Problem I

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<=n<=1000). Each of the next n lines is either a type-1 command, or an integer 2 followed by an integer x. That means after executing a type-2 command, we get an element x without error. 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

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

Output for the Sample Input

queue
not sure
impossible
stack
priority queue

---

#include<stdio.h>

int cmd[1000], x[1000];
int testStack(int n) {
	int Stack[1005], idx = -1;
	int i;
	for(i = 0; i < n; i++) {
		if(cmd[i] == 1) {
			Stack[++idx] = x[i];
		} else {
			if(idx < 0 || Stack[idx] != x[i])
				return 0;
			--idx;
		}
	}
	return 1;
}
int testQueue(int n) {
	int Queue[1005], head = 0, tail = -1;
	int i;
	for(i = 0; i < n; i++) {
		if(cmd[i] == 1)
			Queue[++tail] = x[i];
		else {
			if(head > tail || Queue[head] != x[i])
				return 0;
			++head;
		}
	}
	return 1;
}
int testPriorityQueue(int n) {
	int Heap[1005], L = 0, P, S, tmp; /*max-heap*/
	int i;
	for(i = 0; i < n; i++) {
		if(cmd[i] == 1) {
			Heap[++L] = x[i];
			S = L, P = S>>1;
			while(S >= 2 && Heap[S] > Heap[P]) {
				tmp = Heap[S], Heap[S] = Heap[P], Heap[P] = tmp;
				S = P, P = S>>1;
			}
		} else {
			if(L < 1 || Heap[1] != x[i])
				return 0;
			tmp = Heap[L], Heap[L] = Heap[1], Heap[1] = tmp;
			P = 1, S = P<<1, --L;
			while(S <= L) {
				if(S < L && Heap[S+1] > Heap[S])
					S++;
				if(Heap[S] <= Heap[P])
					break;
				tmp = Heap[S], Heap[S] = Heap[P], Heap[P] = tmp;
				P = S, S = P<<1;
			}
		}
	}
	return 1;
}
int main() {
	int n, i;
	while(scanf("%d", &n) == 1) {
		for(i = 0; i < n; i++)
			scanf("%d %d", &cmd[i], &x[i]);
		int flag = 0, ans;
		if(testStack(n))	
			ans = 1, flag++;
		if(testQueue(n))	
			ans = 2, flag++;
		if(testPriorityQueue(n))	
			ans = 3, flag++;
		if(flag == 0)
			puts("impossible");
		else if(flag == 1) {
			if(ans == 1)
				puts("stack");
			else if(ans == 2)
				puts("queue");
			else
				puts("priority queue");
		} else {
			puts("not sure");
		}
	}
    return 0;
}