{"raw_statement":[{"iden":"statement","content":"See PDF statement in attachment.\n\n"},{"iden":"examples","content":"Input1 0 00 0 11 0 00 1 00 1 00 0 1Output0.785398163397Input1 0 00 0 11 0 00 1 00 1 00 0 -1OutputneverInput0 0 01 0 00 1 00 0 10 1 0-1 0 0OutputneverInput1 0 0-1 0 -1-1 0 10 1 00 1 00 0 1Output0.392699081699Input0 0 10 -1 10 1 1-1 0 -1-1 0 00 -1 0Output0.511669644114Input0 -1 0-1 0 00 0 -11 0 00 0 -10 1 0Output0.785398163397"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ s_1, s_2 $ be two palindromic strings over the alphabet $ \\Sigma = \\{a, b, \\dots, z\\} $.  \nLet $ f: \\Sigma \\to \\mathbb{N} $ be the frequency function of the multiset union $ s_1 \\cup s_2 $, i.e., $ f(c) = \\text{count of } c \\text{ in } s_1 + \\text{count of } c \\text{ in } s_2 $.\n\n**Constraints**  \n1. $ |s_1| \\leq 100 $, $ |s_2| \\leq 100 $  \n2. $ s_1 $ and $ s_2 $ are palindromes.  \n\n**Objective**  \nDetermine whether there exists a permutation of the multiset $ s_1 \\cup s_2 $ that forms a palindrome.  \n\nThis is possible if and only if at most one character in $ f $ has an odd frequency.  \n\n$$\n\\boxed{\\text{YES if } \\left| \\left\\{ c \\in \\Sigma \\mid f(c) \\text{ is odd} \\right\\} \\right| \\leq 1 \\text{, otherwise NO}}\n$$","simple_statement":"Given two palindromic strings, can you rearrange all their characters into one palindrome?","has_page_source":false}