from lib import get_data, add2
from collections import defaultdict

DIRS = {
    "N": (-1, 0),
    "E": (0, 1),
    "S": (1, 0),
    "W": (0, -1),
}

data = get_data(__file__).strip()
g = defaultdict(set)
seen = set()
stack: list[tuple[tuple, int, list]] = [((0, 0), 0, [])]
while len(stack) > 0:
    pos, i, i_outs = stack.pop()

    c = (pos, i, tuple(i_outs))
    if c in seen:
        continue
    else:
        seen.add(c)

    assert i is not None
    while i < len(data):
        c = data[i]
        if c in DIRS.keys():
            npos = add2(pos, DIRS[c])
            g[pos].add(npos)
            g[npos].add(pos)
            pos = npos
            i += 1
        elif c == "(":
            to_continue = [i + 1]
            open_count = 0
            j_out = None
            for j in range(i + 1, len(data)):
                c = data[j]
                if c == "|" and open_count == 0:
                    to_continue.append(j + 1)
                elif c == "(":
                    open_count += 1
                elif c == ")" and open_count != 0:
                    open_count -= 1
                elif c == ")" and open_count == 0:
                    j_out = j
                    break
            assert j_out is not None

            for new_i in to_continue:
                new_i_outs = list(i_outs)
                new_i_outs.append(j_out)
                stack.append((pos, new_i, new_i_outs))
            break
        elif c == "$":
            break
        elif c == ")" and len(i_outs) == 0:
            assert False, "Encountered | without i_out"
        elif c == ")":
            i_new = i_outs.pop()
            assert i == i_new
            i += 1
        elif c == "^":
            i += 1
        elif c == "|" and len(i_outs) == 0:
            assert False, "Encountered | without i_out"
        elif c == "|":
            i = i_outs.pop()
            i += 1
        else:
            assert False

seen = set()
dists = {}
xs = [(0, 0)]
steps = 0
over_thousand = set()
while len(xs) > 0:
    nxs = []
    for x in xs:
        if x in seen:
            continue
        if steps >= 1000:
            over_thousand.add(x)
        seen.add(x)
        dists[x] = steps
        for nb in g[x]:
            if not nb in seen:
                nxs.append(nb)
    xs = nxs
    steps += 1

print(max(dists.values()))
print(len(over_thousand))