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 = 1000100;
int mp[N];
int main() {
  int pos = -1;
  int r = 0;
  int n;
  int l;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> l;
    mp[i] = l;
  }
  pos = max((int)0, n - 1 - mp[n - 1]);
  for (int i = n - 2; i >= 0; i--) {
    if (i >= pos) {
      r++;
    }
    int temp = max((int)0, i - mp[i]);
    if (temp < pos) {
      pos = temp;
    }
  }
  cout << n - r << '\n';
  return 0;
}
