The non-negative integer a is a divisor of the non-negative integer b if and only if there exists a positive integer c such that a × c = b.

Some numbers are really interesting. Commander Surena defines some interesting properties for non-negative integers:

• An integer is happy if it is divisible by at least one of its digits and not by all of them.
• An integer is happier if it is divisible by all of its digits.
• An integer is upset if it's divisible by none of its digits.

Surena asks you to find out if a given number is happy, happier or upset.

Input contains a single non-negative integer n (1 ≤ n ≤ 10⁸).

Write on a single line the type of the integer: happy, happier or upset. Print the type in lowercase letters.