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HS09APR - Approximation

Given coordinates (Xi, Yi ) of N points of the plane, calculate the coefficients A, B, C, and D of the polynomial W(X)=A*X3 + B*X2 + C*X + D, such that value of the function
F(X)=(Y1 – W(X1))2 + (Y2 – W(X2))2 + … + (YN – W(XN))2 is minimized.

Input

The first line of input consists of a single positive integer N (5<=N<=50), representing the number of points. Each of the following N lines contains the coordinates Xi, Yi (-1000<= Xi, Yi <=1000), given with two digits precision after the decimal dot.

Output

Output a single line containing the coefficients A, B, C, D of the sought polynomial, separated by spaces. Print all numbers with two digits precision after the decimal dot.

Example

Input:

9
     -4.00    -74.00
     -3.00    -26.00
     -2.00      0.00
     -1.00     10.00
      0.00     10.00
      1.00      6.00
      2.00      4.00
      3.00     10.00
      4.00     30.00
Output:
1.00 -2.00 -3.00 10.00

Scoring

For solving this problem you will score 10 points.


Added by:Adam Dzedzej
Date:2009-09-15
Time limit:0.200s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:ADA95 ASM32 BASH BF C CSHARP CPP C99 CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PAS-GPC PAS-FPC PERL PHP PIKE PRLG-swi PYTHON RUBY SCM guile SCM qobi ST TCL TEXT WHITESPACE
Resource:Thanks to Talent Association (www.talent.edu.pl)

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