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.*;

/**
 * @auther chao
 * @date 16/5/19
 */
public class A {
    static List<Node> list;
    static int[] a;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(br.readLine());
        String[] nums = br.readLine().split(" ");
        long[] s = new long[n+1];
        a = new int[n+1];
        for (int i = 1; i < n; i++) {
            a[i] = Integer.parseInt(nums[i-1]);
        }
        list = new ArrayList<>();
        //tree = new Node[(n+1)*4];
        //build(1, 1, n);
        long ans = 0;
        for (int i = n-1; i > 0; i--) {
            if (a[i] == n) {
                s[i] = n - i;
            } else {
                int k = findMaxK(a[i]);
                s[i] = (k-i) + s[k] +(n-a[i]);
            }
            Node nd = new Node(i, a[i]);
            put(nd);
            ans += s[i];
        }
        pw.println(ans);
        pw.flush();
        pw.close();
        br.close();
    }
    private static int findMaxK(int val) {
        if (val >= list.get(0).p) {
            return list.get(0).p;
        }

        int st = 0;
        int ed = list.size() - 1;
        while (ed - st > 1) {
            int md = (st+ed)/2;
            if (val >= list.get(md).p) {
                ed = md;
            } else {
                st = md;
            }
        }
        return list.get(ed).p;
    }

    private static void put(Node nd) {
        while (!list.isEmpty()) {
            Node t = list.get(list.size() - 1);
            if (t.r <= nd.r) {
                list.remove(list.size() - 1);
            } else {
                break;
            }
        }
        list.add(nd);
    }
}

class Node{
    int p;
    int r;
    public Node(int p, int r) {
        this.p = p;
        this.r = r;
    }
}