Problem 1: Quantum Numbers

Background

In Quantum Mechanics, a set of four numbers are often used to describe an electron of an atom. The first three of these numbers are integers (they must be integers btw. I won't bore you with the mathematics to show you why though) They are labeled n, l, m in that order. They are subject to the following restrictions:

  1. n: Integer values such that n is greater than or equal to one (n >= 1).
  2. l: Integer values such that zero is less than or equal to l and l is less than or equal to n minus one. (0 <= l <= n - 1).
  3. m: Integer values such that m is between minus l and positive l. (-l <= m <= l)

Your job is to write a program to tell if 3 integers represent a valid quantum set.

Input

Each line of input will be 3 number in the form n l m. A single space separates each number.

Output

For each line of input you must tell if it is a valid set of quantum number or not. If it is an invalid set, then you must say why. The output will be one of the following:

invalid n
invalid l
invalid m
valid

Only print one line of output. The input set could be invalid for a number of reasons. Your program should only print the first one. Check for n, then l, and finally m.

Sample Input

-1 2 3
3 3 4
2 1 -1
3 2 -4

Sample Output

invalid n
invalid l
valid
invalid m