Substitute each of the capital letters by a different base six digit from 0 to 5 to satisfy the following set of alphametic relationships. None of the numbers can contain any leading zero.

• The base six number ICUS is a perfect square, and:
• A is a perfect square, and:
• The base six number MI is a perfect fifth power, and:
• The base six number US is a perfect square.

Determine the value assumed by the base six number AMICUS.