Week 0 ~ hello.X

Farmer Ran wants to welcome his cows to a productive and
enjoyable spring of problem-solving. To do so, he is creating
an ASCII banner that repeatedly prints the pattern

I
I<
I<3
I<3C
I<3Co
I<3Cow
I<3Cows

OR the pattern

I<3Cows
I<3Cow
I<3Co
I<3C
I<3
I<
I

Your task is to create a program that will produce
one or the other of these patterns a specified number of times.
Somewhat unfortunately, the cows are quite fickle and have
very particular rules about when they prefer the former
("growing") or the latter ("shrinking") pattern:

  - in general, unless otherwise specified by the rules
    below, the cows prefer the  "growing" pattern

  - indexing from 1 (i.e., the first pattern == #1),
    prime-numbered patterns should be "shrinking" (1 is not prime)

  - except that prime-numbered patterns whose index has 
    a base-11 representation containing the digit 1 should be "growing"

  - except that prime-numbered patterns whose index has 
    a base-11 representation containing the digit 1 and
    whose binary representation consists of bits summing
    to a multiple of 4 should be "shrinking"



PROBLEM NAME: hello

INPUT FORMAT:

* Line 1: Two integers, L and H, with 1 <= L <= H < 1000000000.
          Also,  0 <= H-L <= 100.


SAMPLE INPUT:

1 4


INPUT DETAILS:

The input indicates the span of indices (inclusive) for which
Farmer Ran wants a cow-pleasing banner.


OUTPUT FORMAT:

* 7*(H-L+1) lines containing the patterns the cows want.


SAMPLE OUTPUT:

I
I<
I<3
I<3C
I<3Co
I<3Cow
I<3Cows
I<3Cows
I<3Cow
I<3Co
I<3C
I<3
I<
I
I<3Cows
I<3Cow
I<3Co
I<3C
I<3
I<
I
I
I<
I<3
I<3C
I<3Co
I<3Cow
I<3Cows


OUTPUT DETAILS:

In this case, the indices are 1, 2, 3, 4, corresponding to
  1: growing
  2: shrinking
  3: shrinking
  4: growing