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.*;
import java.util.*;
public class Main{
        final private int MAX = 1000005;
        private void solve()
        {
                int n = i();
                int[] a = new int[n];
                for (int i = 0; i < n; i++) {
                        a[i] = i-i();
                }
                int ans = 1;
                int start = a[n-1];
                for(int i = n-2; i>=0 ; i--)
                {
                        if(i<start)
                                ans++;
                        start = Math.min(start,a[i]);
                }
                out.println(ans);
        }
        private void run(){
                is = System.in;
                out = new PrintWriter(System.out);
                solve();
                out.flush();
        }
        public static void main(String[] args){
                new Main().run();
        }
        private InputStream is;
        private PrintWriter out;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0, ptrbuf = 0;

        private int readByte()
        {
                if(lenbuf == -1)throw new InputMismatchException();
                if(ptrbuf >= lenbuf){
                        ptrbuf = 0;
                        try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
                        if(lenbuf <= 0)return -1;
                }
                return inbuf[ptrbuf++];
        }
        private int i()
        {
                int num = 0, b;
                boolean minus = false;
                while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
                if(b == '-'){
                        minus = true;
                        b = readByte();
                }
                while(true){
                        if(b >= '0' && b <= '9'){
                                num = num * 10 + (b - '0');
                        }else{
                                return minus ? -num : num;
                        }
                        b = readByte();
                }
        }
}
