In a rectangular array of points, with 5 rows and \(N\) columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through \(N,\) the second row is numbered \(N + 1\) through \(2N,\) and so forth. Five points, \(P_1, P_2, P_3, P_4,\) and \(P_5,\) are selected so that each \(P_i\) is in row \(i.\) Let \(x_i\) be the number associated with \(P_i.\) Now renumber the array consecutively from top to bottom, beginning with the first column. Let \(y_i\) be the number associated with \(P_i\) after the renumbering. It is found that \(x_1 = y_2,\) \(x_2 = y_1,\) \(x_3 = y_4,\) \(x_4 = y_5,\) and \(x_5 = y_3.\) Find the smallest possible value of \(N.\)
(第十九届AIME1 2001 第11题)