13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5e8,

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 $$$998244353$$$.

Note

In the first example, the answer is equal to $$$f(1, 1) + 2 \cdot f(1, 2) + 3 \c

Sum of XOR Functions

Examples