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.
//package codeforces;

import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

/**
 * @author safat
 * @since 11/17/17.
 */

public class BWrath {
    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader(System.in);

        int n = in.readInt();
        int[] claws = in.readIntArray(n);

        int aliveCount = 1;
        int rightToLeftCoverage = (n - 1) - claws[n - 1];

        for (int i = n - 2; i >= 0; i--) {
            if (i < rightToLeftCoverage) {
                aliveCount++;
            }

            rightToLeftCoverage = Math.min(rightToLeftCoverage, i - claws[i]);
        }


        System.out.println(aliveCount);
    }

    public static String join(int[] numbers) {
        if (numbers == null || numbers.length == 0) {
            return null;
        }

        StringBuilder result = new StringBuilder();

        for (int n : numbers) {
            result.append(n).append(", ");
        }

        return result.substring(0, result.length() - 1);
    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int read() {
            try {
                if (curChar >= numChars) {
                    curChar = 0;
                    numChars = stream.read(buf);
                    if (numChars <= 0)
                        return -1;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return buf[curChar++];
        }

        public int readInt() {
            return (int) readLong();
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
                if (c == -1) throw new RuntimeException();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += (c - '0');
                c = read();
            } while (!isSpaceChar(c));
            return negative ? (-res) : (res);
        }

        public int[] readIntArray(int size) {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++) arr[i] = readInt();
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}
