Description
Nick is a mathematician and his speciality is Boolean logic, especially repetition-free functions. The Boolean function is repetition-free if it can be represented as a repetition-free formula. Formula is repetition-free if each variable occurs in the formula only once.
Let us fix the syntax of considered logical formulae:
Variables — letters from ‘a’ to ‘k’;
Parentheses — if E is a formula, then (E) is another;
Negation — ¬E is a formula for any formula E;
Conjunction — E1 ∧ E2 ∧ ⋯ ∧ En;
Disjunction — E1 ∨ E2 ∨ ⋯ ∨ En.
The operations are listed from the highest priority to the lowest.
The problem is to represent given Boolean function by a repetition-free formula.
Input
The only line of input contains the Boolean function represented as a string consisting of characters ‘a’..‘k’, ‘(’, ‘)’, ‘~’, ‘&’ and ‘|’. The last three tokens stand for ¬, ∧ and ∨ respectively. Tokens can be separated by an arbitrary number of spaces. The line contains 1 000 characters at most. The formula in the file is syntactically correct.
Output
The first line of the output file must contain “Yes” if function is repetition-free and “No” otherwise.
In the former case the following line must contain the repetition-free formula for given Boolean function in the same format as in the input file. The line must contain no more than 1 000 characters.
