import torch
from safetensors.torch import save_file

# Layer 1: N1 checks sum >= 1, N2 checks sum <= 1
# Layer 2: AND(N1, N2) = exactly 1
weights = {
    'layer1.weight': torch.tensor([
        [1.0, 1.0, 1.0, 1.0, 1.0],   # N1: sum >= 1
        [-1.0, -1.0, -1.0, -1.0, -1.0]  # N2: sum <= 1
    ], dtype=torch.float32),
    'layer1.bias': torch.tensor([-1.0, 1.0], dtype=torch.float32),
    'layer2.weight': torch.tensor([[1.0, 1.0]], dtype=torch.float32),
    'layer2.bias': torch.tensor([-2.0], dtype=torch.float32)
}
save_file(weights, 'model.safetensors')

def exactly1of5(a, b, c, d, e):
    inp = torch.tensor([float(a), float(b), float(c), float(d), float(e)])
    l1 = (inp @ weights['layer1.weight'].T + weights['layer1.bias'] >= 0).float()
    out = (l1 @ weights['layer2.weight'].T + weights['layer2.bias'] >= 0).float()
    return int(out.item())

print("Verifying exactly1outof5...")
errors = 0
for i in range(32):
    bits = [(i >> j) & 1 for j in range(5)]
    result = exactly1of5(*bits)
    expected = 1 if sum(bits) == 1 else 0
    if result != expected:
        errors += 1
        print(f"ERROR: {bits} -> {result}, expected {expected}")
if errors == 0:
    print("All 32 test cases passed!")
print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.0f}")