FoxSequence

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 < N-1 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[N-1] 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

1. {1,3,5,7,5,3,1,1,1,3,5,7,5,3,1}
   

   Returns: "YES"

   This is the top-left sequence of the image shown in the statement. The next five examples are also from that image.

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

   Returns: "YES"

3. {3,6,9,1,9,5,1}
   

   Returns: "YES"

4. {1,2,3,2,1,2,3,2,1,2,3,2,1}
   

   Returns: "NO"

5. {1,3,4,3,1,1,1,1,3,4,3,1}
   

   Returns: "NO"

6. {6,1,6}
   

   Returns: "NO"