I Can Guess the Data Structure!

There is a bag-like data structure, supporting two operations:

$1\ x$: Throw an element $x$ into the bag.

$2$: Take out an element from the bag.

Given a sequence of operations with return values, you’re going to guess the data structure. It is a stack (Last-In, First-Out), a queue (First-In, First-Out), a priority-queue (Always take out larger elements first) or something else that you can hardly imagine!

There are several test cases. Each test case begins with a line containing a single integer $n$ ($1\leq n\leq 1000$). Each of the next $n$ lines is either a type-1 command, or an integer $2$ followed by an integer $x$. This means that executing the type-2 command returned the element $x$. The value of $x$ is always a positive integer not larger than $100$. The input is terminated by end-of-file (EOF). The size of input file does not exceed 1MB.

For each test case, output one of the following:

`stack`

It’s definitely a stack.

`queue`

It’s definitely a queue.

`priority queue`

It’s definitely a priority queue.

`impossible`

It can’t be a stack, a queue or a priority queue.

`not sure`

It can be more than one of the three data structures mentioned
above.

Sample Input 1 | Sample Output 1 |
---|---|

6 1 1 1 2 1 3 2 1 2 2 2 3 6 1 1 1 2 1 3 2 3 2 2 2 1 2 1 1 2 2 4 1 2 1 1 2 1 2 2 7 1 2 1 5 1 1 1 3 2 5 1 4 2 4 1 2 1 |
queue not sure impossible stack priority queue impossible |