Marginal Distributions Plus Regression With jointplot

Calder Engineering's summary figure puts the paired readings in the middle, with a fitted line through them, and each measurement's own distribution along the top and the right-hand side -- so a lopsided or double-peaked measurement cannot hide inside the cloud. Underneath the figure, the sheet states in writing how tightly the two move together.

Task: Print the correlation between x and y.

Input

The first line holds one integer n, the number of readings, where 2 <= n <= 1000. Then come n lines, each holding a reading's x and y separated by a single space. Neither column holds the same value throughout.

Output

One line holding the Pearson correlation of x and y -- the ordinary straight-line one, running from -1 for a perfect fall through 0 for no straight-line link to +1 for a perfect rise -- rounded to 2 decimal places.

Example:

Input:
4
1 2
2 4
3 5
4 9

Output:
0.96