Trolling
Trolling
In the language of the trolls have 5 consonants: {h, k, m, r, t}, and 3 vowels: {a, o, u}. Each word begins with a consonant letters, with the word can not be two consecutive vowels or consonants.
N trolls in turn called the shortest word that has not called any of the previous trolls. If several options, the troll vibiraem smallest lexicographically. Lexicographic order h < k < m < r < t < a < o < u. In this case, the word is compared first by the first letter. If the first letter of the same, for the second, etc.
Find the word that will call N-th troll.
Input data
The first line contains a single number 1 ≤ T ≤ 100, the number of test cases. Each and subsequent T lines contains one integer 1 ≤ N ≤ 1000000000(1e9) – the number of Troll.
Output data
For each number N of input data, output in a single line answer to the problem in accordance with the format specified in the example.
Examples
3 6 95 13934
Case #1: ha Case #2: tut Case #3: muhomor