from math import log10,ceil;

class InvalidDataError(Exception):
    def __init__(self,data):
        self.Data=data;

cb=log10(2);

def getPot(n):
    pot=ceil(n.bit_length()*cb);
    
    if (n-10**pot) < 0 and (n-10**(pot-1)) >= 0:
        return pot-1;
    elif (n-10**(pot-1)) < 0 and (n-10**(pot-2)) > 0:
        return pot-2;
    else:
        raise InvalidDataError('No power number');
# end def

def getDigit(pot,n):
    dig=0;
    while (n-dig*10**pot) >= 0:
        dig+=1;
    return dig-1;
# end def

def getSumOfDigists(n):
    qs=0;
    maxPot=getPot(n);
    pot=maxPot;
    while n>0:
        # dig=getDigit(pot,n);
        dig=0;
        while (n-dig*10**pot) >= 0:
            dig+=1;
        dig+=-1;
        qs+=dig;
        n=n-dig*10**pot
        pot-=1;
    # end while
    return qs;
# end def

qs=getSumOfDigists(2**(10**5));
# 5 läuft bereits 1,5 Minuten
print(qs);

##    >>> 
##    7
##    >>> ================================ RESTART ================================
##    >>> 
##    115
##    >>> ================================ RESTART ================================
##    >>> 
##    1366
##    >>> ================================ RESTART ================================
##    >>> 
##    13561
##    >>> ================================ RESTART ================================
##    >>> 
##    135178
##    >>>