D. Bullfighting
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
"I want to check the cards..."
— A mysterious gambler with a French accent.

Alice is playing a card game called Bullfighting.

The game is played with a standard deck of cards, but only ranks A through 10 are kept. The point value of each card is defined as follows:

  • A counts as $$$1$$$ point.
  • Number cards 2 through 10 count as their face value (e.g., a 7 counts as $$$7$$$ points).

In each round, Alice is dealt $$$5$$$ cards. She must arrange these $$$5$$$ cards into two groups to determine her hand's power:

  1. Group 1: Consists of exactly $$$3$$$ cards.
  2. Group 2: Consists of the remaining $$$2$$$ cards.

The rank of the hand is determined by the following rules:

  1. Condition (Has Bull): If the sum of the points in Group 1 is a multiple of $$$10$$$, the hand is considered to "Have Bull". Otherwise, the hand is ranked as No Bull.
  2. Bull Rank: If the hand has a Bull, the rank is determined by the sum of points in Group 2. Let $$$S$$$ be the sum of the two cards in Group 2.
    • If $$$S$$$ is also a multiple of $$$10$$$, the rank is Bull Bull (the highest rank).
    • Otherwise, the rank is Bull $$$X$$$, where $$$X$$$ is the remainder of $$$S$$$ divided by $$$10$$$ (i.e., $$$X = S \bmod 10$$$).

The ranks are ordered as follows: $$$$$$ \text{No Bull} \lt \text{Bull } 1 \lt \text{Bull } 2 \lt \dots \lt \text{Bull } 9 \lt \text{Bull Bull} $$$$$$

Given 5 cards, please help Alice find the highest rank she can achieve by arranging them optimally.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 100$$$), representing the number of test cases.

Each test case consists of a single line containing $$$5$$$ integers $$$c_1, c_2, c_3, c_4, c_5$$$ ($$$1 \le c_i \le 10$$$), representing the point values of the $$$5$$$ cards Alice holds.

It is guaranteed that the cards are drawn from a single standard deck, meaning that for any rank $$$k \in [1, 10]$$$, it appears at most $$$4$$$ times in a hand.

Output

For each test case, output the highest rank Alice can obtain in a single line. The output must be one of the following strings:

  • No Bull
  • Bull 1, Bull 2, ..., Bull 9
  • Bull Bull
Example
Input
3
1 2 3 4 5
10 10 10 5 5
1 2 3 4 8
Output
Bull 5
Bull Bull
No Bull
Note

For the first case (1 2 3 4 5):

  • We choose Group 1 as $$$\{1, 4, 5\}$$$. The sum is $$$1+4+5=10$$$, which is a multiple of $$$10$$$.
  • Group 2 is $$$\{2, 3\}$$$. The sum is $$$2+3=5$$$.
  • Since $$$5 \bmod 10 = 5$$$, the rank is Bull 5.

For the second case (10 10 10 5 5):

  • We choose Group 1 as $$$\{10, 10, 10\}$$$. The sum is $$$30$$$ (multiple of $$$10$$$).
  • Group 2 is $$$\{5, 5\}$$$. The sum is $$$10$$$.
  • Since $$$10$$$ is a multiple of $$$10$$$, the rank is Bull Bull.