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 main() {
  int n;
  cin >> n;
  int* arr1 = new int[n];
  for (int i = 0; i < n; i++) {
    cin >> arr1[i];
  }
  int lastPos = n - 1;
  int currentPos;
  int killedPeople = 0;
  for (int j = n - 1; j > 0; j--) {
    if (j < lastPos) {
      lastPos = j;
    }
    currentPos = j - arr1[j];
    if (currentPos < 0) {
      currentPos = 0;
    }
    if (lastPos > currentPos) {
      killedPeople += (lastPos - currentPos);
      lastPos = currentPos;
    }
    if (lastPos == 0) {
      break;
    }
  }
  cout << (n - killedPeople);
  return 0;
}
