问题 I: The Yakumo Family

Ran feels boring at home, and wants to propose a math problem with Yukari and Chen!
So here's The Yakumo Family Problem:
Given an integer array $a$, try to calculate the value of the following equation modulo $998244353$:

∑1≤l1≤r1<l2≤r2<l3≤r3≤nXOR(l1,r1)×XOR(l2,r2)×XOR(l3,r3)\sum_{1\le l_1\le r_1<l_2\le r_2<l_3\le r_3\le n}XOR(l_1, r_1)\times XOR(l_2, r_2)\times XOR(l_3, r_3)∑1≤l1≤r1<l2≤r2<l3≤r3≤nXOR(l1,r1)×XOR(l2,r2)×XOR(l3,r3)

XOR(l,r)XOR(l,r)XOR(l,r) means al⊕al+1⊕al+2⋯⊕ara_l\oplus a_{l+1}\oplus a_{l+2}\dots\oplus a_ral⊕al+1⊕al+2⋯⊕ar, and $\oplus$ means bitwise XOR.

The first line contains one integer $n$ (3≤n≤2×1053\le n\le 2\times 10^53≤n≤2×105), which means the length of $a$.
The next line contains $n$ integers, the $i$-th integer means the value of aia_iai (0≤ai≤1090\le a_i\le 10^90≤ai≤109).

One integer, means the value of the equation modulo $998244353$.

3
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