## MULTQ3 - Multiples of 3

There are N numbers a[0], a[1] ... a[N - 1]. Initially all are 0. You have to perform two types of operations :

1. Increase the numbers between indices A and B (inclusive) by 1. This is represented by the command "0 A B"
2. Answer how many numbers between indices A and B (inclusive) are divisible by 3. This is represented by the command "1 A B".

### Input

The first line contains two integers, N and Q. Each of the next Q lines are either of the form "0 A B" or "1 A B" as mentioned above.

### Output

Output 1 line for each of the queries of the form "1 A B" containing the required answer for the corresponding query.

### Sample

```Input:
4 7
1 0 3
0 1 2
0 1 3
1 0 0
0 0 3
1 3 3
1 0 3

Output:
4
1
0
2```

### Constraints

1 ≤ N ≤ 100000
1 ≤ Q ≤ 100000
0 ≤ A ≤ B ≤ N - 1

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 fighter_4: 2020-04-25 17:36:58 guys there is nothing tricky in 9th test case, you may have done any small mistake if you are getting WA,, took me 4 hours to debug,,,, but finally AC :D, my 20th. perdedor_9: 2020-04-14 10:16:36 naive solution with optimization,AC in one go aditya15: 2020-04-02 12:23:53 Test cases upto case 9 are simple sum queries without any updates, so even a wrong code may pass cases till 9. Just use Segment Trees + lazy propagation as mentioned below. No need to even use Fast IO shivam_vc: 2020-03-31 10:03:49 got wa on 9th test case .can someone help ? sangmai: 2020-02-21 02:43:05 I constantly get WA in test case 9. Is there anyone with the same issue? Is there any common mistakes in lazy prop that beginners usually make? Edit: It is just a stupid typo. Cost me a day :(( Last edit: 2020-02-21 04:31:32 subodh898: 2019-11-15 06:24:49 segment tree + Lazy +Fast I/O only sourav1996: 2019-09-20 19:47:30 Can it be solved without lazy propagation? rezagoodarzi: 2019-08-08 06:03:48 badihi jat landofkings: 2019-07-28 05:31:57 A good problem to learn lazy propogation. saurabh8522: 2019-07-10 18:50:22 AC in one go !!!!!!!

 Added by: Varun Jalan Date: 2010-09-12 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: NODEJS OBJC VB.NET Resource: own problem