"""
Verify the 7-day schedule for the 24-person rowing meet.
"""
import itertools, json

N, TOTAL = 24, 276

def norm(p, q):
    return (min(p, q), max(p, q))

sched = json.loads('''[
  [[0,1,2,21,22,23],[3,4,5,18,19,20],[6,7,8,15,16,17],[9,10,11,12,13,14]],
  [[3,4,5,21,22,23],[0,1,2,6,7,8],[9,10,11,18,19,20],[12,13,14,15,16,17]],
  [[6,7,8,21,22,23],[3,4,5,9,10,11],[0,1,2,12,13,14],[15,16,17,18,19,20]],
  [[9,10,11,21,22,23],[6,7,8,12,13,14],[3,4,5,15,16,17],[0,1,2,18,19,20]],
  [[12,13,14,21,22,23],[9,10,11,15,16,17],[6,7,8,18,19,20],[0,1,2,3,4,5]],
  [[15,16,17,21,22,23],[12,13,14,18,19,20],[0,1,2,9,10,11],[3,4,5,6,7,8]],
  [[18,19,20,21,22,23],[0,1,2,15,16,17],[3,4,5,12,13,14],[6,7,8,9,10,11]]
]''')

# Verify each day partitions 0..23 into 4 groups of 6
for di, day in enumerate(sched):
    items = set()
    for boat in day:
        assert len(boat) == 6, f"Day {di+1}: boat has {len(boat)} elements"
        items.update(boat)
    assert len(items) == 24, f"Day {di+1}: has {len(items)} distinct elements (need 24)"
    print(f"Day {di+1}: ✓ (24 people, 4 boats of 6)")

# Count all pairs covered
pairs = set()
for day in sched:
    for boat in day:
        pairs.update(norm(p, q) for p, q in itertools.combinations(boat, 2))

print(f"\nDistinct pairs covered: {len(pairs)} / {TOTAL}")

if len(pairs) == TOTAL:
    print("SUCCESS! All 276 pairs share a boat on at least one day. ✓")
else:
    missing = set(norm(i, j) for i in range(N) for j in range(i + 1, N)) - pairs
    print(f"FAILED! Missing {len(missing)} pairs: {sorted(missing)}")