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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {
	public static void main(String[] args) throws IOException {
		FastScanner in= new FastScanner(System.in);
		PrintWriter out= new PrintWriter(System.out);
		
		int n= in.nextInt();
		int [] a= new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i]= in.nextInt();
		}
		int cur= 0;
		int res=n;
		for (int i = n-1; i >= 0; i--){
			if (cur > 0)
				res--;
			cur--;
			cur = Math.max(cur, a[i]);
		}
		System.out.println(res);
		
	}
	static class p implements Comparable<p>{
		int id;
		long val;
		public p(int a, long b) {
			id=a;
			val=b;
		}
		public int compareTo(p o) {
			return Long.compare(o.val, this.val);
		}
	}
	static class FenwickTree {
		long[] ft;
		public FenwickTree(int n) {
			ft = new long[n + 1];
		}

		int rsq(int b) {
			int sum = 0;
			for (; b > 0; b -= (b & (-b)))
				sum += ft[b];
			return sum;
		}

		int rsq(int a, int b) {
			return rsq(b) - (a == 1 ? 0 : rsq(a - 1));
		}

		void update(int k, int v) {
			for (; k < ft.length; k += (k & (-k)))
				ft[k] += v;
		}
	}

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer("");
		}

		public String next() throws IOException {
			if (!st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
				return next();
			}
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
	}
}