Creating Strings

Given a string, your task is to generate all different strings that can be created using its characters.

Input

The only input line has a string of length n. Each character is between a–z.

Output

First print an integer k: the number of strings. Then print k lines: the strings in alphabetical order.

Constraints

$1 \le n \le 8$

Example

Input

aabac

Output

20
aaabc
aaacb
aabac
aabca
aacab
aacba
abaac
abaca
abcaa
acaab
acaba
acbaa
baaac
baaca
bacaa
bcaaa
caaab
caaba
cabaa
cbaaa