2001 AIME I Problem 11

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 2 N, 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 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.