gistfile1.py

import sys
sys.setrecursionlimit(20000)

stack = [[[]]]
for c in input().strip('^$'):
    if    c == '(':  stack.append([[]])    # new fork
    elif  c == '|':  stack[-1].append([])  # new tine
    elif  c == ')':  fork = stack.pop(); stack[-1][-1].append(fork)
    else:            stack[-1][-1].append(c)
[[maze]] = stack


world = set()
def carve(maze, x=0, y=0):
    global world
    world |= {(x,y)}
    if maze == []: return
    if maze[0] == 'N': world |= {(x,y-1),(x,y-2)}; return carve(maze[1:], x, y-2)
    if maze[0] == 'S': world |= {(x,y+1),(x,y+2)}; return carve(maze[1:], x, y+2)
    if maze[0] == 'W': world |= {(x-1,y),(x-2,y)}; return carve(maze[1:], x-2, y)
    if maze[0] == 'E': world |= {(x+1,y),(x+2,y)}; return carve(maze[1:], x+2, y)

    tines, *rest = maze
    if tines[-1] == []: # dead end
        carve(tines[0], x, y)
        carve(rest, x, y)
    else:
        assert rest == []
        for t in tines: carve(t, x, y)

carve(maze)

xmin = min(x for x,y in world)
xmax = max(x for x,y in world)
ymin = min(y for x,y in world)
ymax = max(y for x,y in world)

#for y in range(ymin-2, ymax+3):
#  for x in range(xmin-2, xmax+3):
#    print('\N{FULL BLOCK} '[(x,y) in world], end='')
#  print()

frontier = {(0, 0)}
depth = 0
seen = set()
distance = {}
while frontier:
  for k in frontier: distance[k] = depth
  seen |= frontier
  frontier = {(x+dx, y+dy) for (x, y) in frontier for (dx,dy) in [(-1,0), (1,0), (0,-1), (0,1)] if (x+dx, y+dy) in world and (x+dx,y+dy) not in seen}
  depth += 0.5
depth -= 0.5
print(depth)
print( len([(x,y) for (x,y) in world if (x%2,y%2) == (0,0) and distance[x,y] >= 1000]))