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!

Input

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.

Output

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