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;
#pragma GCC optimize("-O3")
using ld = long double;
const long long mod = 1e9 + 7;
const long long inf = 1e18;
const long long rk = 256;
const long long mod2 = 998244353;
const ld PI = 3.141592653589793;
ostream& operator<<(ostream& os, pair<long long, long long> const& x) {
  os << x.first << "," << x.second;
  return os;
}
template <class T>
ostream& operator<<(ostream& os, vector<T> const& x) {
  os << "{ ";
  for (auto& y : x) os << y << " ";
  return os << "}";
}
template <class T>
ostream& operator<<(ostream& os, set<T> const& x) {
  os << "{ ";
  for (auto& y : x) os << y << " ";
  return os << "}";
}
template <class Ch, class Tr, class Container>
basic_ostream<Ch, Tr>& operator<<(basic_ostream<Ch, Tr>& os,
                                  Container const& x) {
  os << "{ ";
  for (auto& y : x) os << y << " ";
  return os << "}";
}
template <class X, class Y>
ostream& operator<<(ostream& os, pair<X, Y> const& p) {
  return os << "[ " << p.first << ", " << p.second << "]";
}
const int mxn = 1e6 + 5;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int n;
  cin >> n;
  vector<int> freq(n + 1, 0);
  vector<int> arr(n, 0);
  for (int i = 0; i < n; i++) cin >> arr[i];
  for (int ii = 1; ii <= n; ii++) {
    int i = ii - 1;
    int x = arr[i];
    if (x) {
      freq[max(ii - x, 0)]--;
      freq[ii]++;
    }
  }
  for (int i = 1; i <= n; i++) {
    freq[i] += freq[i - 1];
  }
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (freq[i] >= 0) {
      cnt++;
    }
  }
  cout << cnt << '\n';
  return 0;
}
