from scipy.special import gammaln
from scipy.optimize import bisect
import math as mt


def inverse_log_gamma(logarg):
    assert(logarg > 0)
    a = 1
    b = 2
    while b < logarg:
        b = b*2
    return bisect(lambda x: gammaln(x) - logarg, a, b)

def inverse_factorial(logarg):
    g = inverse_log_gamma(logarg)
    return round(g)-1 




print(inverse_factorial(mt.log(mt.factorial(42))))
print(inverse_factorial(mt.log(mt.factorial(171))))



print(inverse_factorial(gammaln(2025)/2))