A bag contains \( N \) balls out of which \( 3 \) balls are white, \( 6 \) balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For \( i = 1, 2, 3 \), let \( W_i, G_i \) and \( B_i \) denote the events that the ball drawn in the \( i^{\text{th}} \) draw is a white ball, green ball, and blue ball, respectively. If the probability \( P(W_1 \cap G_2 \cap B_3) = \frac{2}{5N} \) and the conditional probability \( P(B_3 \mid W_1 \cap G_2) = \frac{2}{9} \), then \( N \) equals ______.
