IZhO 2009 Problem 6

In a checked $17\times 17$ table, $n$ squares are colored in black. We call a line any of rows, columns, or any of two diagonals of the table. In one step, if at least $6$ of the squares in some line are black, then one can paint all the squares of this line in black. Find the minimal value of $n$ such that for some initial arrangement of $n$ black squares one can paint all squares of the table in black in some steps.