{"raw_statement":[{"iden":"statement","content":"Your task for this problem is to take the three side lengths of a triangle and to determine if these side lengths could create a \"valid\" triangle. A triangle is considered valid if the addition of any two side lengths is less than the length of the other side, in other words, the following must evaluate to true: a+b>c, a+c>b, b+c>a. \n\nThe first line contains three space separated integers that correspond to the lengths of sides a, b, and c respectively.\n\nOutput either \"VALID\" or \"INVALID\" depending on if the provided side lengths create a valid or invalid triangle.\n\n"},{"iden":"input","content":"The first line contains three space separated integers that correspond to the lengths of sides a, b, and c respectively."},{"iden":"output","content":"Output either \"VALID\" or \"INVALID\" depending on if the provided side lengths create a valid or invalid triangle."},{"iden":"examples","content":"Input1 5 1\nOutputINVALID\nInput4 5 6\nOutputVALID\n"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ a, b, c \\in \\mathbb{R}^+ $ be the side lengths of a triangle.\n\n**Constraints**  \nNone beyond positivity (implied by context).\n\n**Objective**  \nDetermine whether:  \n$$ a + b > c \\quad \\land \\quad a + c > b \\quad \\land \\quad b + c > a $$  \nIf true, output \"VALID\"; otherwise, output \"INVALID\".","simple_statement":"Given three side lengths, check if they can form a valid triangle. A triangle is valid if the sum of any two sides is greater than the third side. Print \"VALID\" if yes, \"INVALID\" if no.","has_page_source":false}