)get "input.ivy"
sample = 7 7 rho '....#..' '..###.#' '#...#.#' '.#...##' '#.###..' '##.#.##' '.#..#..'

#board = sample == '#'
board = input == '#'
#board

op north a = 1 flip a
op south a = -1 flip a
op west a = 1 rot a
op east a = -1 rot a

#north 3 3 rho iota 9

op lift a = (1,rho a) rho a
op n moveNSWE a = (lift n flip a[1]), (lift (-n) flip a[2]), (lift n rot a[3]), (lift (-n) rot a[4])

op a coalesce b =
    a: a
    b

op any a = or/,a
op pad a = 0,(transp (0,(transp a),0)),0
op needsPad a = (any 0 != a[1,(rho a)[1]]) or (any 0 != a[;(1,(rho a)[2])])
op maybePad a =
    needsPad a: pad a
    a

op maybePad1 a =
    c1 = any a[1]
    c2 = any a[(rho a)[1]]
    c1 and c2: 0,a,0
    c1: 0,a
    c2: a,0
    a

op maybePad a =
    a = maybePad1 a
    (any a[;1]) or (any a[;(rho a)[2]]): transp maybePad1 transp a
    a

op smearWE a = a or (west a) or (east a)
op smearNS a = a or (north a) or (south a)

op show a = (text ".#23456789"[1+a]),"\n-"

M = 0

op axis1 a = 3 1 2 transp a

op look a =
    ns = lift smearNS a
    we = lift smearWE a
    -1 moveNSWE (we, we, ns, ns)

op dup4 a = (4,rho a) rho a

# look in each direction
# an elf can move in a direction if there is no elf in said direction and there is an elf somewhere nearby
# returns a 4x(rho a) matrix
op canMove a =
    C = look a
    (not C) and dup4 (a and or/axis1 C)


# prepare moves
# assign each move a priority and take the max
# remove lower priority moves
op p prepare choices =
    best = max/ p * axis1 choices  # select best direction
    p o.== best                    # decompose into 4x?x? matrix

# count how many elves want to move to each square
# filter out moves which conflict
op unblocked moves =
    open = 1 == +/axis1 1 moveNSWE moves
    moves and -1 moveNSWE dup4 open

priority = 4 3 2 1
M = 0
changed = 0

op M round a =
    a = maybePad a
    moves = unblocked (M flip priority) prepare canMove a
    moved = or/axis1 moves
    changed; changed = +/, moved
    b = (a and not moved) + +/axis1 1 moveNSWE moves
    b

op round a = M round a

# this is implemented using globals
# to store the board instead of recursion
# in order to avoid keeping a bunch of large
# intermediate values alive on the stack
B = 0
op i loop n =
    i > n: i
    changed; changed = 0
    B = M round B
    M = M - 1
    changed == 0: i
    (i+1) loop n

op n rounds a =
    B; B = a
    M; M = 0
    1 loop n
    B

op n numrounds a =
    B; B = a
    M; M = 0
    1 loop n

op score a =
    a = maybePad a
    n = */ (rho a) - 2
    n - +/, a

show round board
show 10 rounds board
score 10 rounds board

1000 numrounds board
#numrounds board