After his leave from DMOJ, Wesley is very angry and demands you to construct an array 
~x~ of length 
~N~ consisting of positive integers such that each element 
~x_i~ satisfies the following requirements:
- There are
~a_i~ elements before index 
~i~ that are strictly smaller than ~x_i~
- There are
~b_i~ elements after index ~i~ that are strictly smaller than ~x_i~
- There are
~c_i~ elements before index ~i~ that are strictly greater than ~x_i~
- There are
~d_i~ elements after index ~i~ that are strictly greater than ~x_i~
Luckily, Wesley is a kind person and will allow for your array to violate at most 
~1~ of the requirements above. In particular, you can pick an index ~i~ and modify exactly one of ~a_i~, ~b_i~, ~c_i~ and ~d_i~. In exchange however, he requests that your array is the lexicographically least one (it must be the lexicographically least array that violates at most ~1~ requirement).
Note: We say that array ~x~ is lexicographically less than array 
~y~ if 
~x \ne y~ and at the smallest index ~i~ where ~x_i~ and 
~y_i~ differ, 
~x_i < y_i~.
Constraints
~2 \le N \le 2 \times 10^5~
~0 \le a_i,b_i,c_i,d_i~
~a_i+c_i < i~
~b_i+d_i \le N-i~
Subtask 1 [12%]
~N \le 7~
Subtask 2 [23%]
~b_i, c_i = 0~
Subtask 3 [43%]
~N \le 5 \times 10^3~
Subtask 4 [22%]
No additional constraints.
Input Specification
The first line contains a single integer ~N~.
The next line contains ~N~ integers 
~a_1, \ldots, a_N~.
The next line contains ~N~ integers 
~b_1, \ldots, b_N~.
The next line contains ~N~ integers 
~c_1, \ldots, c_N~.
The next line contains ~N~ integers 
~d_1, \ldots, d_N~.
Output Specification
If no such array exists, output -1.
Otherwise, output the elements of the lexicographically least array on a single line.
Sample Input
5
0 0 2 2 1
1 0 2 1 0
0 1 0 1 2
2 1 0 0 0
Sample Output
2 1 4 3 2
Explanation for Sample
The array above satisfies all the requirements except for 
~d_2~. It can be shown that this is the lexicographically least array that violates at most one requirement.
Comments
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