Let us define a complexity of an integer as the number of its divisors. Your task is to find the most complex integer in range from 1 to n. If there are many such integers, you should find the minimal one.
Input
The first line contains the number of testcases t (1 ≤ t ≤ 100). The ith of the following t lines contains one integer n_{i} (1 ≤ n_{i} ≤ 10^{18}).
Output
For each testcase output the answer on a separate line. The ith line should contain the most complex integer in range from 1 to n_{i} and its complexity, separated with space.
Sample
input  output 

5
1
10
100
1000
10000
 1 1
6 4
60 12
840 32
7560 64

Problem Author: Petr Lezhankin
Problem Source: Ufa SATU Contest. Petrozavodsk Summer Session, August 2009