import math
def digits_in_factorial(n: int) -> int:
    # Escribe tu solución aquí
    value = 0
    for k in range(1,n+1):
        value += math.log(k,10)    
    
    value += 1
    # return str(int(sum(math.log(k,10) for k in range(1,n+1))+1))

    return int(value)