
ZOJ Problem Set  3665
Today is Yukari's nth birthday. Ran and Chen hold a celebration party for her. Now comes the most important part, birthday cake! But it's a big challenge for them to place n candles on the top of the cake. As Yukari has lived for such a long long time. Though she herself insists that she is a 17yearold girl. To make the birthday cake look more beautiful, Ran and Chen decide to place them like r ≥ 1 concentric circles. They place k^{i} candles equidistantly on the ith circle, where k ≥ 2, 1 ≤ i ≤ r. And it's optional to place at most one candle at the center of the cake. In case that there are a lot of different pairs of r and k satisfying these restrictions, they want to minimize r × k. If there is still a tie, minimize r. InputThere are about 10,000 test cases. Process to the end of file. Each test consists of only an integer 18 ≤ n ≤ 10^{12}. OutputFor each test case, output r and k. Sample Input18 111 1111 Sample Output1 17 2 10 3 10 Author: WU, Zejun Contest: The 2012 ACMICPC Asia Changchun Regional Contest 