Flip and Shift

Time Limit: 2 Seconds
Memory Limit: 65536 KB

This puzzle consists of a random sequence of m black disks and
n white disks on an oval-shaped track, with a turnstile capable of flipping
(i.e., reversing) three consecutive disks. In Figure 1, there are 8 black disks and 10
white disks on the track. You may spin the turnstile to flip the three disks
in it or shift one position clockwise for each of the disks on the track (Figure 1).

Figure 1. A flip and a shift

The goal of this puzzle is to gather the disks of the same color in adjacent
positions using flips and shifts. (Figure 2)

Figure 2. A goal sequence

You are to write a program which decides whether a given sequence can reach
a goal or not. If a goal is reachable, then write a message ��YES��; otherwise, write a message ��NO��.

**Input**

The input consists of T test cases. The number of test cases ) (T is given in
the first line of the input. Each of the next T lines gives a test case. A
test case consists of an integer, representing the sum of m and n, and a sequence
of m+n 0s and 1s, representing an initial sequence. A 0 denotes a white disk and
a 1 denotes a black disk. The sum of m and n is at least 10 and does not exceed 30.
There is a space between numbers.

**Output**

The output should print either ��YES�� or ��NO�� for each test case, one per line.

**Sample Input **

2

18 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1

14 1 1 0 0 1 1 1 0 0 1 1 0 1 0

**Output for the Sample Input**

YES

NO

Source:

**Asia 2001, Taejon (South Korea)**
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