AT_arc211_b [ARC211B] Three Sequences

You are given a triple of positive integers $ (X,Y,Z) $ such that $ X\leq Y\leq Z $ . Output one triple of sequences of non-negative integers $ (S_1,S_2,S_3) $ that satisfies all of the following conditions: - The lengths of $ S_1,S_2,S_3 $ are each between $ 1 $ and $ 1000 $ , inclusive. - The length of a longest sequence that is both a contiguous subsequence of $ S_1 $ and a contiguous subsequence of $ S_2 $ is $ X $ . - The length of a longest sequence that is both a contiguous subsequence of $ S_1 $ and a contiguous subsequence of $ S_3 $ is $ Y $ . - The length of a longest sequence that is both a contiguous subsequence of $ S_2 $ and a contiguous subsequence of $ S_3 $ is $ Z $ . - $ \max(\max(S_1),\max(S_2),\max(S_3)) $ is minimized among all triples satisfying the above four conditions. It can be proved that under the constraints of this problem, a triple $ (S_1,S_2,S_3) $ satisfying the conditions always exists. If there are multiple such triples, you may output any of them.

The input is given from Standard Input in the following format: > $ X $ $ Y $ $ Z $

Output three lines. The first line should contain $ S_1 $ in the following format, where $ |S_1| $ denotes the length of $ S_1 $ and $ S_{1,i} $ denotes the $ i $ -th element of $ S_1 $ : > $ |S_1| $ $ S_{1,1} $ $ S_{1,2} $ $ \dots $ $ S_{1,|S_1|} $ The second line should contain $ S_2 $ and the third line should contain $ S_3 $ , both in the same format as $ S_1 $ . If there are multiple solutions, you may output any of them.

### Sample Explanation 1 It can be verified that $ S_1=(1,1,0,0,1,0,1,0,1,1),S_2=(1,1,0,1,0,0,1,1),S_3=(1,0,0,0,1,1,0,1,0,1,0) $ satisfies the conditions as follows: - The lengths of $ S_1,S_2,S_3 $ are $ 10,8,11 $ , respectively, all of which are between $ 1 $ and $ 1000 $ , inclusive. - The longest sequences that are both a contiguous subsequence of $ S_1 $ and a contiguous subsequence of $ S_2 $ are $ (1,0,0,1) $ and $ (1,0,1,0) $ , with length $ X=4 $ . - The longest sequences that are both a contiguous subsequence of $ S_1 $ and a contiguous subsequence of $ S_3 $ are $ (1,0,1,0,1) $ and $ (0,1,0,1,0) $ , with length $ Y=5 $ . - The longest sequence that is both a contiguous subsequence of $ S_2 $ and a contiguous subsequence of $ S_3 $ is $ (1,1,0,1,0) $ , with length $ Z=5 $ . - $ \max(\max(S_1),\max(S_2),\max(S_3))=1 $ , and it can be shown that it is impossible to satisfy the above four conditions with $ \max(\max(S_1),\max(S_2),\max(S_3))=0 $ , so this is minimal. ### Constraints - $ 1\leq X\leq Y\leq Z\leq 100 $ - All input values are integers.