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 int maxn = 1e6 + 10;
const long long inf = 1e18 + 10;
struct node {
  int kt;
  int len;
} p[maxn];
int vis[maxn];
int main() {
  int i, j;
  ios::sync_with_stdio(0);
  int n;
  while (cin >> n) {
    for (i = 1; i <= n; i++) {
      cin >> p[i].len;
      p[i].kt = 1;
    }
    memset(vis, 0, sizeof(vis));
    int pre = 1e9 + 10;
    int flag = 0;
    int cnt = 1;
    for (i = n - 1; i >= 1; i--) {
      pre = min(pre, i + 1 - p[i + 1].len);
      if (pre > i) cnt++;
    }
    cout << cnt << endl;
  }
  return 0;
}
