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;
static int rowNbr[] = {-1, -1, -1, 0, 0, 1, 1, 1};
static int colNbr[] = {-1, 0, 1, -1, 1, -1, 0, 1};
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
long long int power(long long int base, long long int p) {
  long long int ans = 1;
  while (p) {
    if (p & 1) ans = (ans * base);
    base = (base * base);
    p /= 2;
  }
  return ans;
}
long long int modPower(long long int base, long long int p, long long int mod) {
  long long int ans = 1;
  while (p) {
    if (p & 1) ans = (ans * base) % mod;
    base = (base * base) % mod;
    p /= 2;
  }
  return ans;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    a[i] = i - a[i];
  }
  int cnt = 1;
  int curr = a[n - 1];
  for (int i = n - 2; i >= 0; --i) {
    if (i < curr) {
      cnt++;
    }
    curr = min(curr, a[i]);
  }
  cout << cnt << endl;
}
