so the answer is also 6.

Consider the second sample: 

  * ρ1, 2 = 1
  * ρ1, 3 = 2
  * ρ1, 4 = 3
  * ρ1, 5 = 3
  * ρ2, 3 = 1
  * ρ2, 4 = 2
  * ρ2, 5 = 2
  * ρ3, 4 = 1
  * ρ3, 5 = 1
  * ρ4, 5 = 1



Thus the answer equals 1 + 2 + 3 + 3 + 1 + 2 + 2 + 1 + 1 + 1 = 17.
import java.io.*;
import java.util.*;

public class Main{
	static int[]log,max[],in;
	static int query(int l,int r) {
		int len = r - l + 1;
		int lg = log[len];
		int u = max[l][lg];
		int v = max[r - (1 << lg) + 1][lg];
		int bestIdx = in[u] >= in[v] ? u : v;
		return bestIdx;
	}
	public static void main(String[] args) throws Exception{
		PrintWriter pw=new PrintWriter(System.out);
		MScanner sc = new MScanner(System.in);
		int n=sc.nextInt();
		in=new int[n+1];
		for(int i=1;i<=n-1;i++)in[i]=sc.nextInt();
		long[]ans=new long[n+1];
		in[n]=n;
		log = new int[n+1];
		for (int i = 2; i <= n; i++)
			log[i] = log[i / 2] + 1;
		
		max=new int[n+1][22];
		for(int i=0;i<=n;i++) {
			max[i][0]=i;
		}
		for(int i=1,len=2;len<=n;i++,len<<=1) {
			for(int j=0;j<=n;j++) {
				int u=max[j][i-1],v=j+(len>>1)>n?0:max[j+(len>>1)][i-1];
				max[j][i]=(in[u]>=in[v]?u:v);
			}
		}
		
		for(int i=n-1;i>=1;i--) {
			int nxt=query(i+1, in[i]);
//			System.out.println(i+" "+nxt);
			ans[i]=nxt-(i+1)+1;
			if(nxt<n) {
				int afterNxt=n-nxt;
				ans[i]+=ans[nxt]+afterNxt;
				ans[i]-=(in[i]-nxt);
			}
		}
//		System.out.println(Arrays.toString(ans));
		long res=0;
		for(long i:ans)res+=i;
		pw.println(res);
		pw.flush();
	}
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		static void shuffle(int[]in) {
			for(int i=0;i<in.length;i++) {
				int idx=(int)(Math.random()*in.length);
				int tmp=in[i];
				in[i]=in[idx];
				in[idx]=tmp;
			}
		}
		static void shuffle(long[]in) {
			for(int i=0;i<in.length;i++) {
				int idx=(int)(Math.random()*in.length);
				long tmp=in[i];
				in[i]=in[idx];
				in[idx]=tmp;
			}
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void addX(int[]in,int x) {
		for(int i=0;i<in.length;i++)in[i]+=x;
	}
	static void addX(long[]in,int x) {
		for(int i=0;i<in.length;i++)in[i]+=x;
	}
}