MATSUM  Matrix Summation
A N × N matrix is filled with numbers. BuggyD is analyzing the matrix, and he wants the sum of certain submatrices every now and then, so he wants a system where he can get his results from a query. Also, the matrix is dynamic, and the value of any cell can be changed with a command in such a system.
Assume that initially, all the cells of the matrix are filled with 0. Design such a system for BuggyD. Read the input format for further details.
Input
The first line of the input contains an integer t, the number of test cases. t test cases follow.
The first line of each test case contains a single integer N (1 <= N <= 1024), denoting the size of the matrix.
A list of commands follows, which will be in one of the following three formats (quotes are for clarity):
 "SET x y num"  Set the value at cell (x, y) to num (0 <= x, y < N).
 "SUM x1 y1 x2 y2"  Find and print the sum of the values in the rectangle from (x1, y1) to (x2, y2), inclusive. You may assume that x1 <= x2 and y1 <= y2, and that the result will fit in a signed 32bit integer.
 "END"  Indicates the end of the test case.
Output
For each test case, output one line for the answer to each "SUM" command. Print a blank line after each test case.
Example
Input: 1 4 SET 0 0 1 SUM 0 0 3 3 SET 2 2 12 SUM 2 2 2 2 SUM 2 2 3 3 SUM 0 0 2 2 END Output: 1 12 12 13
hide comments
cake_is_a_lie:
20170228 17:24:28
cin/cout (optimized to avoid flushes); bit2d<int> 0.30s; bit2d<long long> 0.33s


rraj001:
20161211 10:32:38
Nice problem to learn 2D BIT


lt:
20161128 17:10:05
2dSegment Tree with most optimizations => TLE


Chandan Kumar Rai:
20161109 05:40:09
In java , Bit2d give TLE .. any suggestions for AC 

haozx1997:
20160807 14:08:14
Hi guys ......if you got a Runtime error(SIGSEGV),change all the long long to int . 

Mahtab:
20160709 17:07:55
can any one give some test cases , I am getting error(SIGSEGV) .


narutorocks:
20160615 18:37:24
NICE QUESTION TO LEARN 2D BIT 

vsp4:
20160604 07:10:11
Damn Its 1024**** Costed me few WA. Int works too :) 

Opu:
20160406 10:52:46
I used long long and got ac and took .69s. @Whatever. 

:.Mohib.::
20160224 13:41:25
Awesome question...!! 
Added by:  Matthew Reeder 
Date:  20061029 
Time limit:  1.029s 
Source limit:  30000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  AlKhawarizm 2006 