Primes triangle is a triangle that contain all prime numbers.

          2
        3   5
      7   11  13
    17  19  23  29
  ... ... ...

Your task is very easy given an integer from 1 to 10⁹ prints its place in the primes triangle.

Input

in the first line integer 1 ≤ T ≤ 10⁴, followed by T lines each line contain integer 1 ≤ n ≤ 10⁹.

Output

One line contain pair of integers i and j, where i is the row number and j is the column number, 1 based. Or -1 if n is not found in the primes triangle.

Example

Input:
3
3
23
4
Output:
2 1
4 3
-1

if you find time limit is small, you can solve the tutorial version here: www.spoj.com/problems/PTR22/