#!/usr/bin/env python3
"""Evaluate any chaos-chip genome at any (n, k). Pure numpy."""
import sys
import numpy as np
from itertools import combinations

PI = np.pi

def decode(byte):
    qi = (byte >> 4) & 0xF
    si = byte & 0xF
    return qi / 15.0 * 2 * PI - PI, si / 15.0 * 2 * PI - PI

def chirp(n, q, s, c=2.0, alpha=1.5):
    i = np.arange(n)[:, None]
    j = np.arange(n)[None, :]
    return alpha * np.cos(s * i - c * q * j)

def coloring(n, q, s):
    p = chirp(n, q, s)
    return np.sign(p - np.median(p) + 1e-9)

def mono(C, k):
    n = C.shape[0]
    count = 0
    for combo in combinations(range(n), k):
        total = sum(C[combo[a], combo[b]]
                    for a in range(k) for b in range(a+1, k))
        if abs(total) == k * (k - 1) // 2:
            count += 1
    return count

def eval_byte(byte, n, k):
    q, s = decode(byte)
    C = coloring(n, q, s)
    return mono(C, k)

if __name__ == "__main__":
    if len(sys.argv) == 3:
        byte = int(sys.argv[1], 0)
        n = int(sys.argv[2])
        for k in [3, 4, 5]:
            m = eval_byte(byte, n, k)
            print(f"n={n}, k={k}: mono = {m}")
    else:
        print("usage: python eval.py <byte> <n>")