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;
struct debugger {
  template <typename T>
  debugger& operator,(const T& v) {
    cout << v << " ";
    return *this;
  }
} dbg;
int dx[] = {-1, 1, 0, 0, -1, -1, 1, 1};
int dy[] = {0, 0, 1, -1, -1, 1, -1, 1};
int a[1000010];
int main() {
  int t = 0, z = 0, len;
  int n = 0, k = 0, m = 0;
  int ans = 0;
  scanf("%d", &n);
  for (int l = 0; l < n; l++) scanf("%d", &a[l]);
  ans = INT_MAX;
  for (int l = n - 1; l > -1; l--) {
    if (l < ans) m++;
    ans = min(ans, l - a[l]);
  }
  printf("%d", m);
  return 0;
}
