import time
from functools import reduce
from tools import algebra

def jump(num):
    if 9 > num % 10:
        return 1
    else:
        num += 1
        offset = 0
        while not num % 10:
            num //= 10
            offset += 1
        return 1 + (10 ** offset - 1) // 9 * (num % 10)

def gen_pick(digit):
    maxi = 10 ** (digit + 1) - 1
    num = maxi // 9
    while num < maxi:
        yield num
        num += jump(num)
    yield maxi

def judge(num):
    while True:
        a = 0
        while num != 0:
            a += (num % 10) ** 2
            num //= 10
        if a == 1:
            return False
        elif a == 89:
            return True
        else:
            num = a

def count(limit, s_num):
    total = 1
    for i in range(len(s_num)):
        total *= (limit - i)
    for ch in set(list(s_num)):
        total //= algebra.factorial(s_num.count(ch))
    return total

def statistic(limit):
    total = 0
    for digit in range(limit):
        for num in gen_pick(digit):
            if judge(num):
                total += count(limit, str(num))
    return total

print(statistic(7))
print(time.process_time())