The MEX of a sequence of non-negative integers (s_1, s_2, \dots, s_n) is the smallest non-negative integer that does not appear in this sequence. Given an array (a_1, a_2, \dots, a_n), where each element is an integer from (-1) to (n). For each (i) from (1) to (n), calculate (f(a_1, a_2, \dots, a_i)), where (f(s)) for an array (s) is defined as follows: consider all distinct arrays (s') that can be obtained from the array (s) by replacing all elements equal to (-1) with integers from (0) to (n); (f(s)) is the sum of the MEX of all such arrays (s'). The first line contains a single integer (n) ((1 \le n \le 2 \cdot 10^5)). The second line contains (n) integers (a_1, a_2, \dots, a_n) ((-1 \le a_i \le n)). An additional constraint on the input: the array (a) contains no more than (300) elements equal to (-1). For each (i) from (1) to (n), output a single integer — (f(a_1, a_2, \dots, a_i)), taken modulo (998244353). Consider (i=3) in the first example. We need to calculate (f(-1, 1, -1)). There are (36) different arrays that can be obtained by replacing each element (-1) with an integer from (0) to (5). For (25) of them (those that do not contain (0)), the MEX is (0). Let's consider the remaining (11): The MEX of the array (0, 1, 0) is (2); The MEX of the array (0, 1, 1) is (2); The MEX of the array (0, 1, 2) is (3); The MEX of the array (0, 1, 3) is (2); The MEX of the array (0, 1, 4) is (2); The MEX of the array (0, 1, 5) is (2); The MEX of the array (1, 1, 0) is (2); The MEX of the array (2, 1, 0) is (3); The MEX of the array (3, 1, 0) is (2); The MEX of the array (4, 1, 0) is (2); The MEX of the array (5, 1, 0) is (2). The sum of these values is (24). If we consider (i=4),