While looking at the kitchen fridge, the little boy Tyler noticed magnets with symbols, that can be aligned into a string $s$.

Tyler likes strings, and especially those that are lexicographically smaller than another string, $t$. After playing with magnets on the fridge, he is wondering, how many distinct strings can be composed out of letters of string $s$ by rearranging them, so that the resulting string is lexicographically smaller than the string $t$? Tyler is too young, so he can't answer this question. The alphabet Tyler uses is very large, so for your convenience he has already replaced the same letters in $s$ and $t$ to the same integers, keeping that different letters have been replaced to different integers.

We call a string $x$ lexicographically smaller than a string $y$ if one of the followings conditions is fulfilled:

• There exists such position of symbol $m$ that is presented in both strings, so that before $m$-th symbol the strings are equal, and the $m$-th symbol of string $x$ is smaller than $m$-th symbol of string $y$.
• String $x$ is the prefix of string $y$ and $x \neq y$.

Because the answer can be too large, print it modulo $998\,244\,353$.