Beautiful Coordinates

You are given N coordinates. For the i^th coordinate with parameters \(X_i, Y_i, Z_i, Q_i\) and the j^th coordinate with parameters \(X_j, Y_j, Z_j, Q_j\), if they satisfy

\[ X_i - X_j = Y_i - Y_j = Z_i - Z_j = Q_i - Q_j, \]

then the pair of coordinates is called a beautiful coordinate pair.

Your task is to determine, among all beautiful coordinate pairs (with \(i < j\)), the minimum value of \(j-i\) and the maximum value of \(i+j\).

Note: The index of the coordinates is 1-indexed according to their input order.

inputFormat

The first line contains an integer \(N\) \( (N \geq 2)\) representing the number of coordinates.

Each of the following \(N\) lines contains four space-separated integers \(X_i\), \(Y_i\), \(Z_i\), and \(Q_i\) representing the parameters of the i^th coordinate.

outputFormat

Output two space-separated integers: the minimum value of \(j-i\) and the maximum value of \(i+j\) among all beautiful coordinate pairs.

sample

4
1 2 3 4
2 3 4 5
1 1 1 1
2 2 2 2

1 7