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Lowbit

Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1298    Accepted Submission(s): 295


Problem Description
Lucida has a sequence of $n$ integers $a_1, a_2, \dots, a_n$. He asks you to perform two types of operations for him, which are described as follows:


  • $\texttt{1 L R}$, add $lowbit(a_i)$ to each $a_i$ in the interval $[L, R]$.

  • $\texttt{2 L R}$, query the sum of the numbers in the interval $[L, R]$.


$lowbit(x)$ is defined as the largest power of 2 that divides $x$.
For example, lowbit(4)=4, lowbit(5)=1. Specially, lowbit(0)=0.

Lucida wants you to give the answer modulo $998244353$ for each of his queries.
 

Input
This problem contains multiple test cases.

The first line contains a single integer $T$ ($1\leq T \leq 20$) indicating the number of test cases.

For each case, the first line contains an integer $n$ ($1 \leq n \leq 10^5$), the length of the sequence.

The next line contains $n$ integers $a_i$ ($1 \leq a_i < 998244353$) separated by spaces, representing the sequence.

The next line contains an integer $m$ ($1 \leq m \leq 10^5$), the number of operations.

The next $m$ lines, each line contains 3 integers $op, L, R$ ($1 \leq op \leq 2$, $1 \leq L \leq R \leq n$), represents one operation. The specific meaning is described above.
 

Output
For each query, output a line contains the answer modulo $998244353$.
 

Sample Input
1 5 1 2 3 4 5 5 2 2 4 1 1 3 2 2 4 1 1 5 2 4 5
 

Sample Output
9 12 14
 

Source
 

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