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<stack>  
#include<queue>  
using namespace std;  
const int maxn = 1000+100;  
int id[maxn],x[maxn],n;  
bool isStack()
{  
    stack<int> s;  
    for(int i=0;i<n;i++)
	{  
        if(id[i]==1) s.push(x[i]);  
        else
		{  
            if(s.empty())  return false;  
            int val=s.top();  s.pop();  
            if(x[i]!=val) return false;  
        }  
    }  
    return true;  
}  
bool isQueue()
{  
	queue<int >q;  
	for(int i=0;i<n;i++)
	{  
        if(id[i]==1) q.push(x[i]);  
        else
		{  
            if(q.empty()) return false;  
            int val=q.front();  q.pop();  
            if(x[i]!=val) return false;  
        }  
    }  
    return true;  
}  
bool isPriority()
{  
    priority_queue<int > q;  
	for(int i=0;i<n;i++)
	{  
        if(id[i]==1) 
			q.push(x[i]);  
        else
		{  
			if(q.empty()) 
				return false;  
            int val=q.top();  
			q.pop();  
            if(x[i]!=val) return false;  
        }  
    }  
    return true;  
}  
int main(){  
    while(scanf("%d",&n)!=EOF)
	{  
        bool st=false,qu=false,pr=false;  
        for(int i=0;i<n;i++)
		{  
            scanf("%d %d",&id[i],&x[i]);  
        }  
        st=isStack(); 
		qu=isQueue();  
		pr=isPriority();  
        if(!st&&!qu&&!pr)  
			puts("impossible");  
        else if((!st&&qu&&pr)||(!qu&&st&&pr)||(!pr&&qu&&st)||pr&&qu&&st)
		{  
            puts("not sure");  
        }  
        else if(st) puts("stack");  
        else if(qu) puts("queue");  
        else if(pr) puts("priority queue");  
    }  
    return 0;  
}