Test Cases:

$ python3.6 encode2.py

Enter a string: acccccccccc
a10[c]
Enter a string: aecccccccccccdecccccccccccdecccccccccccd
a3[e11[c]d]
Enter a string: eeeeeeeeeeee
12[e]
Enter a string: aabcabc
a2[abc]
Enter a string: abcabcc
2[abc]c
Enter a string: abcdbcdefgefgh
a2[bcd]2[efg]h
Enter a string: abcdcdbcdcdbcdcde
a3[b2[cd]]e
Enter a string: abcdcdbcdcdbcdcdfggggghfggggghfggggghfggggghe
a3[b2[cd]]4[f5[g]h]e
Enter a string: abcdfggcdfggbcdfggcdfggbcdfggcdfgge
a3[b2[cdf2[g]]]e