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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class CFB {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    int n;
    int[] arr;
    int[] tree;
    long[] dp;
    void build_tree(int node, int nodeStartIndex, int nodeEndIndex) {
        if(nodeStartIndex > nodeEndIndex) return; // Out of range
        if(nodeStartIndex == nodeEndIndex) { // Leaf node
            tree[node] = nodeStartIndex; // Init value
            return;
        }

        build_tree(node * 2, nodeStartIndex, (nodeStartIndex + nodeEndIndex) / 2); // Init left child
        build_tree(node * 2 + 1, 1 + (nodeStartIndex + nodeEndIndex) / 2, nodeEndIndex); // Init right child
        int left = tree[node * 2];
        int right = tree[node * 2 + 1];
        tree[node] = arr[left] > arr[right] ? left : right;
    }

    int query_tree(int node, int nodeStartIndex, int nodeEndIndex, int queryStartIndex, int queryEndIndex) {
        if(nodeStartIndex > nodeEndIndex || nodeStartIndex > queryEndIndex || nodeEndIndex < queryStartIndex) return -1; // Out of range
        if(nodeStartIndex >= queryStartIndex && nodeEndIndex <= queryEndIndex) // Current segment is totally within range [i, j]
            return tree[node];

        int q1 = query_tree(node * 2, nodeStartIndex, (nodeStartIndex + nodeEndIndex) / 2, queryStartIndex, queryEndIndex); // Query left child
        int q2 = query_tree(1 + node * 2, 1 + (nodeStartIndex + nodeEndIndex) / 2, nodeEndIndex, queryStartIndex, queryEndIndex); // Query right child
        if (q1 == -1) {
            return q2;
        }
        if (q2 == -1) {
            return q1;
        }
        return arr[q1] > arr[q2] ? q1 : q2;
    }
    void solve() throws IOException {
        n = nextInt();
        arr = new int[n];
        for (int i = 0; i < n - 1; i++) {
            arr[i] = nextInt() - 1;
        }
        arr[n - 1] = n - 1;
        dp = new long[n];

        tree = new int[5 * n];
        build_tree(1, 0, n - 1);
        for (int i = n - 2; i >= 0; i--) {
            //[i + 1, arr[i]]
            int m = query_tree(1, 0, n - 1, i + 1, arr[i]);
            dp[i] = dp[m] - (arr[i] - m) + n - i - 1;
        }

        long res = 0;
        for (long v : dp) {
            res += v;
        }

        outln(res);
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFB() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFB();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}