'''
    When is probability = 0.5 that in an image
    with N pixels, c point-like objects 
    will not overlap (occupy the same pixel)?
'''
from numpy import around,sqrt
N = int(input("N pixels = "))
ratio = 1.
c = 0
while(c < N):    # c is the number of people/obj.
    c += 1
    ratio = ratio *(N-c+1)/N
    p = 1 - ratio
    print("i",c,"P(none), P(some)",
          around(ratio,6),around(p,6))
    if (p < 0.5): 
        confusion = c+1
    if (ratio < 1e-4): 
        break
        
print("confusion limit  =", confusion,
     "  sqrt(N)=",around(sqrt(N),2),
     " limit/sqrt(N) = ", around(confusion/sqrt(N),4))