D. Sum of XOR Functions
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$998244353$$$.

Input

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 $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^9)$$$.

Output

Print the one integer — the value of $$$\sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) \cdot (r - l + 1)$$$, taken modulo $$$998244353$$$.

Examples
Input
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
Note

In the first example, the answer is equal to $$$f(1, 1) + 2 \cdot f(1, 2) + 3 \cdot f(1, 3) + f(2, 2) + 2 \cdot f(2, 3) + f(3, 3) = $$$ $$$= 1 + 2 \cdot 2 + 3 \cdot 0 + 3 + 2 \cdot 1 + 2 = 12$$$.