Joy's Territory

You live in a city shaped like a grid of roads. Many roads run very far in the north to south direction, and many other roads run very far in the east to west direction. The gap between two neighbouring north to south roads is 1 km. The gap between two neighbouring east to west roads is also 1 km.

The city has one city hall. The crossing where the city hall stands is written as $(0, 0)$. Every crossing of this city is written as crossing $(i, j)$ with two integers $i$ and $j$. Crossing $(i, j)$ is the crossing reached from crossing $(0, 0)$ by going $i$ km east ($-i$ km west when $i < 0$) and $j$ km north ($-j$ km south when $j < 0$).

The city hall keeps one dog named Joy. Joy made a walking plan for $K$ days. The plan is the following.

• On the morning of the first of the $K$ days, Joy is at crossing $(0, 0)$. Joy leaves a mark on crossing $(0, 0)$. No crossing other than $(0, 0)$ has a mark from Joy yet.
• Joy walks in the daytime on each of the $K$ days. One day of walking consists of $N$ steps. In each step Joy moves from the current crossing to a neighbouring crossing and leaves a mark on the crossing it moved to. Joy moves in exactly the same way on every day.
• After the daytime walk ends, Joy sleeps at the crossing it stands on until the next morning.

The city hall talks about the territory Joy builds over the $K$ days of walking. If Joy left a mark at least once on all four crossings $(a, b)$, $(a+1, b)$, $(a+1, b+1)$ and $(a, b+1)$, then the block enclosed by these four crossings belongs to Joy's territory.

The roads of this city are very long, and there are enough roads in both the north to south direction and the east to west direction, so Joy never reaches the end of a road or the end of the city during a walk.

Given Joy's walking plan, write a program that computes the number of blocks that belong to Joy's territory.

The first line contains two integers $N$ and $K$ separated by a single space. One day of walking consists of $N$ steps, and the walking plan lasts $K$ days.

The second line contains a string $S$ of length $N$. The $p$-th character $C_p$ ($1 \le p \le N$) of $S$, counted from the left, is one of E, N, W, S. The characters mean the following.

• If $C_p$ is E, the $p$-th step moves to the crossing neighbouring on the east.
• If $C_p$ is N, the $p$-th step moves to the crossing neighbouring on the north.
• If $C_p$ is W, the $p$-th step moves to the crossing neighbouring on the west.
• If $C_p$ is S, the $p$-th step moves to the crossing neighbouring on the south.

For crossing $(i, j)$, the crossings neighbouring on the east, north, west and south are crossing $(i+1, j)$, crossing $(i, j+1)$, crossing $(i-1, j)$ and crossing $(i, j-1)$.

Print the number of blocks that belong to Joy's territory on one line.

• $1 \le N \le 100000$
• $1 \le K \le 1000000000$