There are squares whose digits can be rearranged to make another squares. Lets call them S2S numbers.

for example: 144 → 441

Input

Single line containing two integers X Y (Xth, Yth term in the list of S2S numbers). Xth, Yth term<=10^12.

Output

Print all the numbers from Xth to Yth term of S2S numbers list (both inclusive).

Example

Input:
1 3
Output:
144
169
196

(Source Code Limit= 500B)
Note: 1 → 100 → 1 or other similar numbers are NOT S2S numbers (example 9 → 900 → 9)
Try Tutorial at http://www.spoj.com/problems/SQ2SQ2/