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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int i, n, l, el, count, index;
  scanf("%lld", &n);
  long long int data[n];
  for (i = 0; i < n; i++) {
    scanf("%lld", &el);
    data[i] = el;
  }
  count = 1;
  index = n - 1 - data[n - 1];
  for (i = n - 1; i >= 0; i--) {
    if (i < index) {
      count = count + 1;
    }
    if (i - data[i] < index) {
      index = i - data[i];
    }
  }
  cout << count << endl;
  return 0;
}
