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>
const int N = 1e6 + 1;
const long long inf = (long long)1e18 + 1;
using namespace std;
long long n;
int a[N];
long long s[N], l, r;
long long ans;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  reverse(a + 1, a + n + 1);
  for (int i = 1; i <= n; i++) {
    if (a[i] > 0) {
      l = i + 1;
      r = i + a[i];
    }
    r = min(n, r);
    if (l <= r) {
      s[l]++;
      s[r + 1]--;
    }
  }
  for (int i = 1; i <= n; i++) {
    s[i] += s[i - 1];
    if (s[i] == 0) {
      ans++;
    }
  }
  cout << ans;
  exit(0);
}
