D. Sum of XOR Functionstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a of length n consisting of non-negative integers.You have to calculate the value of \sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) \cdot (r - l + 1), where f(l, r) is a_l \oplus a_{l+1} \oplus \dots \oplus a_{r-1} \oplus a_r (the character \oplus denotes bitwise XOR).Since the answer can be very large, print it modulo 998244353.InputThe first line contains one integer n (1 \le n \le 3 \cdot 10^5) — the length of the array a.The second line contains n integers a_1, a_2, \dots, a_n (0 \le a_i \le 10^9).OutputPrint the one integer — the value of \sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) \cdot (r - l + 1), taken modulo 998244353.ExamplesInput
3
1 3 2
Output
12
Input
4
39 68 31 80
Output
1337
Input
7
313539461 779847196 221612534 488613315 633203958 394620685 761188160
Output
257421502
NoteIn the first example, the answer is equal to f(1, 1) + 2 \cdot f(1, 2) + 3 \cdot f(1, 3) + f(2, 2) + 2 \cdot f(2, 3) + f(3, 3) =  = 1 + 2 \cdot 2 + 3 \cdot 0 + 3 + 2 \cdot 1 + 2 = 12.
3
1 3 2

12 
['bitmasks', 'combinatorics', 'divide and conquer', 'dp', 'math', '*1700']