Pogo Stick

You just got a pogo stick. You stand on it and jump: the first jump moves you 1 unit, the second jump moves you 2 units, the third jump moves you 3 units, and every later jump is one unit longer than the one before it.

Each jump goes in exactly one of four directions: north ($y$ increases), south ($y$ decreases), east ($x$ increases), or west ($x$ decreases). You cannot skip a jump and you cannot shorten one.

You start at $(0, 0)$ on an infinite plane and want to land exactly on $(X, Y)$. The target is never $(0, 0)$, and it can always be reached.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains two integers $X$ and $Y$ separated by a single space, the coordinates of the target.

• $1 \le T \le 50$
• $0 \le |X|, |Y| \le 100$
• $(X, Y) \ne (0, 0)$

For each test case print one line in the form Case #x: y, where $x$ is the case number starting from 1 and $y$ is a string of directions. Write N for north, S for south, E for east, and W for west. The $i$-th character is the direction of the $i$-th jump, which covers $i$ units.

Use the smallest possible number of jumps. When several shortest sequences land on $(X, Y)$, print the alphabetically smallest of them, comparing letters in the order E < N < S < W.