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 CPP):

Solution:
#include <bits/stdc++.h>
const int N = 30010;
const int N2 = 2010;
const int INF = 0x3f3f3f3f;
int n, d;
int w[N];
class DP2DMax {
 public:
  void Init(int max1, int max2, int min1 = 0, int min2 = 0) {
    max1_ = max1;
    max2_ = max2;
    min1_ = min1;
    min2_ = min2;
    for (int i = min1_; i <= max1_; ++i) {
      for (int j = min2_; j <= max2_; ++j) {
        dp[Id1(i)][Id2(j)] = -INF;
      }
    }
  }
  void InitState(int a, int b, int w) { dp[a - min1_][b - min2_] = w; }
  void Update(int a, int b, int a2, int b2, int w) {
    if (!Valid(a, b) || !Valid(a2, b2)) {
      return;
    }
    a = Id1(a);
    b = Id2(b);
    a2 = Id1(a2);
    b2 = Id2(b2);
    if (dp[a2][b2] < dp[a][b] + w) {
      dp[a2][b2] = dp[a][b] + w;
    }
  }
  int Value(int a, int b) {
    if (!Valid(a, b)) {
      return -INF;
    }
    return dp[Id1(a)][Id2(b)];
  }

 private:
  int Id1(int x) { return x - min1_; }
  int Id2(int x) { return x - min2_; }
  bool Valid(int a, int b) {
    return a >= min1_ && a <= max1_ && b >= min2_ && b <= max2_;
  }
  int max1_;
  int max2_;
  int min1_;
  int min2_;
  int dp[N][N2];
} dp2_max;
int main() {
  scanf("%d%d", &n, &d);
  int mx_x = 0;
  for (int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    ++w[x];
    mx_x = std::max(mx_x, x);
  }
  int k_max = 0;
  int sum = 0;
  while (1) {
    sum += (d + k_max);
    if (sum >= mx_x) {
      break;
    }
    ++k_max;
  }
  int k_min = 0;
  sum = 0;
  while (1) {
    sum += (d - k_min);
    if (d - k_min == 1 || sum >= mx_x) {
      break;
    }
    ++k_min;
  }
  dp2_max.Init(mx_x, k_max, d, -k_min);
  dp2_max.InitState(d, 0, w[d]);
  for (int i = d; i <= mx_x; ++i) {
    for (int j = -k_min; j <= k_max; ++j) {
      if (dp2_max.Value(i, j) != -INF) {
        int step = d + j;
        assert(step >= 1);
        dp2_max.Update(i, j, i + step, j, w[i + step]);
        dp2_max.Update(i, j, i + step + 1, j + 1, w[i + step + 1]);
        dp2_max.Update(i, j, i + step - 1, j - 1, w[i + step - 1]);
      }
    }
  }
  int ans = 0;
  for (int i = d; i <= mx_x; ++i) {
    for (int j = -k_min; j <= k_max; ++j) {
      ans = std::max(ans, dp2_max.Value(i, j));
    }
  }
  printf("%d\n", ans);
  return 0;
}