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() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  bool die[1000000 + 5] = {false};
  int r = n - 1, res = 0;
  for (int l = n - 1; l > 0; l--) {
    int newr = max(l - a[l], 0);
    if (newr < r) {
      for (int i = min(r - 1, l - 1); i >= newr; i--) die[i] = true;
      r = newr;
    }
    if (newr == 0) break;
  }
  for (int i = 0; i < n; i++) res += !die[i];
  cout << res;
  return 0;
}
