'''
Copyright (c) 2019 Serguei Zolotov

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

'''
import math

def counter(astr, N): 

    n = len(astr)
    Q = int(N * (N + 1) / 2)
    dX = [0] * (n - N)

    if n > N:
        dX[0] = 1
        for e in astr[N + 1:]:
            if e == 'a':
                dX[0] += 1
            else:
                break

    l = N
    r = l - 1

    for i in range(N + 1, n):
        u = 1
        if i <= r:
            u = min(dX[l + r - i - N], r - i + 1)

        while i - u >= 0 and i + u < n and astr[i - u] == astr[i + u]:
            u += 1

        dX[i - N] = u
        if i + u - 1 > r:
            l = i - u + 1
            r = i + u - 1

    Q = Q + sum(dX)

    dX = [0] * (n - N)
    l = N
    r = l - 1

    for i in range(N + 1, n):
        u = 0
        if i <= r:
            u = min(dX[l + r - i + 1 - N], r - i + 1)

        while i - u - 1 >= 0 and i + u < n and astr[i - u - 1] == astr[i + u]:
            u += 1

        dX[i - N] = u
        if i + u - 1 > r:
            l = i - u
            r = i + u - 1

    Q = Q + sum(dX)
    return Q 

def getnextstring(astr, N):

    l = len(astr)
    for k in range(l):
        p = l - k - 1
        o = astr[p]
        if o in astr[0:p]:
            astr = astr[0:p] + chr(ord(o) + 1) + astr[p + 1:]
            break

        astr = astr[0:p] + 'a' + astr[p + 1:]

    N = min(N, p)
    return astr, N

def buildcloseststring(k):

    N = int(math.sqrt(2 * k))
    while (N * (N + 1) / 2 > k):
        N = N - 1

    mstr = 'a' * N
    r = k - int(N * (N + 1) / 2)

    if r > 0:
        Q = int(math.sqrt(2 * r))
        while (Q * (Q + 3) // 2 > r):
            Q = Q - 1
        mstr = mstr + 'b' + 'a' * Q

    return mstr, N

# Complete the solve function below.
def calculate(k):
 
    mstr, N = buildcloseststring(k)
    while (True):

        ret = counter(mstr, N)
        if (ret == k):
            break
        elif (ret < k):
            mstr = mstr + 'a'
            if N == len(mstr) + 1:
                N = N + 1
        else:
            mstr, N = getnextstring(mstr, N)

    return len(mstr), mstr

if __name__ == '__main__':

    # open output files
    fb = open("b340458.txt",'w')
    fa = open("a340458.txt",'w')

    # loop through boundaries
    for n in range(1, 5001):
        num, mstr = calculate(n)
        print ("%d %d"%(n, num), file=fb)
        print ("%d %d %s"%(n, num, mstr), file=fa)

    # close output
    fb.close()
    fa.close()