5. An integer n with at least 4 digits is called happy if it has the following four properties. All of its digits are nonzero. For every set of four consecutive digits of n, the four-digit integer formed by those digits is a multiple of 3. (For example, 3591 is the integer formed by the second, third, fourth, and fifth digits of 435912). The second leftmost digit equals the third leftmost digit. The tens digit equals the hundreds digit. For example, 51182442 is a happy integer. Suppose n= ABCDEFGH is an eight-digit happy integer. Prove that n is a multiple of 3. (For your consideration: does it actually matter how many digits n has?)