You would like to construct a string (s), consisting of lowercase Latin letters, such that the following condition holds: For every pair of indices (i) and (j) such that (s_{i} = s_{j}), the difference of these indices is even, that is, (|i - j| \bmod 2 = 0). Constructing any string is too easy, so you will be given an array (c) of (26) numbers — the required number of occurrences of each individual letter in the string (s). So, for every (i \in 1, 26), the (i)-th letter of the Latin alphabet should occur exactly (c_i) times. Your task is to count the number of distinct strings (s) that satisfy all these conditions. Since the answer can be huge, output it modulo (998\,244\,353). Each test consists of several test cases. The first line contains a single integer (t) ((1 \le t \le 10^{4}))— the number of test cases. The description of test cases follows. Each test case contains (26) integers (c_{i}) ((0 \le c_{i} \le 5 \cdot 10^{5}))— the elements of the array (c). Additional constraints on the input data: The sum of (c_{i}) for every test case is positive; The sum of (c_{i}) over all test cases does not exceed (5 \cdot 10^{5}). For each test case, print one integer — the number of suitable strings (s), taken modulo (998\,244\,353). In the first test case, there are (4) suitable strings: " abak ", " akab ", " baka " and " kaba ".