Problem G: Longest Chain

Let us compare two triples a = (x_a, y_a, z_a) and b = (x_b, y_b, z_b) by a partial order ∠ defined as follows.

a ∠ b ⇔ x_a < x_b and y_a < y_b and z_a < z_b

Your mission is to find, in the given set of triples, the longest ascending series a₁ ∠ a₂ ∠ ... ∠ a_k.

Input

The input is a sequence of datasets, each specifying a set of triples formatted as follows.

m n A B
x1 y1 z1
x2 y2 z2
...
xm ym zm

Here, m, n, A and B in the first line, and all of x_i, y_i and z_i (i = 1, . . . , m) in the following lines are non-negative integers.

Each dataset specifies a set of m + n triples. The triples p₁ through p_m are explicitly specified in the dataset, the i-th triple p_i being (x_i, y_i, z_i). The remaining n triples are specified by parameters A and B given to the following generator routine.

int a = A, b = B, C = ~(1<<31), M = (1<<16)-1;
int r() {
  a = 36969 * (a & M) + (a >> 16);
  b = 18000 * (b & M) + (b >> 16);
  return (C & ((a << 16) + b)) % 1000000;
}

Repeated 3n calls of r() defined as above yield values of x_m+1, y_m+1, z_m+1, x_m+2, y_m+2, z_m+2, ..., x_m+n, y_m+n, and z_m+n, in this order.

You can assume that 1 ≤ m + n ≤ 3 × 10⁵, 1 ≤ A,B ≤ 2¹⁶, and 0 ≤ x_k, y_k, z_k < 10⁶ for 1 ≤ k ≤ m + n.

The input ends with a line containing four zeros. The total of m + n for all the datasets does not exceed 2 × 10⁶.

Output

For each dataset, output the length of the longest ascending series of triples in the specified set. If p_i1 ∠ p_i2 ∠ ... ∠ p_ik is the longest, the answer should be k.

Sample Input

6 0 1 1
0 0 0
0 2 2
1 1 1
2 0 2
2 2 0
2 2 2
5 0 1 1
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
10 0 1 1
3 0 0
2 1 0
2 0 1
1 2 0
1 1 1
1 0 2
0 3 0
0 2 1
0 1 2
0 0 3
0 10 1 1
0 0 0 0

Output for the Sample Input

3
5
1
3

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