halving_interval = 210000
cycle_interval = 1260000  # LCM of 210000 and 2016 for cycle conjunctions
initial_subsidy = 5000000000  # 50 BTC in sats

def subsidy(height):
    return initial_subsidy >> (height // halving_interval)

def starting_sat(height):
    total = 0
    full_epochs = height // halving_interval
    for e in range(full_epochs):
        subs = initial_subsidy >> e
        total += halving_interval * subs
    remaining = height % halving_interval
    subs = initial_subsidy >> full_epochs
    total += remaining * subs
    return total

# Epic sats: first sat of halving epochs 1 to 32
epic_sats = []
for n in range(1, 33):
    h = n * halving_interval
    sat = starting_sat(h)
    epic_sats.append((n, h, sat))

# Legendary sats: first sat of cycles 1 to 5
legendary_sats = []
for m in range(1, 6):
    h = m * cycle_interval
    sat = starting_sat(h)
    legendary_sats.append((m, h, sat))

# Output
print("Epic Sats:")
for n, h, sat in epic_sats:
    print(f"Epoch {n}, Block {h}, Sat {sat}")

print("\nLegendary Sats:")
for m, h, sat in legendary_sats:
    print(f"Cycle {m}, Block {h}, Sat {sat}")