D. Sum of XOR Functions
bitmasks; combinatorics; divide and conquer; dp; math
You 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 \(998244353\).
The 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 \(a_1, a_2, \dots, a_n\) (\(0 \le a_i \le 10^9)\).
Print the one integer — the value of \(\sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) \cdot (r - l + 1)\), taken modulo \(998244353\).
In the first example, the answer is equal to \(f(1, 1) + 2 \cdot f(1, 2) + 3 \cdot f(1, 3) + f(2, 2) + 2 \cdot f(2, 3) + f(3, 3) = \) \(= 1 + 2 \cdot 2 + 3 \cdot 0 + 3 + 2 \cdot 1 + 2 = 12\).