#484 Problem Numbers Aren't Sorted by Difficulty

Statement

Statement language

hy9360 tried to solve DOJ problems in problem-number order, and discovered that problem numbers are unrelated to difficulty order.

Each problem difficulty is represented by a pair consisting of a tier name and a tier number. From easiest to hardest, the tier names are

Bronze, Silver, Gold, Platinum, Diamond, Ruby.

Within the same tier name, a larger number means an easier problem: $5$ is the easiest and $1$ is the hardest. For example, Bronze $5$ is easier than Bronze $1$ , and Gold $1$ is easier than Platinum $5$ .

You are given $N$ problems and a threshold difficulty $(C,D)$ . Print the problem numbers of all problems whose difficulty is at most $(C,D)$ , meaning that they are not harder than $(C,D)$ , in increasing order of difficulty.

Problems with exactly the same difficulty may be printed in any order.

Input

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

Output

For each test case, print the problem numbers satisfying the condition, one by one, in increasing order of difficulty. Problems with exactly the same difficulty may be printed in any order.

If no problem satisfies the condition, print -1.

Constraints

$1 \le T \le 100$ .
$1 \le N \le 385$ .
The sum of $N$ over all test cases does not exceed .

Subtasks

#	Score	Constraints
1	35	The threshold tier and every problem's tier are `Bronze`.
2	65	No additional constraints.

Samples

Input

2
Silver 4
rubyhard Ruby 1
bronzeone Bronze 1
silverfour Silver 4
bronzefive Bronze 5
silverfive Silver 5
goldfive Gold 5
Bronze 5
a Bronze 4
b Silver 5
c Ruby 1

Output

In the first test case, the problems with difficulties Bronze $5$ , Bronze $1$ , Silver $5$ , and Silver $4$ satisfy the threshold.

In the second test case, no problem has difficulty at most Bronze $5$ .