Maximum Score

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You are given N integer sequences A_{1}, A_{2}, ..., A_{N}. Each of these sequences contains N elements. You should pick N elements, one from each sequence; let's denote the element picked from sequence A_{i} by E_{i}. For each i (2 ≤ i ≤ N), E_{i} should be strictly greater than E_{i1}.
Compute the maximum possible value of E_{1} + E_{2} + ... + E_{N}. If it's impossible to pick the elements E_{1}, E_{2}, ..., E_{N}, print 1 instead.
Input
 The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
 The first line of each test case contains a single integer N.
 N lines follow. For each valid i, the ith of these lines contains N spaceseparated integers A_{i1}, A_{i2}, ..., A_{iN} denoting the elements of the sequence A_{i}.
Output
For each test case, print a single line containing one integer — the maximum sum of picked elements.
Constraints
 1 ≤ T ≤ 10
 1 ≤ N ≤ 700
 1 ≤ sum of N in all testcases ≤ 3700
 1 ≤ A_{ij} ≤ 10^{9} for each valid i, j
Subtasks
Subtask #1 (18 points): 1 ≤ A_{ij} ≤ N for each valid i, j
Subtask #2 (82 points): original constraints
Example
Input: 1 3 1 2 3 4 5 6 7 8 9 Output: 18
Explanation
Example case 1: To maximise the score, pick 3 from the first row, 6 from the second row and 9 from the third row. The resulting sum is E_{1}+E_{2}+E_{3} = 3+6+9 = 18.
Author:  hruday968 
Editorial  https://discuss.codechef.com/problems/MAXSC 
Tags  cakewalk, hruday968, hruday968, jan18 
Date Added:  28122017 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, FS 
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