Symmetric or not?


This problem asks you to think about a simple question -- given a graph 
with n nodes and m edges, is it true that for each directed edge e = (u,v), 
does there an exist an edge e' = (v,u)? A graph that contains edge (u,v) 
if and only if it contains (v,u) is called symmetric.   


Input

You are given several graphs. Each graph is specified by values of n, m
and a list of edges. For each instance the first line has 2 integers: n, m. 
This is followed by m lines, each containing a pair of integers denoting 
an edge. Note that nodes are numbered 1 through n. You may assume that 
n<1000 and m < 1,000,000 and there are no self-loops in the input graphs.

The last line of input has 0 0 and should not be processed.


Output

For each graph output "symmetric" if it is symmetric and "asymmetric" otherwise.


Sample Input

3 4 
1 2
2 1
1 3
3 1
0 0 

Sample Output

symmetric