Problem: The Shuseki Islands are an archipelago of 30001 small islands in the Yutampo Sea. The islands are evenly spaced along a line, numbered from 0 to 30000 from the west to the east. These islands are known to contain many treasures. There are n gems in the Shuseki Islands in total, and the i-th gem is located on island pi.

Mr. Kitayuta has just arrived at island 0. With his great jumping ability, he will repeatedly perform jumps between islands to the east according to the following process: 

  * First, he will jump from island 0 to island d. 
  * After that, he will continue jumping according to the following rule. Let l be the length of the previous jump, that is, if his previous jump was from island prev to island cur, let l = cur - prev. He will perform a jump of length l - 1, l or l + 1 to the east. That is, he will jump to island (cur + l - 1), (cur + l) or (cur + l + 1) (if they exist). The length of a jump must be positive, that is, he cannot perform a jump of length 0 when l = 1. If there is no valid destination, he will stop jumping. 



Mr. Kitayuta will collect the gems on the islands visited during the process. Find the maximum number of gems that he can collect.

Input

The first line of the input contains two space-separated integers n and d (1 ≤ n, d ≤ 30000), denoting the number of the gems in the Shuseki Islands and the length of the Mr. Kitayuta's first jump, respectively.

The next n lines describe the location of the gems. The i-th of them (1 ≤ i ≤ n) contains a integer pi (d ≤ p1 ≤ p2 ≤ ... ≤ pn ≤ 30000), denoting the number of the island that contains the i-th gem.

Output

Print the maximum number of gems that Mr. Kitayuta can collect.

Examples

Input

4 10
10
21
27
27


Output

3


Input

8 8
9
19
28
36
45
55
66
78


Output

6


Input

13 7
8
8
9
16
17
17
18
21
23
24
24
26
30


Output

4

Note

In the first sample, the optimal route is 0  →  10 (+1 gem)  →  19  →  27 (+2 gems)  → ...

In the second sample, the optimal route is 0  →  8  →  15  →  21 →  28 (+1 gem)  →  36 (+1 gem)  →  45 (+1 gem)  →  55 (+1 gem)  →  66 (+1 gem)  →  78 (+1 gem)  → ...

In the third sample, the optimal route is 0  →  7  →  13  →  18 (+1 gem)  →  24 (+2 gems)  →  30 (+1 gem)  → ...

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class A_Round_286_Div1 {

	public static long MOD = 1000000007;
	static int[][][] dp;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int d = in.nextInt();
		int[] data = new int[30001];
		dp = new int[2][300][30001];
		
		for (int i = 0; i < n; i++) {
			data[in.nextInt()]++;
		}
		int result = 0;
		dp[0][0][d] = data[0];
		
		boolean[][][]check = new boolean[2][300][30001];
		check[0][0][d] = true;
		for(int i = d; i < 30001; i++){
			for(int j = 0; j < 300; j++){
				for(int k = 0; k < 2;k++){
					if(check[k][j][i]){
						//System.out.println(i);
						
						result = Math.max(result, dp[k][j][i] + data[i]);
						int nxt = d + (k == 0? 1 : -1)*j;
						if(nxt <= 0){
							continue;
						}
						if(i + nxt < 30001){
							dp[k][j][i + nxt] = Math.max(dp[k][j][i] + data[i] , dp[k][j][i + nxt]);
							check[k][j][i  + nxt] = true;
						}
						if(nxt  > 1 && i + nxt - 1 < 30001){
							int sign = k;
							int step = j;
							if(k == 1){
								step++;
							}else{
								step--;
								if(step <= 0){
									step = -step;
									sign = 1;
								}
							}
							dp[sign][step][i + d + step*(sign == 0 ? 1 : -1)] =  Math.max(dp[k][j][i] + data[i] , dp[sign][step][i + d + step*(sign == 0 ? 1 : -1)]);
							check[sign][step][i + d + step*(sign == 0 ? 1 : -1)] = true;
						}
						if(i + nxt + 1 < 30001){
							int sign = k;
							int step = j;
							if(k == 1){
								step--;
								if(step < 0){
									step = -step;
									sign = 0;
								}
							}else{
								step++;
								
							}
							dp[sign][step][i + d + step*(sign == 0 ? 1 : -1)] =  Math.max(dp[k][j][i] + data[i] , dp[sign][step][i + d + step*(sign == 0 ? 1 : -1)]);
							check[sign][step][i + d + step*(sign == 0 ? 1 : -1)] = true;
						}
					}
				}
			}
		}
		out.println(result );
		out.close();
	}

	static int cal(int index, int step, int neg, int d, int[] data) {
		if (index >=  data.length) {
			return 0;
		}
		
		if (dp[neg][step][index] != -1) {
			return dp[neg][step][index];
		}
		int result = data[index];
		int l = d + (neg == 1 ? -1 : 1) * step;
		if (l > 1 && index + l - 1 < data.length) {
			int nxt = step;
			int sign = neg;
			if (neg == 1) {
				nxt++;
			} else {
				nxt--;
				if (nxt < 0) {
					nxt = -nxt;
					sign = 1;
				}
			}
			result = Math.max(result,
					data[index] + cal(index + l - 1, nxt, sign, d, data));
		}
		if (index + l < data.length) {
			result = Math.max(result,
					data[index] + cal(index + l, step, neg, d, data));
		}
		if (index + l + 1 < data.length) {
			int nxt = step;
			int sign = neg;
			if (neg == 1) {
				nxt--;
				if (nxt < 0) {
					nxt = -nxt;
					sign = 0;
				}
			} else {
				nxt++;

			}
			result = Math.max(result,
					data[index] + cal(index + l + 1, nxt, sign, d, data));
		}
		return dp[neg][step][index] = result;
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}