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() {
  std::ios::sync_with_stdio(false);
  int n;
  cin >> n;
  int arr[n], i;
  for (i = 0; i < n; i++) cin >> arr[i];
  int flag = 0;
  int end, ans = 0;
  for (i = n - 1; i >= 1; i--) {
    if (arr[i] == 0) continue;
    int k = i - arr[i];
    if (k < 0) k = 0;
    int a = n - i;
    int b = n - 1 - k;
    if (flag == 0) {
      flag = 1;
      ans = a;
      end = b;
    } else {
      if (a > end) ans += a - end - 1;
      if (b > end) end = b;
    }
  }
  if (flag == 1)
    ans += n - (end + 1);
  else
    ans = n;
  cout << ans << endl;
  return 0;
}
