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;
const int N = 1e6 + 100;
int arr[N];
int vis[N];
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  memset(vis, 0, sizeof vis);
  int i, j;
  for (i = n - 1; i >= 0; i--) {
    int pp = 1;
    for (j = i - 1; j >= i - arr[i] && j >= 0; j--) {
      vis[j] = 1;
      if (j - arr[j] < i - arr[i]) {
        i = j + 1;
        pp = 0;
        break;
      }
    }
    if (pp) i = j + 1;
  }
  int cnt = 0;
  for (int i = 0; i < n; i++)
    if (!vis[i]) cnt++;
  cout << cnt << endl;
  return 0;
}
