Given a string, find the rank of the string amongst its permutations sorted lexicographically.
Note that the characters might be repeated. If the characters are repeated, we need to look at the rank in unique permutations.
Look at the example for more details.
The answer might not fit in an integer, so return your answer % 1000003
Assume the number of characters in string < 1000003 1<=n <= 100
Input format:
In the first line take the input n. Next n lines contain the string.
Output Format:
Print the rank for each string in each line.
Example :
Input :
1
'aba'
Output :
2
The order permutations with letters 'a', 'a', and 'b' :
aab
aba
baa