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>
int main() {
  int n;
  scanf("%d", &n);
  std::vector<int> a(n);
  for (auto& it : a) {
    scanf("%d", &it);
  }
  std::vector<bool> live(n, true);
  int last = n;
  for (int i = n - 1; i > 0; --i) {
    if (a[i] == 0) {
      continue;
    }
    if (i - a[i] >= last) {
      continue;
    } else if (i - a[i] < last) {
      for (int j = std::min(last - 1, i - 1); j >= std::max(i - a[i], 0); --j) {
        live[j] = false;
      }
      last = std::max(i - a[i], 0);
    }
  }
  int sum = 0;
  for (int i = 0; i < n; ++i) {
    sum += live[i];
  }
  printf("%d", sum);
  return 0;
}
