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;
long long read() {
  long long x = 0;
  int zf = 1;
  char ch;
  while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
  if (ch == '-') zf = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return x * zf;
}
void write(long long y) {
  if (y < 0) putchar('-'), y = -y;
  if (y > 9) write(y / 10);
  putchar(y % 10 + '0');
}
inline int min(int x, int y) {
  if (x < y) return x;
  return y;
}
inline int max(int x, int y) {
  if (x > y) return x;
  return y;
}
void printk() { puts(""); }
inline void writeln(long long x) {
  write(x);
  printk();
}
int i, j, k, m, n, x, y, z, cnt, all, num;
long long ans = 0;
long long a[1000010], cf[1000010];
int main() {
  n = read();
  for (register int i = 1; i <= n; i++) a[i] = read();
  for (register int i = 1; i <= n; i++) {
    cf[i] -= 1;
    cf[max(1, i - a[i])] += 1;
  }
  for (register int i = 1; i <= n; i++) {
    ans += cf[i];
    if (!ans) k++;
  }
  cout << k;
  return 0;
}
