The 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 10⁸ print its place in the primes triangle.

Input

In the first line integer 1 ≤ T ≤ 10⁵, followed by T lines each line contain integer 1 ≤ n ≤ 10⁸.

Output

One line contain pair of integers i, j, where i is the row number and j is the column number, 1 base. 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 here you can solve the tutorial version here: PTRI2.