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;
int Array[1000005];
int main() {
  int index, Num, N, i, Ans = 0;
  scanf("%d", &N);
  for (i = 1; i <= N; ++i) scanf("%d", Array + i);
  index = N + 1;
  for (i = N; i >= 1; --i) {
    Num = i - Array[i];
    if (index > i) ++Ans;
    index = min(index, max(1, Num));
  }
  printf("%d\n", Ans);
  return 0;
}
