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)