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.util.Scanner;

public class water {
	
	
	public static void main(String args[])
	{	
		Scanner reader = new Scanner(System.in);  // Reading from System.in
		int n = reader.nextInt(); // Scans the next token of the input as an int.
		int deadID=n;
		int claws[] = new int[n];
		int alive = 1;
		for(int j=0;j<n;j++)
			claws[j]=reader.nextInt();

		for(int i=n-1;i>0;i--)
		{
			//if the claw is 0 for the i'th player, then he can't kill anyone, but make sure the deadid isn't less than i, if it was less then the j player is dead by an other player
			//else increase the alive variable and continue.
			if(claws[i]==0)
				if(i>deadID)
					continue;
				else
					alive++;
			else
				// if the claw wasn't 0, make sure i- claw is greater or equal to deadID, that means j is dead, otherwise change deadID dead j players will be updated.
			{
				if(i-claws[i] < 0)
					break;
				if(i-claws[i]>=deadID)
					continue;
				deadID = i-claws[i];
			}
		
		}
		
		System.out.println(alive);
		
		
	}

}





	
	
	
	
