I I U C   O N L I N E   C O N T E S T   2 0 0 8

Problem I: Tri-Isomorphism

Input: standard input

Output: standard output

 

Let V(G) be the vertex set of a simple graph & E(G) its edge set. An Isomorphism from a simple graph G to a simple graph H is a bijection f: V(G)→V(H) such that uv є E(G) if & only if f(u)f(v) є E(H). We say, G is isomorphic to H if there is an isomorphism from G to H.

 

A complete graph is a simple graph whose vertices are pairwise adjacent: the unlabeled complete graph with n vertices is denoted K­n. For example, the following figure shows K5.

 

Finally, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list.

 

Now, given a positive integer n, you are to determine if Kn decomposes into three pairwise-isomorphic subgraphs.

 

Input

First line of each test case consists of a positive integer n (n<=100). The end of input will be indicated by a case where n=0. This case should not be processed.

 

Output

For each test case, print YES if Kn can be decomposed into three pairwise-isomorphic subgraphs & NO otherwise.

 

Constraints

-           n < 100

 

Sample Input

Output for Sample Input

4

5

0

YES

NO

 

Problem setter: Mohammad Mahmudur Rahman