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.
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Solution {
	public static void main(String[] args) throws Exception {
		Reader in = new Reader(new BufferedReader(new InputStreamReader(System.in)));
		int n = in.nextInt();
		int[] a = new int[n];
		for(int i = 0; i<n; i++) a[i] = in.nextInt();
		int ans = 0;
		int last = n;
		for(int i = n-1; i>=0; i--) {
			if(last>i) ans++;
			last = Math.min(last, i-a[i]);
		}
		System.out.println(ans);
	}
	static class Reader{
		static BufferedReader br;
		static StringTokenizer st;
		public Reader(BufferedReader br) {
			this.br = br;
		}
		public long nextLong() throws Exception {
			if(st==null||!st.hasMoreTokens())
				readLine();
			return Long.parseLong(st.nextToken());
		}
		public int nextInt() throws Exception{
			if(st==null||!st.hasMoreTokens())
				readLine();
			return Integer.parseInt(st.nextToken());
		}
		public static void readLine() throws Exception{
			st = new StringTokenizer(br.readLine());
		}
	}
}
