High School Programming League Problems Archive

Given coordinates (X_i, Y_i ) 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 + … + (Y_N – W(X_N))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 X_i, Y_i (-1000<= X_i, Y_i <=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.