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 long long inf = (long long)1e18;
long long gcd(long long a, long long b) {
  long long r;
  while (b) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long fpow(long long n, long long k, int p = 1000000007) {
  long long r = 1;
  for (; k; k >>= 1) {
    if (k & 1) r = r * n % p;
    n = n * n % p;
  }
  return r;
}
int inv(int a, int p = 1000000007) { return fpow(a, p - 2, p); }
long long spf[1000001 + 1];
void sieve() {
  for (int i = 1; i < 1000001; i++) {
    spf[i] = i;
  }
  for (long long i = 2; i < 1000001; i += 2) {
    spf[i] = 2;
  }
  for (long long i = 3; i < 1000001; i += 2) {
    if (spf[i] == i) {
      for (long long j = i * i; j < 1000001; j += i) {
        spf[j] = min(i, (long long)spf[j]);
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  long long lastindex = n, cnt = 0;
  for (long long i = n - 1; i > -1; i--) {
    if (lastindex > i) cnt++;
    lastindex = min(lastindex, i - a[i]);
  }
  cout << cnt;
}
