A16194. Sum of XOR Functions

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) = $ $= 1 + 2 \cdot 2 + 3 \cdot 0 + 3 + 2 \cdot 1 + 2 = 12$ .