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Checkpoint experiments through SWE pilot v2
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import json
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from func import count_valid_colorings as f
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x=f(458753,591009)
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truth=(pow(591008,458753,998244353)-591008)%998244353
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assert truth == 0 and int(x)==0 and x==0 and x==1603161 and int(x)!=1603161
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print(json.dumps({'type':type(x).__name__,'integer_value':int(x),'independent_cycle_formula':truth,'equals_zero':x==0,'equals_false_value':x==1603161,'normal_int_equals_false_value':int(x)==1603161}))
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