{"raw_statement":[{"iden":"problem statement","content":"Aoki is playing with a sequence of numbers $a_{1}, a_{2}, ..., a_{N}$. Every second, he performs the following operation :\n\n*   Choose a positive integer $k$. For each element of the sequence $v$, Aoki may choose to replace $v$ with its remainder when divided by $k$, or do nothing with $v$. The cost of this operation is $2^{k}$ (regardless of how many elements he changes).\n\nAoki wants to turn the sequence into $b_{1}, b_{2}, ..., b_{N}$ (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 50$\n*   $0 \\leq a_{i}, b_{i} \\leq 50$\n*   All values in the input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_{1}$ $a_{2}$ $...$ $a_{N}$\n$b_{1}$ $b_{2}$ $...$ $b_{N}$"},{"iden":"sample input 1","content":"3\n19 10 14\n0 3 4"},{"iden":"sample output 1","content":"160\n\nHere's a possible sequence of operations :\n\n*   Choose $k = 7$. Replace $19$ with $5$, $10$ with $3$ and do nothing to $14$. The sequence is now $5, 3, 14$.\n    \n*   Choose $k = 5$. Replace $5$ with $0$, do nothing to $3$ and replace $14$ with $4$. The sequence is now $0, 3, 4$.\n    \n\nThe total cost is $2^{7} + 2^{5} = 160$."},{"iden":"sample input 2","content":"3\n19 15 14\n0 0 0"},{"iden":"sample output 2","content":"2\n\nAoki can just choose $k = 1$ and turn everything into $0$. The cost is $2^{1} = 2$."},{"iden":"sample input 3","content":"2\n8 13\n5 13"},{"iden":"sample output 3","content":"\\-1\n\nThe task is impossible because we can never turn $8$ into $5$ using the given operation."},{"iden":"sample input 4","content":"4\n2 0 1 8\n2 0 1 8"},{"iden":"sample output 4","content":"0\n\nAoki doesn't need to do anything here. The cost is $0$."},{"iden":"sample input 5","content":"1\n50\n13"},{"iden":"sample output 5","content":"137438953472\n\nBeware of overflow issues."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}