CF870D Something with XOR Queries

This is an interactive problem. Jury has hidden a permutation $ p $ of integers from $ 0 $ to $ n-1 $ . You know only the length $ n $ . Remind that in permutation all integers are distinct. Let $ b $ be the inverse permutation for $ p $ , i.e. $ p_{bi}=i $ for all $ i $ . The only thing you can do is to ask xor of elements $ p_{i} $ and $ b_{j} $ , printing two indices $ i $ and $ j $ (not necessarily distinct). As a result of the query with indices $ i $ and $ j $ you'll get the value , where  denotes the xor operation. You can find the description of xor operation in notes. Note that some permutations can remain indistinguishable from the hidden one, even if you make all possible $ n^{2} $ queries. You have to compute the number of permutations indistinguishable from the hidden one, and print one of such permutations, making no more than $ 2n $ queries. The hidden permutation does not depend on your queries.

The first line contains single integer $ n $ ( $ 1

When your program is ready to print the answer, print three lines. In the first line print "!". In the second line print single integer $ answers_cnt $ — the number of permutations indistinguishable from the hidden one, including the hidden one. In the third line print $ n $ integers $ p_{0},p_{1},...,p_{n-1} $ ( $ 0

xor operation, or bitwise exclusive OR, is an operation performed over two integers, in which the $ i $ -th digit in binary representation of the result is equal to $ 1 $ if and only if exactly one of the two integers has the $ i $ -th digit in binary representation equal to $ 1 $ . For more information, see [here](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). In the first example $ p=[0,1,2] $ , thus $ b=[0,1,2] $ , the values  are correct for the given $ i,j $ . There are no other permutations that give the same answers for the given queries. The answers for the queries are: - , - , - , - , - , - . In the second example $ p=[3,1,2,0] $ , and $ b=[3,1,2,0] $ , the values  match for all pairs $ i,j $ . But there is one more suitable permutation $ p=[0,2,1,3] $ , $ b=[0,2,1,3] $ that matches all $ n^{2} $ possible queries as well. All other permutations do not match even the shown queries.