Arggggggh!

You inherited a treasure map from a long dead ancestor who was a pirate. Instead of a picture with a big X on it, the map is a list of instructions that walks you to the spot where you should start digging.

The first instruction is the starting location, given as two integers $x$ and $y$. Every later instruction is a direction and a distance. N 7 means walk 7 feet north, and SW 6 means walk 6 feet southwest. Follow all of them in order and you end up standing over the digging spot.

Moving north increases $y$ and leaves $x$ unchanged. Moving east increases $x$ and leaves $y$ unchanged. A diagonal move of $d$ feet changes both coordinates by $d/\sqrt{2}$. NE adds $d/\sqrt{2}$ to $x$ and to $y$, SE adds it to $x$ and subtracts it from $y$, SW subtracts it from both, and NW subtracts it from $x$ and adds it to $y$.

Walking the whole route one instruction at a time takes a while, so compute the final location and go straight there.

One more thing: the ancestor was a Pittsburgh Pirate, and the treasure is a pile of old baseballs and a very moldy mitt.

The first line contains one integer $n$ ($1 \le n \le 100$), the number of instructions.

Each of the next $n$ lines contains one instruction. The first instruction is two integers $x$ and $y$ ($0 \le x, y \le 100$), the starting point. Each remaining instruction has the form dir d, where dir is one of N, NE, E, SE, S, SW, W, NW and $d$ ($1 \le d \le 100$) is the distance to walk.

Print the $x$ and $y$ coordinates of the final location on one line, separated by a single space. Round both values to 8 decimal places and always print exactly 8 digits after the decimal point.

Every coordinate is either an integer or an irrational number, so it never lands exactly on a rounding boundary. When a coordinate is zero, print 0.00000000 and not -0.00000000.