G. Pool Recordstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlice and Bob are swimming in the pool under the guidance of their instructor Monocarp.The pool can be represented as a segment on the OX-axis from 0 to 50. Both Alice and Bob started at moment 0 at point 0 with positive real speeds v_A and v_B correspondingly.Both Alice and Bob swim from 0 to point 50, then instantly turn back and swim from 50 to 0. At 0 they turn back again and swim to 50 and so on.Monocarp logged all valuable info about Alice and Bob, including moments of time when they met at the same point (Alice and Bob swim on parallel lanes, so they don't bother each other). Let's name that moments of time as sequence t_1, t_2, \dots, t_n.Due to some incident, Monocarp lost almost all data he recorded, and all he has now is array t. Monocarp remembers that Alice and Bob had distinct positive real swimming speeds v_A and v_B (v_A > 0; v_B > 0; v_A \neq v_B) and that sequence t contains the first n meeting moments.But looking at sequence t he noticed that all t_i are integer values, and now he doubts is sequence t valid or there are some errors in it. Help Monocarp to check array t!InputThe first line contains a single integer c (1 \le c \le 10^4) — the number of test cases. Then c cases follow.The first line of each test case contains a single integer n (1 \le n \le 2 \cdot 10^5) — the size of array t.The second line of each test case contains n integers t_1, t_2, \dots, t_n (1 \le t_1 < t_2 < \dots < t_n \le 10^9) — the meeting moments in the increasing order.It's guaranteed that the sum of n over all test cases doesn't exceed 2 \cdot 10^5.OutputFor each test case, print VALID if the array t is a valid array, or (in other words) exist such real values v_A and v_B (v_A, v_B > 0; v_A \neq v_B) that array t contains the first n meeting moments of Alice and Bob in the pool.Otherwise, print INVALID.You can output the answer in any case (upper or lower). For example, the strings "vALid", "valid", "Valid", and "VALID" will be recognized as positive responses.ExampleInput
714243 4 6 851 2 3 4 53999999998 999999999 100000000054 6 8 12 1646 11 12 14210 30Output
VALID
VALID
VALID
INVALID
VALID
INVALID
INVALID
NoteIn the first test case, imagine a situation: v_A = 1 and v_B = \frac{29}{21}. Then, at moment 42 Alice and Bob will be at point 42.In the second test case, imagine a situation: v_A = \frac{175}{6} and v_B = \frac{25}{6}. Then, at moment 3 Alice and Bob will meet at point 12.5, at 4 they'll meet at point \frac{50}{3}, at moment 6 they'll meet at 25 and at moment 8 — at point \frac{100}{3}. Since it's exactly the first 4 meeting moments. Array t may be valid.In the third test case, one of the possible situations is v_A = 25 and v_B = 75.
714243 4 6 851 2 3 4 53999999998 999999999 100000000054 6 8 12 1646 11 12 14210 30
VALID VALID VALID INVALID VALID INVALID INVALID 
['*special problem', 'greedy', '*2700']