A. Dual Triggertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputNgọt - LẦN CUỐI (đi bên em xót xa người ơi)ඞThere are n lamps numbered 1 to n lined up in a row, initially turned off. You can perform the following operation any number of times (possibly zero):   Choose two non-adjacent{}^\dagger lamps that are currently turned off, then turn them on. Determine whether you can reach configuration s, where s_i = 1 means the i-th lamp is turned on, and s_i = 0 otherwise.{}^\dagger Only lamp i and i + 1 are adjacent for all 1 \le i < n. Note that lamp n and 1 are not adjacent when n \ne 2.InputEach test contains multiple test cases. The first line contains an integer t (1 \le t \le 1000) — the number of test cases. The description of the test cases follows.The first line of each test case contains an integer n (1 \le n \le 50) — the number of lamps.The second line of each test case contains a binary string s of size n — the final desired configuration.OutputFor each test case, print on one line "YES" if we can reach the configuration s via applying the given operation any number of times. Otherwise, print "NO".ExampleInput
510110101011010100100111060000001112111111111111Output
YES
NO
YES
NO
YES
NoteIn the first test case, the sequence of operation could have been as follows (note that initially s is all zero): \mathtt{0000000000} \to \mathtt{\color{red}{1}0000000\color{red}{1}0} \to \mathtt{1\color{red}{1}00000\color{red}{1}10} \to \mathtt{110\color{red}{1}0\color{red}{1}0110}.In the third test case, we don't have to do any operation.In the fourth test case, we cannot do any operation, but we need the first lamp to be on. Therefore, it is impossible to achieve the desired state.
510110101011010100100111060000001112111111111111
YES NO YES NO YES 
['constructive algorithms', 'greedy', 'math', '*900']