## Problem F. Function with constraints ≡

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 Author: A. Baranov Time limit: 1 sec Input file: Standard input Memory limit: 256 Mb Output file: Standard output

### Statement

Let's consider a function of the following form: F(X, Y) = AB ⋅ X + CD ⋅ Y.

The task is to find integer values for A, B, C and D, such that for a given set of points (Xi, Yi)
the specified function satisfies pre-determined conditions:
RoundDawn(F(Xi, Yi)) = Zi or RoundUp(F(Xi, Yi)) = Zi,
where RoundDawn() и RoundUp() — denote rounding down and rounding up, respectively.

### Input format

The input begins with the number N, followed by N conditions, each written in the following format.

First, the operation sign is indicated: '>' for RoundDawn or '<' for RoundUp.

Then, three integers follow: Xi, Yi, Zi.

### Output format

If the problem has a solution, the output contains the number 1,
followed by the found values of A, B, C and D.

If there is more than one solution, any of them can be output.

If there is no solution, the output is the single number 0.

### Constraints

All input values are integers.

− 40 ≤ (Xi, Yi, Zi) ≤ 40, 0 < N ≤ 2000

### Sample tests

No. Standard input Standard output
1
4

> -2 -5 -6
<  3  7  8
> -1  1  1
<  4 -3 -5

1
-16 37
93 74

2
4

> -3 -1  1
<  5 -3 -6
>  7  4  1
<  2 -1 -3

0


0.093s 0.008s 13