Password change every two months

In my company, we have to change password every two months. The new password cannot be similar to any of the previous 24 passwords. i.e., It will not allow, if you just change one character in the previous password. It should contain uppercase letters, lowercase letters, digits, and special characters.

I can remember one very big password which has more than 30 characters with digits, lowercase/uppercase letters, special characters. I can make sure that, nobody sees the password while typing. I can also make sure that, I will not type this password except in office on my computer, and not anywhere else. But, that does not satisfy the security team in my company. But, I don't have that much memory power to remember a new password every two months.

So, what do I do? Write down the password some where.

Rule is followed, but the spirit is violated.