PTR22 - primes triangle (II)

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primes triangle is a triangle that contain all prime numbers .

          2

         3 5

      7 11 13

   17 19 23 29

  .........

you task is very easy given an integer from 1 to 10^8 prints its place in the primes triangle .

you task is very easy given an integer from 1 to 10^9 prints its place in the primes triangle .

 

Input

in the first line integer 1<= T <= 10^4  , followed by T lines each line contain integer 1 <= n <= 10^9 .

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 not exist in the primes triangle .

Example

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


Added by:abdou_93
Date:2013-06-08
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:tutorial version of http://www.spoj.com/problems/PTR2/