Your task is the exact same as for the easy version. But this time, the marmots subtract the village's population *P* from their random number before responding to Heidi's request.

Also, there are now villages with as few as a single inhabitant, meaning that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bf7241381f0b584c267cdf93e7f9ed4911278437.png" style="max-width: 100.0%;max-height: 100.0%;"/>.

Can you help Heidi find out whether a village follows a Poisson or a uniform distribution?
Same as for the easy and medium versions. But remember that now 1 ≤ *P* ≤ 1000 and that the marmots may provide positive as well as negative integers.
none
for i in range(int(input())):
  a=list(map(int,input().split()))
  mx=max(list(map(abs,a)))
  std=(sum(list(map(lambda x:x*x,a)))/len(a))**0.5
  print('poisson'if mx/std>2 else'uniform')