---{"category_name":"easy","problem_code":"CRYCOLR","problem_name":"Crying Colours","problemComponents":{"constraints":"- $1 \\leq T \\leq 1000$\n- $1 \\leq N \\leq 1000$\n- $0 \\leq R_i, G_i, B_i \\leq N$\n- $R_1 + G_1 + B_1 = R_2 + G_2 + B_2 = R_3 + G_3 + B_3 = N$\n- $R_1 + R_2 + R_3 = G_1 + G_2 + G_3 = B_1 + B_2 + B_3 = N$","constraintsState":true,"subtasks":"**Subtask #1 (100 points):** Original constraints\n","subtasksState":true,"inputFormat":"- The first line of input contains a single integer $T$, denoting the number of test cases. The description of $T$ test cases follows.\n- Each test case consists of $4$ lines of input.\n- The first line of each test case contains a single integer $N$, denoting the number of balls of each colour.\n- The $i$-th of the next three lines contains three space-separated integers $R_i, G_i$ and $B_i$ — the number of red, green, and blue balls in the $i$-th box respectively.\n","inputFormatState":true,"outputFormat":"For each test case, output a single line containing one integer — the minimum number of operations required such that the given condition is satisfied.\n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"2\n3\n3 0 0\n0 3 0\n0 0 3\n5\n2 1 2\n1 4 0\n2 0 3","output":"0\n3","explanation":"**Test case $1$:** Initially,\n- The first box has $3$ red balls and none of any other colours\n- The second box has $3$ green balls and none of any other colours\n- The third box has $3$ blue balls and none of any other colours\n\nThe condition is already satisfied, and so no moves are required.\n\n**Test case $2$:** One sequence of moves is as follows:\n- Swap a green ball from the first box with a red ball from the second box.\n- Swap a blue ball from the first box with a red ball from the third box.\n- Once again, swap a blue ball from the first box with a red ball from the third box.\n\nNow the first box has only red balls, the second has only green balls, and the third has only blue ones — as required.\nIt can be verified that no sequence of less than three moves achieves this result.","isDeleted":false}}},"video_editorial_url":"","languages_supported":{"0":"CPP14","1":"C","2":"JAVA","3":"PYTH 3.6","4":"CPP17","5":"PYTH","6":"PYP3","7":"CS2","8":"ADA","9":"PYPY","10":"TEXT","11":"PAS fpc","12":"NODEJS","13":"RUBY","14":"PHP","15":"GO","16":"HASK","17":"TCL","18":"PERL","19":"SCALA","20":"LUA","21":"kotlin","22":"BASH","23":"JS","24":"LISP sbcl","25":"rust","26":"PAS gpc","27":"BF","28":"CLOJ","29":"R","30":"D","31":"CAML","32":"FORT","33":"ASM","34":"swift","35":"FS","36":"WSPC","37":"LISP clisp","38":"SQL","39":"SCM guile","40":"PERL6","41":"ERL","42":"CLPS","43":"ICK","44":"NICE","45":"PRLG","46":"ICON","47":"COB","48":"SCM chicken","49":"PIKE","50":"SCM qobi","51":"ST","52":"SQLQ","53":"NEM"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"munch_01","problem_tester":"","date_added":"11-01-2022","tags":{"0":"jan222","1":"munch_01","2":"simple"},"problem_difficulty_level":"Simple-Easy","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/CRYCOLR","time":{"view_start_date":1642411800,"submit_start_date":1642411800,"visible_start_date":1642411800,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=CRYCOLR","is_proctored":false,"visitedContests":{},"layout":"problem"}---This is an example statement in markdown. This is the statement of the problem [TANDC](https://codechef.com/problems/TANDC) on CodeChef. The main statement starts with the next paragraph. Please make sure to remove this paragraph from your statement before publishing your problem. If your problem doesn't contain Subtasks, you should remove the section subtask too. We are using markdown the syntax of which can be seen [at](https://github.com/showdownjs/showdown/wiki/Showdown's-Markdown-syntax). We request you to not use any HTML tags in the statement, e.g. no p, ul, li, pre, br or b tags. If you face any issue, please contact admins or email us at help@codechef.com.Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$.Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N, 2^N, 3^N, \dot, \text{so on}$. This teaches him exponentiation.Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list and take their difference. These differences then form the new list for the next iteration of the game. Eg, if $N$ was 6, the list proceeds as $[1, 64, 729, 4096 ... ]$ to $[63, 685, 3367 ...]$, and so on $5$ more times.After the subtraction game, Charlie has to correctly tell Tracy the $N$-th element of the list. This number is the *value of the game*.After practice Charlie became an expert in the game. To challenge him more, Tracy will give two numbers $M$ (where $M$ is a prime) and $R$ instead of just a single number $N$, and the game must start from $M_R - 1$ instead of $N$. Since the *value of the game* can now become large, Charlie just have to tell the largest integer $K$ such that $M_K$ divides this number. Since even $K$ can be large, output $K$ modulo 1000000007 ($10^9 + 7$).<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>