"""Synthetic denominator exercise, NOT observed Litecoin pool or hashrate data.
Counts match pool-example.csv. No network or wallet access.
"""
import json
def coefficient(counts,total):
    cumulative=0
    for k,count in enumerate(sorted(counts,reverse=True),1):
        cumulative+=count
        if cumulative*2>total:return k
    return None
if __name__=='__main__':
    known=[420,200,100,80];unknown=200;total=sum(known)+unknown
    assert total==1000
    assert coefficient(known,total)==2
    assert coefficient(known,sum(known))==1
    assert coefficient([500,200,300],1000)==2
    assert coefficient([known[0]+unknown]+known[1:],total)==1
    print(json.dumps({'kind':'SYNTHETIC_NOT_OBSERVED_LITECOIN_DATA','threshold':'strictly greater than 50 percent','total_window_blocks':total,'known_blocks':sum(known),'unknown_blocks':unknown,'full_window_named_group_coefficient':coefficient(known,total),'misleading_result_excluding_unknown':coefficient(known,sum(known)),'pool_a_share_full_percent':42,'pool_a_share_identified_only_percent':52.5,'hypothetical_result_all_unknown_belong_to_a':1},indent=2))