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.* ;
import java.io.* ;

public class Wrath
{
	static int livingCounter(int[] L)
	{
		
		int len = L.length ;
		int counter = len ;
		int deathC = len-1 ;
		boolean[] dead = new boolean[len] ;
		for(int i=len-1;i>=0;i--)
		{
			int val = L[i] ;
			if(L[i]!=0 && deathC!=0 && i-L[i]<deathC)
			{
				// System.out.println("Considering "+i+" th index: "+ L[i]) ;
				int dcOld = deathC<i?deathC:i ;
				deathC = i-L[i] ;
					for(int j=dcOld-1;j>=(deathC>0?deathC:0);j--)
					{
						// System.out.println("	"+j+" is dead") ;
						dead[j] = true ;
						counter-- ;
					}
			}
		}
		// for(int i=0;i<dead.length;i++)
		// {
			// if(!dead[i])
				// counter++ ;
		// }
		return counter ;
	}
	public static void main(String args[]) throws Exception
	{
		// BufferedReader br = new BufferedReader(new InputStreamReader(System.in)) ;
		// String line1 = br.readLine() ;
		// String line2 = br.readLine() ;
		
		
		// int N = Integer.parseInt(line1.split(" ")[0]) ;
		// int[] L =  new int[N] ;
		// for(int i=0;i<N;i++)
		// {
			// L[i] = Integer.parseInt(line2.split(" ")[i]) ;
		// }
		Scanner in  = new Scanner(System.in) ;
		int N = in.nextInt() ;
		int[] L = new int[N] ;
		for(int i=0;i<N;i++)
		{
			L[i] = in.nextInt() ;
		}
		System.out.println(livingCounter(L)) ;
	}
}