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;
void out() {}
template <typename Head, typename... Tail>
void out(Head H, Tail... T) {
  cout << H << ' ';
  out(T...);
}
void init();
void solve();
int main() {
  init();
  solve();
  return 0;
}
int n;
int L[1000006];
bool killed[1000006] = {false};
void init() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> L[i];
}
void solve() {
  int len = L[n - 1];
  int answer = n;
  for (int i = n - 2; i >= 0; i--) {
    if (len > 0) {
      killed[i] = true;
      answer--;
    }
    len--;
    len = max(len, L[i]);
  }
  out(answer);
}
