CF548A Mike and Fax

While Mike was walking in the subway, all the stuff in his back-bag dropped on the ground. There were several fax messages among them. He concatenated these strings in some order and now he has string $ s $ . He is not sure if this is his own back-bag or someone else's. He remembered that there were exactly $ k $ messages in his own bag, each was a palindrome string and all those strings had the same length. He asked you to help him and tell him if he has worn his own back-bag. Check if the given string $ s $ is a concatenation of $ k $ palindromes of the same length.

The first line of input contains string $ s $ containing lowercase English letters ( $ 1

Print "YES"(without quotes) if he has worn his own back-bag or "NO"(without quotes) otherwise.

Palindrome is a string reading the same forward and backward. In the second sample, the faxes in his back-bag can be "saddas" and "tavvat".