# -*- coding: utf-8 -*-
from collections import defaultdict

############################
# T(n,k) from OEIS A276158 #
############################
def T(n,k): 
    
    return n+1 if k==0 else 6*k*(n+1-k)

########################
# kaprekar_successor() #
########################
def kaprekar_successor(n_digits, n):

    a = sorted(f'{n:0{n_digits}d}') # characters; smallest to largest
    l = int(''.join(a))             # int with digits smallest to largest
    u = int(''.join(a[::-1]))       # int with digits largest to smallest
    
    return u-l

#########
# main #
########
if __name__ == "__main__":
    
    ND = 3          # Number of digits
    N  = 10**ND     # Number of nodes
    
    # Create dictionary where keys are the non-leaf nodes and the value
    # is a count of the key node's predecessor nodes(mostly leaf nodes.)  
    #
    nodes = defaultdict(int)
    for i in range(N):
        nodes[kaprekar_successor(ND, i)] +=1 # count predecessors
     
    # Order keys, format and print result
    #
    n = len(nodes)-1
    for k, key in enumerate(sorted(nodes.keys())):
        if nodes[key] != T(n,k):
            print("TEST FAILED")
            break
        pred_counts = f'node {key:0{ND}d} indegree = {nodes[key]:{ND}d}'
        oeis_result = f' = T({n},{k:2d})'
        print(f'{k:2d}:', pred_counts + oeis_result)