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.util.*;
import java.io.*;

/**
 *
 * @author usquare
 * 
 */

public class ProblemA {

    public static int mod = (int) (1e9+7);
    public static InputReader in;
    public static PrintWriter out;
    public static int[] arr;
    
    public static class SegmentTree{
        Pair st[];
 
        SegmentTree(int n ){
            st = new Pair[4*n];
            build(0, n - 1, 1);
        }
    
        public int getMid(int s, int e) {
            return (s+e)>>1;
        }

        public Pair merge(Pair a,Pair b){
            if(a.x>=b.x) return a;
            return b;
        }
        
        public Pair get(int s, int e, int x, int y, int si){

            if(s == x && e == y){
                return st[si];
            }
            int mid = getMid(s, e);
            if(y <= mid)
                return get(s, mid, x, y, 2*si);
            else if(x > mid)
                return get(mid + 1, e, x, y, 2*si + 1);
            return merge(get(s, mid, x, mid, 2*si), get(mid + 1, e, mid + 1, y, 2*si + 1));
        }

        public void build(int ss, int se, int si){
            if (ss == se) {
                st[si] = new Pair(arr[ss], ss);
                return;
            }

            int mid = getMid(ss, se);
            build(ss, mid, si * 2 );
            build(mid + 1, se, si * 2 + 1);
            st[si]=merge(st[2*si],st[2*si+1]);
        }
    }
    
    public static void main(String[] args) throws FileNotFoundException {

        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        
        int n=in.nextInt();
        arr=new int[n];
        for(int i=0;i<n-1;i++) arr[i]=in.nextInt()-1;
        long[] dp=new long[n];
        long ans=0;
        dp[n-1]=0;
        SegmentTree segmentTree=new SegmentTree(n);

        for(int i=n-2;i>=0;i--){
            Pair p=segmentTree.get(0, n-1, i+1, arr[i], 1);
            dp[i]=dp[p.y]-arr[i]+p.y+n-i-1;
            ans+=dp[i];
        }
        
        out.println(ans);
        
        out.close();
    }
    
    static class Pair implements Comparable<Pair>{

        int x,y;
        
//	Pair (int x,int y,int i){
//		this.x=x;
//		this.y=y;
//		this.i=i;
//	}

	Pair (int x,int y){
		this.x=x;
		this.y=y;
	}
        
	public int compareTo(Pair o) {
                    return Long.compare(this.x,o.x);
		//return 0;
	}

        public boolean equals(Object o) {
            if (o instanceof Pair) {
                Pair p = (Pair)o;
                return p.x == x && p.y == y ;
            }
            return false;
        }
        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }
    
    } 
    
    static long[] shuffle(long[] a, Random gen){ 
        for(int i = 0, n = a.length;i < n;i++){ 
            int ind = gen.nextInt(n-i)+i; 
            long d = a[i]; 
            a[i] = a[ind]; 
            a[ind] = d; 
        } 
        return a; 
    }

        
    public static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }

    public static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }
    
    public static long mul(long a,long b){
        a%=mod;
        b%=mod;
        long x=(a*b);
        return x%mod;
    }
    
    static boolean isPal(String s){
        for(int i=0, j=s.length()-1;i<=j;i++,j--){
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    static String rev(String s){
            StringBuilder sb=new StringBuilder(s);
            sb.reverse();
            return sb.toString();
    }

    static long gcd(long x,long y){
        if(y==0) return x;
    if(x%y==0)
            return y;
    else
            return gcd(y,x%y);
    }

    static int gcd(int x,int y){
        if(y==0) return x;
    if(x%y==0)
            return y;
    else 
            return gcd(y,x%y);
    }

    static long gcdExtended(long a,long b,long[] x){

        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);

        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];

        return gcd;
    }

    static int abs(int a,int b){
    return (int)Math.abs(a-b);
    }

    static long abs(long a,long b){
    return (long)Math.abs(a-b);
    }

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

    static int min(int a,int b){
    if(a>b)
            return b;
    else 
            return a;
    }

    static long max(long a,long b){
    if(a>b)
            return a;
    else
            return b;
    }

    static long min(long a,long b){
    if(a>b)
            return b;
    else 
            return a;
    }


    public static long pow(long n,long p,long m){
	 long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
    }
    
    public static long pow(long n,long p){
	long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;	    
	    p >>=1;
	    n*=n;	    
	}
	return result;
    }
    
     static void debug(Object... o) {
            System.out.println(Arrays.deepToString(o));
    }

    static class InputReader {

            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;

            InputReader(InputStream stream) {
                    this.stream = stream;
            }

            int snext() {
                    if (snumChars == -1)
                            throw new InputMismatchException();
                    if (curChar >= snumChars) {
                            curChar = 0;
                            try {
                                    snumChars = stream.read(buf);
                            } catch (IOException e) {
                                    throw new InputMismatchException();
                            }
                            if (snumChars <= 0)
                                    return -1;
                    }
                    return buf[curChar++];
            }

            int nextInt() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    int sgn = 1;
                    if (c == '-') {
                            sgn = -1;
                            c = snext();
                    }
                    int res = 0;
                    do {
                            if (c < '0' || c > '9')
                                    throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res * sgn;
            }

            long nextLong() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    int sgn = 1;
                    if (c == '-') {
                            sgn = -1;
                            c = snext();
                    }
                    long res = 0;
                    do {
                            if (c < '0' || c > '9')
                                    throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res * sgn;
            }

            int[] nextIntArray(int n) {
                    int a[] = new int[n];
                    for (int i = 0; i < n; i++) {
                            a[i] = nextInt();
                    }
                    return a;
            }

            long[] nextLongArray(int n) {
                    long a[] = new long[n];
                    for (int i = 0; i < n; i++) {
                            a[i] = nextInt();
                    }
                    return a;
            }

            String readString() {
                    int c = snext();
                    while (isSpaceChar(c)) {
                            c = snext();
                    }
                    StringBuilder res = new StringBuilder();
                    do {
                            res.appendCodePoint(c);
                            c = snext();
                    } while (!isSpaceChar(c));
                    return res.toString();
            }

            String nextLine() {
                    int c = snext();
                    while (isSpaceChar(c))
                            c = snext();
                    StringBuilder res = new StringBuilder();
                    do {
                            res.appendCodePoint(c);
                            c = snext();
                    } while (!isEndOfLine(c));
                    return res.toString();
            }

            boolean isSpaceChar(int c) {
                    if (filter != null)
                            return filter.isSpaceChar(c);
                    return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            private boolean isEndOfLine(int c) {
                    return c == '\n' || c == '\r' || c == -1;
            }

            interface SpaceCharFilter {
                    boolean isSpaceChar(int ch);
            }
    }
}    

