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 P892B
{
	public static void main(String[] args)
	{
		FastScanner scan = new FastScanner();
		int n = scan.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = scan.nextInt();
		int rem = 0;
		int alive = n;
		for (int i = n-1; i >= 0; i--)
		{
			if (rem > 0)
				alive--;
			rem--;
			rem = Math.max(rem, arr[i]);
		}
		System.out.println(alive);
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

		public int nextInt()
		{
			return Integer.parseInt(next());
		}

		public long nextLong()
		{
			return Long.parseLong(next());
		}

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
