Hands that shed innocent blood!

There are n guilty people in a line, the i-th of them holds a claw with length Li. The bell rings and every person kills some of people in front of him. All people kill others at the same time. Namely, the i-th person kills the j-th person if and only if j < i and j ≥ i - Li.

You are given lengths of the claws. You need to find the total number of alive people after the bell rings.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — the number of guilty people.

Second line contains n space-separated integers L1, L2, ..., Ln (0 ≤ Li ≤ 109), where Li is the length of the i-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Examples

Input

4
0 1 0 10


Output

1


Input

2
0 0


Output

2


Input

10
1 1 3 0 0 0 2 1 0 3


Output

3

Note

In first sample the last person kills everyone in front of him.
import java.io.*;
import java.util.*;

public class wrath {

  public static void main(String[] args) {

      Scanner sc = new Scanner(System.in);

      int n = sc.nextInt();

      int[] L = new int[n];
    //   Boolean[] L_mark = new Boolean[n];

      for (int i = 0; i < n; i++) {
        L[i] = sc.nextInt();
        // L_mark[i] = true;
      }

      n--;

      int step = 0;
      int count = n + 1;

      while (n >= 0) {
        if (step > 0) {
          step--;
        //   L_mark[n] = false;
          count--;
        }
        if (step < L[n])
          step += Math.abs(L[n] - step);
        n--;

      }

    //   System.out.println(Arrays.toString(L_mark));
      System.out.println(count);

      sc.close();
    

  }

}
