D. MEX Sequencestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet's call a sequence of integers x_1, x_2, \dots, x_k MEX-correct if for all i (1 \le i \le k) |x_i - \operatorname{MEX}(x_1, x_2, \dots, x_i)| \le 1 holds. Where \operatorname{MEX}(x_1, \dots, x_k) is the minimum non-negative integer that doesn't belong to the set x_1, \dots, x_k. For example, \operatorname{MEX}(1, 0, 1, 3) = 2 and \operatorname{MEX}(2, 1, 5) = 0.You are given an array a consisting of n non-negative integers. Calculate the number of non-empty MEX-correct subsequences of a given array. The number of subsequences can be very large, so print it modulo 998244353. Note: a subsequence of an array a is a sequence [a_{i_1}, a_{i_2}, \dots, a_{i_m}] meeting the constraints 1 \le i_1 < i_2 < \dots < i_m \le n. If two different ways to choose the sequence of indices [i_1, i_2, \dots, i_m] yield the same subsequence, the resulting subsequence should be counted twice (i. e. two subsequences are different if their sequences of indices [i_1, i_2, \dots, i_m] are not the same).InputThe first line contains a single integer t (1 \le t \le 10^5) — the number of test cases.The first line of each test case contains a single integer n (1 \le n \le 5 \cdot 10^5).The second line contains n integers a_1, a_2, \dots, a_n (0 \le a_i \le n).The sum of n over all test cases doesn't exceed 5 \cdot 10^5.OutputFor each test case, print a single integer — the number of non-empty MEX-correct subsequences of a given array, taken modulo 998244353.ExampleInput
4
3
0 2 1
2
1 0
5
0 0 0 0 0
4
0 1 2 3
Output
4
2
31
7
NoteIn the first example, the valid subsequences are [0], [1], [0,1] and [0,2].In the second example, the valid subsequences are [0] and [1].In the third example, any non-empty subsequence is valid. 
4
3
0 2 1
2
1 0
5
0 0 0 0 0
4
0 1 2 3

4 2 31 7 
['dp', 'math', '*1900']