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>
namespace {
using i64 = long long;
using ui64 = unsigned long long;
}  // namespace
int main() {
  int N;
  std::cin >> N;
  std::vector<int> L(N);
  for (auto& el : L) {
    scanf("%d", &el);
  }
  int cur = 0;
  int alive = 0;
  for (auto it = L.rbegin(); it != L.rend(); ++it) {
    if (cur == 0) {
      ++alive;
    }
    if (cur > 0) {
      --cur;
    }
    if (cur < *it) {
      cur = *it;
    }
  }
  std::cout << alive << std::endl;
  return 0;
}
