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Rahul's Lucky ID Number
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Rahul will be assigned his college id number soon. 

He considers the id number to be lucky for himself if it can be expressed in the form-

                                 \(2^x+2^y\) ( \(x \neq y , x \geq 0 , y \geq 0\)). 

He plays a game in which he decides to make N guesses for his id number and wants you to perform some queries on his guesses, which fall in either of the two categories- 

Category 1:

Given p,q change his p-th guess to q 

Category 2:

Given p,q find how many lucky id numbers exist from his p-th guess to q-th guess.(both inclusive).

If p > q then print 0.

Input Format: 

The first line contains T, the number of testcases. 

For each testcase,

 A separate line contains N, the number of guesses Rahul makes.

The next line contains N space separated integers denoting the guesses for his id number. 

The next line contains Q, the number of queries. 

Each query contains three space separated integers m, p, q.  

m denotes the category of the query (1 or 2) and p, q are the parameters to be used by each of the query. 

Output Format:

Answer category 2 of the query by printing the required integer on a new line. 

For Instance- Using 1-based indexing, category 2 asks you to count the number of lucky guesses among the guess at p-th index, guess at (p+1)-th index and so on till the guess at q-th index.

If m=2 and p > q then print 0.

Constraints: 

0<=Rahul’s Guess(id number)<= (10^9+1) 

0 < T <= 2 

0 < N <= 10^5 

0 < Q <= 10^5 

m is either 1 or 2 

1 <= p <= N 

0 <= q <= (10^9+1) (if m is 1) 

1 <= q<= N (if m is 2) 

SAMPLE INPUT
1
2
3 1
4
1 2 6
2 1 2
1 1 2
2 1 1
SAMPLE OUTPUT
2
0
Explanation

(T=1) 

The N = 2 guesses are as below: 

1st guess 3 

2nd guess 1 

Q=4 

1st query-(category 1)

p=2 q=6 

Change p th guess i.e 2nd guess to 6 

Therefore, 2nd guess becomes 6 

2nd query-(category 2)

p=1 q=2 

We find number of lucky id numbers from 1st guess to 2nd guess (both inclusive)

1st guess is 3=2^1+2^0 (lucky) 

2nd guess is 6=2^1+2^2 (lucky) 

So, we print 2 as the answer to this query. 

3rd query-(category 1)

Similarly, this query makes 1st guess as 2 

and  

4th query-(category 2)

 we find the number of lucky guesses from 1st guess to 1st guess- 

1st guess is 2 (can't be expressed as 2^x+2^y where x!=y,x>=0,y>=0) 

So this guess is unlucky and we print 0. 

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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