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## Goal

Futoshiki is a Japanese numeric logic puzzle similar to the more popular Sudoku.
See https://en.wikipedia.org/wiki/Futoshiki
Like in Sudoku, in a Futoshiki of size n every row and every column must contain every number from 1 to n.
Unlike Sudoku there may be greater than / less than relations between cells.

For a n×n Futoshiki the input will be 2n-1 lines of digits 0..n (0 meaning empty), and either spaces or inequality constraints ^ v < > separating the digits of length 2n-1.

^ meaning the cell below the symbol has a higher value than the one above the symbol and so on.

Example: A 2×2 Futoshiki
0>0v ^0<0
having the solution:
2112
Input
Line 1: number size of lines to read
Next size lines:
even numbered lines: string of length n alternating between a number 0..n and a space or < or >.
odd numbered lines: string of length n containing spaces and v or ^ on even numbered positions and spaces on off numbered positions.
Output
n lines: n digits for each row of the solved board
(for n such that size = 2×n - 1)
Constraints
1 ≤ size ≤ 13
Example
Input
3
1 0

0 0
Output
12
21

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