Chef And Land Labeling
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ChefsLand can be viewed as a graph consisting of N cities and bidirectional roads. Each pair of cities is directly connected by a road. Recently, Chef came up with following game to make the Number Theory course more interesting for students in country schools.
At the beginning of each lesson, Chef draws ChefsLand as a graph with N vertices corresponding to cities and N(N-1)/2 edges corresponding to roads between them. Then he labels the cities; each city is given a distinct label between 1 and N (inclusive). Next, he labels each edge — the label of the edge between vertices u and v is the common divisor count of lblu and lblv (the number of positive integers which divide both lblu and lblv), where lblu and lblv denote the labels of vertices u and v respectively.
Now, Chef erases the vertex labels, retaining only edge labels in the graph. You, as the number theory student, should find some assignment of labels to vertices which produces a graph with the given edge labels.
- 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 denoting the number of vertices in the graph.
- The following N lines describe the labels of edges. For each valid i, the i-th of these lines contains N space-separated integers Mi1, Mi2, ..., MiN; for each valid j ≠ i, Mij represents the label of the edge connecting vertices i and j.
For each test case, print N lines. For each valid i, the i-th of these lines should contain a single integer — the label of the i-th vertex.
If there are multiple solutions, you may output any one.
- 1 ≤ N ≤ 1000
- for each valid i, Mii = 0
- it's guaranteed that for the given edge labels, at least one possible assignment of labels to vertices exists
Subtask #1 (15 points): sum of N for all test cases ≤ 10
Subtask #2 (85 points): sum of N for all test cases ≤ 1000
Input: 1 4 0 1 1 1 1 0 1 1 1 1 0 2 1 1 2 0 Output: 3 1 2 4
|Tags||feb18, isomorphism, kamranmaharov , medium-hard, number-theory|
|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, PYP3, CLOJ, COB, FS|
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