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;
template <class T>
void p(vector<T>& a) {
  for (int i = 0; i < a.size(); i++) cout << a[i] << " ";
  cout << endl;
}
int main() {
  std::ios::sync_with_stdio(false);
  int i, n;
  cin >> n;
  vector<int> l(n + 1);
  vector<int> v(n + 1, 0);
  for (i = 1; i < n + 1; i++) {
    cin >> l[i];
  }
  int alive = 0;
  int suf_sum = 0;
  for (i = n; i >= 1; i--) {
    suf_sum += v[i];
    if (suf_sum == 0) alive++;
    if (l[i] > 0) {
      if (i - l[i] - 1 > 0) v[i - l[i] - 1]--;
      v[i]++;
      suf_sum++;
    }
  }
  cout << alive << endl;
  return 0;
}
