SP12609 DIFFV - Different Vectors

You are given set of **N** vectors, each vector consists of **K** integers. Vector ex equals ey **iff** there exist function bijection **f** and integer **r**, such that ex\[i\] = f( ey\[(i+r)%K\] ), for each i in range \[0, K> Eg. (1, 2, 2, 3) == (22, 3, 4, 22), with r=2 and f(22)=2, f(3)=3 and f(4)=1. But (22,3,22,4) is not equal to (1, 2, 2, 3). How many different vectors are there in set of N given vectors ? Constraints : n

First number contains T (T

Output one number, number of different vectors. ``` Input:2 3 4 22 3 4 22 1 2 2 3 22 3 22 4 5 5 3 3 3 0 3 8 4 4 4 0 1 1 1 1 1 1 1 8 6 1 1 3 3 3 5 ``` **Output:** `2` `3`