Problem Statement 
 Fox Ciel likes sequences. One day, she invented a new type of sequence and named it the fox sequence. A sequence seq containing N elements is called a fox sequence if and only if there exist four integers a, b, c and d such that 0 < a < b <= c < d < N1 and the following five conditions are met:
 seq[0], seq[1], ... , seq[a] forms an arithmetic progression with a positive common difference. An arithmetic progression is a sequence where the difference between successive elements is equal. The difference between successive elements is called the common difference. Note that 0 is neither positive nor negative.
 seq[a], seq[a+1], ... , seq[b] forms an arithmetic progression with a negative common difference.
 seq[b], seq[b+1], ... , seq[c] are all equal.
 seq[c], seq[c+1], ... , seq[d] forms an arithmetic progression with a positive common difference.
 seq[d], seq[d+1], ... , seq[N1] forms an arithmetic progression with a negative common difference.
In the following image, the top 3 sequences are fox sequences, while the bottom 3 sequences are not:
You are given a sequence seq. Return "YES" if it is a fox sequence, or "NO" if it is not (all quotes for clarity). 

Definition 
 Class:  FoxSequence  Method:  isValid  Parameters:  int[]  Returns:  String  Method signature:  String isValid(int[] seq)  (be sure your method is public) 




Constraints 
  seq will contain between 1 and 50 elements, inclusive. 
  Each element of seq will be between 1 and 2,000, inclusive. 

Examples 
0)  
 {1,3,5,7,5,3,1,1,1,3,5,7,5,3,1}

 Returns: "YES"  This is the topleft sequence of the image shown in the statement. The next five examples are also from that image. 


1)  
 {1,2,3,4,5,4,3,2,2,2,3,4,5,6,4}

 Returns: "YES"  

2)  
 
3)  
 {1,2,3,2,1,2,3,2,1,2,3,2,1}

 Returns: "NO"  

4)  
 {1,3,4,3,1,1,1,1,3,4,3,1}

 Returns: "NO"  

5)  
 