Problem Description

    Today is Yukari's n-th 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 17-year-old girl.

    To make the birthday cake look more beautiful, Ran and Chen decide to place them like r ≥ 1 concentric circles. They place ki candles equidistantly on the i-th 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.

    Input

    There are about 10,000 test cases. Process to the end of file.

    Each test consists of only an integer 18 ≤ n ≤ 1012.

    Output

    For each test case, output r and k.

    Sample Input

    18

    111

    1111

    Sample Output

    1 17

    2 10

    3 10

    Source

    2012 Asia ChangChun Regional Contest