pattern_size = 6
from collections import Counter
from dataclasses import dataclass

@dataclass(eq=True, frozen=True)
class ScheduledNode:
    type: str
    chunk: int
    stage: int
    minibatch: int
    start_time: int
    completion_time: int

def transform_schedule(schedule, f, b, w, c):
    result = []

    stage_order = []
    local_prev = {}
    stages = len(schedule)
    
    for sid, stage in enumerate(schedule):
        counter = Counter()
        order = []
        for p in stage:
            if not p.strip():
                continue
            mb = counter.get(p, 0)
            if order:
                local_prev[(sid, p, mb)] = order[-1]
            order.append((p, mb))
            counter.update(p)
        stage_order.append(order)
    nmb = max(counter.values())
    time_map = {}
    cost = {
        'F': f,
        'B': b,
        'W': w,
        'f': f,
        'b': b,
        'w': w,
    }
    def get_time(stage, type, mb):
        if (stage, type, mb) in time_map:
            return time_map.get((stage, type, mb))
        time = 0
        if (stage, type, mb) in local_prev:
            time = get_time(stage, *local_prev[(stage, type, mb)])
        if type in "FB" and stage > 0:
            time = max(time, get_time(stage - 1, type, mb) + c)
        if type in "fb" and stage + 1< len(schedule):
            time = max(time, get_time(stage + 1, type, mb) + c)
        # print(f'{stage} {type}:{mb}', time + cost[type])
        time_map[(stage, type, mb)] = time + cost[type]
        return time_map[(stage, type, mb)]
    r = 0
    for sid, stage in enumerate(schedule):
        r = max(get_time(sid, 'W', nmb - 1) - get_time(sid, 'F', 0) + f, r)
        r = max(get_time(sid, 'w', nmb - 1) - get_time(sid, 'F', 0) + f, r)

    for sid, stage in enumerate(stage_order):
        result_stage = []
        for p, mb in stage:
            result_stage.append(ScheduledNode(
                p.upper(),
                p in "fBW",
                sid,
                mb,
                get_time(sid, p, mb) - cost[p],
                get_time(sid, p, mb)
            )
            )
        result.append(result_stage)
    return result


    


def evaluate_schedule(schedule, f, b, w, c):
    stage_order = []
    local_prev = {}
    stages = len(schedule)
    
    for sid, stage in enumerate(schedule):
        counter = Counter()
        order = []
        for p in stage:
            if not p.strip():
                continue
            mb = counter.get(p, 0)
            if order:
                local_prev[(sid, p, mb)] = order[-1]
            order.append((p, mb))
            counter.update(p)
        stage_order.append(order)
    nmb = max(counter.values())
    time_map = {}
    cost = {
        'F': f,
        'B': b,
        'W': w,
        'f': f,
        'b': b,
        'w': w,
    }
    def get_time(stage, type, mb):
        if (stage, type, mb) in time_map:
            return time_map.get((stage, type, mb))
        time = 0
        if (stage, type, mb) in local_prev:
            time = get_time(stage, *local_prev[(stage, type, mb)])
        if type in "FB" and stage > 0:
            time = max(time, get_time(stage - 1, type, mb) + c)
        if type in "fb" and stage + 1< len(schedule):
            time = max(time, get_time(stage + 1, type, mb) + c)
        # print(f'{stage} {type}:{mb}', time + cost[type])
        time_map[(stage, type, mb)] = time + cost[type]
        return time_map[(stage, type, mb)]
    r = 0
    for sid, stage in enumerate(schedule):
        r = max(get_time(sid, 'W', nmb - 1) - get_time(sid, 'F', 0) + f, r)
        r = max(get_time(sid, 'w', nmb - 1) - get_time(sid, 'F', 0) + f, r)
    return r

def get_pattern_str(pos):
    pattern = [" "] * pattern_size
    notations = "FfBbWw"
    for i, v in enumerate(pos):
        if v < 0:
            continue
        pattern[v] = notations[i]
    _str = ""
    for v in pattern:
        _str += v
    return _str


def get_peak_mem(schedules, return_all=False):
    max_peak = 0
    all_peak = []
    for schedule_ in schedules:
        peak, mem = 0, 0
        for v in schedule_:
            if v in "Ff":
                mem += 1
            elif v in "Ww":
                mem -= 1
            peak = max(peak, mem)
        all_peak.append(peak)
        max_peak = max(max_peak, peak)
    if return_all:
        return all_peak
    return max_peak


def calc_bubble(schedules):
    stage_bubbles = []
    for i in range(len(schedules)):
        max_len = 0
        count = 0
        for j in range(len(schedules[i])):
            if schedules[i][j] != ' ':
                max_len = j + 1
                count += 1
        stage_bubbles.append(max_len - count - i)
    return stage_bubbles


def init_repeated_schedule(p, m, patterns):
    repeated = []
    _len = 4 * p + m + 1
    for i in range(p):
        str_i = get_pattern_str(patterns[i]) * _len
        repeated_i = []
        for v in str_i:
            repeated_i.append(v)
        repeated.append(repeated_i)
    return repeated


def clear_invalid(repeated, stage, pos, offset=-1):
    while 0 <= pos < len(repeated[stage]):
        repeated[stage][pos] = ' '
        pos += offset * pattern_size
    return repeated


def clear_invalid_index(repeated, m):
    p = len(repeated)
    index = pattern_size
    for identifier in "FfBb":
        if identifier in "FB":
            _iter = range(p)
        else:
            _iter = range(p - 1, -1, -1)
        for i in _iter:
            for j in range(pattern_size):
                if repeated[i][index] == identifier:
                    clear_invalid(repeated, i, index - pattern_size, offset=-1)
                    clear_invalid(repeated, i, index + pattern_size * m, offset=1)
                    index += 1
                    if identifier in "Bb":
                        w_identifier = {'B': 'W', 'b': 'w'}[identifier]
                        for k in range(pattern_size):
                            if repeated[i][index + k] == w_identifier:
                                clear_invalid(repeated, i, index + k - pattern_size, offset=-1)
                                clear_invalid(repeated, i, index + k + pattern_size * m, offset=1)
                                break
                    break
                index += 1
    return repeated


def process_warmup_without_increasing_peak_mem(schedules, m):
    """
    FFFFFFFFFF     fBWfBWfBWfBWfBW  b
     FFFFFFFFF    f fBWfBWfBWfBWFBWb
      FFFFFFFF   f f fBWfBWfBWFBW b
       FFFFFFF  f f f fBWfBWFBW Bb
        FFFFFF f f f f fBWFBWFBWb
         FFFFFfFf f f f  BWFBW b
          FFFfFfFfFf f    BW Bb
           FfFfFfFfFfF     BWb
    We reorganize the warmup phase in the following way (i -> pipeline stage from 0):
        1. Before the first B, we set #f = min(i+1, peak_mem//2), #F = peak_mem - #f
        2. Before the first b, #f = peak_mem//2
        3. The offset between the first B is 1
        4. Before the first b, we use the pattern of (BWf)*j + (BWF)*k,
           where j = max(0, peak_mem//2 - (i+1)), k = max(0, #W - j - 1)
    """
    # process warmup phase (before the first b)
    p = len(schedules)
    peak_mem = get_peak_mem(schedules)
    peak_mem = min(peak_mem, 2 * p)
    cnt_f, cnt_ff = [], []
    for i in range(p):
        cc_ff = min(i + 1, peak_mem // 2)
        cc_ff = min(cc_ff, m)
        cc_f = min(peak_mem - cc_ff, m)
        cnt_f.append(cc_f)
        cnt_ff.append(cc_ff)
    distance_b2bb = 0
    for j in range(len(schedules[p - 1])):
        if schedules[p - 1][j] == 'B':
            for k in range(j, len(schedules[p - 1])):
                if schedules[p - 1][k] == 'b':
                    distance_b2bb = k - j
                    break
            break
    for i in range(p):
        c_f, c_ff, c_b, c_w = 0, 0, 0, 0
        for j in range(len(schedules[i])):
            char = schedules[i][j]
            if char == 'F':
                c_f += 1
            elif char == 'f':
                c_ff += 1
            elif char == 'B':
                c_b += 1
            elif char == 'W':
                c_w += 1
            elif char == 'b':
                bj = j
                while j < len(schedules[i]):
                    char = schedules[i][j]
                    if char == 'f' and c_ff < cnt_ff[p - 1]:
                        schedules[i][j] = ' '
                        c_ff += 1
                    if char == 'B' and c_b < c_ff:
                        if c_b < (2 * (p - i) + distance_b2bb) // 3 or c_b < cnt_ff[p - 1] - cnt_ff[i]:
                            # there is empty space, or the number of B is not enough to cover extra f
                            schedules[i][j] = ' '
                            c_b += 1
                    if char == 'W' and c_w < c_b:
                        if c_w < (2 * (p - i) + distance_b2bb - 1) // 3 or c_w < cnt_ff[p - 1] - cnt_ff[i]:
                            # there is empty space, or the number of W is not enough to cover extra f
                            schedules[i][j] = ' '
                            c_w += 1
                    j += 1
                j = bj
                while j < len(schedules[i]):
                    if schedules[i][j] == 'F':
                        if c_f < c_ff or c_f < cnt_f[i] or c_f - cnt_f[i] + c_ff - cnt_ff[i] < c_w - 1:
                            # put enough F, or there are some unused BW
                            schedules[i][j] = ' '
                            c_f += 1
                    j += 1
                break
            else:
                assert char == ' '
            schedules[i][j] = ' '
        assert c_f >= cnt_f[i] and c_ff >= cnt_ff[i]
        assert c_w >= cnt_ff[p - 1] - cnt_ff[i] and c_b >= cnt_ff[p - 1] - cnt_ff[i]
        j = i
        u_f, u_ff, u_b, u_w = 0, 0, 0, 0
        for _ in range(2 * (p - 1 - i)):
            if u_f < cnt_f[i] and u_f < c_f:
                schedules[i][j] = 'F'
                u_f += 1
            j += 1
        for _ in range(i + 1):
            if u_f < cnt_f[i] and u_f < c_f:
                schedules[i][j] = 'F'
                u_f += 1
            j += 1
            if u_ff < cnt_ff[i] and u_ff < c_ff:
                schedules[i][j] = 'f'
                u_ff += 1
            j += 1
        while u_f < c_f or u_ff < c_ff or u_b < c_b or u_w < c_w:
            if u_b < c_b:
                schedules[i][j] = 'B'
                u_b += 1
            j += 1
            if u_w < c_w:
                schedules[i][j] = 'W'
                u_w += 1
            j += 1
            if u_ff < c_ff:
                assert u_ff < u_f
                schedules[i][j] = 'f'
                u_ff += 1
            elif u_f < c_f:
                schedules[i][j] = 'F'
                u_f += 1
            j += 1
    return schedules



def squeeze_without_change_order(schedules, m):
    p = len(schedules)
    squeezed = [[' '] * len(schedules[_]) for _ in range(p)]
    max_len = 0
    for seq in squeezed:
        assert max_len == 0 or max_len == len(seq)
        max_len = max(max_len, len(seq))

    identifier_cnt = [{_id: 0 for _id in "FfBbWw"} for _ in range(p)]
    identifier_index = [{_id: -1 for _id in "FfBbWw"} for _ in range(p * m)]
    stage_index = [0 for _ in range(p)]
    for j in range(max_len):
        for _dir in range(2):
            if _dir == 0:
                _iter = range(p)
            else:
                _iter = range(p - 1, -1, -1)
            for i in _iter:
                identifier = schedules[i][j]
                if identifier == ' ':
                    continue
                if _dir == 0 and identifier in "fbw":
                    continue
                if _dir == 1 and identifier in "FBW":
                    continue
                _cnt = identifier_cnt[i][identifier]
                assert _cnt < m, "{} - {}, {}".format(i, identifier, _cnt)
                if identifier in "Ww" or (i == 0 and identifier in "FB") or (i == p - 1 and identifier in "fb"):
                    if i == 0 and identifier == 'B':
                        assert identifier_index[_cnt * p + i]['f'] >= 0
                    if i == p - 1 and identifier == 'f':
                        assert identifier_index[_cnt * p + i]['F'] >= 0
                    if i == p - 1 and identifier == 'b':
                        assert identifier_index[_cnt * p + i]['B'] >= 0
                    index = stage_index[i]
                elif identifier in "FB":
                    assert identifier_index[_cnt * p + i - 1][identifier] >= 0, "{} {} {}".format(i,identifier,_cnt)
                    index = max(identifier_index[_cnt * p + i - 1][identifier] + 1, stage_index[i])
                elif identifier in "fb":
                    assert identifier_index[_cnt * p + i + 1][identifier] >= 0, "{} {} {}".format(i,identifier,_cnt)
                    index = max(identifier_index[_cnt * p + i + 1][identifier] + 1, stage_index[i])
                else:
                    raise
                squeezed[i][index] = identifier
                identifier_cnt[i][identifier] += 1
                identifier_index[_cnt * p + i][identifier] = index
                stage_index[i] = index + 1
    return squeezed


def process_cooldown(schedules, m):
    """
           fBW       bwbwbwbw
          fBWBW     bwbwbwbw
         fBWBWBW   bwbwbwbw
        fBWBWBWBW bwbwbwbw
       f  BWBWBWBbWbwbwbww
      f    BWBWBbBbWbWbwwww
     f      BWBbBbBbWbWWwwww
    f        BbBbBbBbWWWWwwww
    We reorganize the cooldown phase in the following way (i -> pipeline stage from 0):
        1. After the last f, we set #b = (peak_mem+1)//2, and #B = min(i+1, peak_mem - #b)
        2. After the last f, we make all the dependencies as tight as possible
    """
    p = len(schedules)

    peak_mem = get_peak_mem(schedules)
    assert peak_mem <= 2 * p
    max_bb = (peak_mem + 1) // 2
    max_bb = min(max_bb, m)
    max_b = min(peak_mem - max_bb, m)

    # 1: reorganize B/b and remove W/w in cooldown phase
    starting_index = -1
    for i in range(p):
        c_b, c_bb, c_w, c_ww = 0, 0, 0, 0
        last_ff_index = -1
        # collect B/b which can be reorganized
        for j in range(len(schedules[i]) - 1, -1, -1):
            char = schedules[i][j]
            if char == 'f' and last_ff_index == -1:
                last_ff_index = j
            if char == 'B' and c_b < i + 1 and c_b < max_b:
                schedules[i][j] = ' '
                c_b += 1
            if char == 'b' and c_bb < max_bb:
                schedules[i][j] = ' '
                c_bb += 1
        # clear W in the tail (#W + #w = peak_mem)
        for j in range(len(schedules[i]) - 1, -1, -1):
            char = schedules[i][j]
            if char == 'W' and c_w + c_ww < peak_mem:
                schedules[i][j] = ' '
                c_w += 1
            if char == 'w' and c_w + c_ww < peak_mem:
                schedules[i][j] = ' '
                c_ww += 1
        if i == 0:
            starting_index = last_ff_index
        # reorganize B/b in the tail
        for k in range(c_bb):
            index = starting_index - i + 2 * p - 2 * k
            assert schedules[i][index] == ' ', "{} {} {}".format(schedules[i][index], k, i)
            schedules[i][index] = 'b'
        for k in range(c_b):
            index = starting_index + 1 + i - 2 * k
            assert schedules[i][index] == ' ', schedules[i][index]
            schedules[i][index] = 'B'

    # 2: squeeze cooldown phase without change order
    schedules = squeeze_without_change_order(schedules, m)

    # 3: add W back in cooldown phase
    for i in range(p):
        c_w, c_ww = 0, 0
        last_w_index = -2
        for j in range(len(schedules[i]) - 1, -1, -1):
            if schedules[i][j] in "Ww":
                if last_w_index < 0:
                    schedules[i][j] = ' '
                    last_w_index += 1
                else:
                    last_w_index = j
                    break
        for j in range(len(schedules[i])):
            char = schedules[i][j]
            if char == 'B':
                c_w += 1
            elif char == 'b':
                c_ww += 1
            elif char == 'W':
                c_w -= 1
            elif char == 'w':
                c_ww -= 1
            if char == ' ' and j > last_w_index:
                if c_w > 0:
                    schedules[i][j] = 'W'
                    c_w -= 1
                elif c_ww > 0:
                    schedules[i][j] = 'w'
                    c_ww -= 1

    schedules = squeeze_without_change_order(schedules, m)
    return schedules


def schedule_by_pattern(p, m, patterns, max_mem):
    schedules = init_repeated_schedule(p, max(m, 2 * p), patterns)
    schedules = clear_invalid_index(schedules,  max(m, 2 * p))
    init_peak_mem = get_peak_mem(schedules)
    if init_peak_mem > max_mem:
        return None, init_peak_mem, [6 *  max(m, 2 * p)] * p
    schedules = process_warmup_without_increasing_peak_mem(schedules,  max(m, 2 * p))
    
    for sid in range(len(schedules)):
        cnt = {_id: 0 for _id in "FfBbWw"}
        for i in range(len(schedules[sid])):
            if(schedules[sid][i] == ' '):
                continue
            if cnt[schedules[sid][i]] >= m:
                schedules[sid][i] = ' '
            else:
                cnt[schedules[sid][i]] += 1
    peak_mem = get_peak_mem(schedules)
    if peak_mem > init_peak_mem:
        return None, init_peak_mem, [6 * m] * p

    schedules = squeeze_without_change_order(schedules, m)

    schedules = process_cooldown(schedules, m)
    peak_mem = get_peak_mem(schedules)
    if peak_mem > init_peak_mem:
        return None, init_peak_mem, [6 * m] * p
    stage_bubbles = calc_bubble(schedules)
    return schedules, peak_mem, stage_bubbles


def fill_w_in_pattern(pattern):
    f, ff, b, bb, w, ww = 0, 1, 2, 3, 4, 5
    vis = [False] * pattern_size
    for v in pattern:
        if v >= 0:
            vis[v] = True
    assert pattern[b] >= 0 and pattern[bb] >= 0
    for v, vw in [(b, w), (bb, ww)]:
        for j in range(pattern_size):
            pos = (pattern[v] + j) % pattern_size
            if not vis[pos]:
                pattern[vw] = pos
                vis[pos] = True
                break
    return pattern


def get_whole_pattern(pattern_0, offset_0, offset_1, len_0, p):
    whole_pattern = [pattern_0]
    for i in range(p - 1):
        last_pattern = whole_pattern[i]
        new_pattern = [-1] * pattern_size
        vis = [False] * pattern_size
        if i < len_0:
            offset = offset_0
        else:
            offset = offset_1
        for v, v_o in enumerate(offset):
            pos = (last_pattern[v] + v_o + pattern_size) % pattern_size
            assert 0 <= pos < pattern_size
            if vis[pos]:
                return None
            vis[pos] = True
            new_pattern[v] = pos
        new_pattern = fill_w_in_pattern(new_pattern)
        whole_pattern.append(new_pattern)
    return whole_pattern


        
def schedule(p, m, cost, max_mem):
    f, ff, b, bb, w, ww = 0, 1, 2, 3, 4, 5
    available_patterns = []
    for ff_i in range(1, pattern_size):
        for b_i in range(1, pattern_size):
            for bb_i in range(1, pattern_size):
                if ff_i == b_i or ff_i == bb_i or b_i == bb_i:
                    continue
                pattern = [0, ff_i, b_i, bb_i, -1, -1]
                pattern = fill_w_in_pattern(pattern)
                available_patterns.append(pattern)

    print(len(available_patterns))
    available_offsets = [
        [1, -1, 1, -1],
        [2, -1, 2, -1],
        [3, -1, 3, -1],
        [4, -1, 4, -1],
        [5, -1, 5, -1]
    ]

    best_schedule = None
    best_bubble = None
    for pattern_0 in available_patterns:
        for i_0 in range(len(available_offsets)):
            for i_1 in range(i_0 + 1):
                for len_0 in range(1, p):
                    offset_0 = available_offsets[i_0]
                    offset_1 = available_offsets[i_1]
                    whole_pattern = get_whole_pattern(pattern_0, offset_0, offset_1, len_0, p)
                    if whole_pattern is None:
                        continue
                    s, peak_mem, bubbles = schedule_by_pattern(p, m, whole_pattern, min(2 * p, max_mem))
                    if peak_mem > 2 * p or peak_mem > max_mem:
                        break
                    if s is None:
                        continue
                    max_bubble = max(bubbles)
                    max_bubble = evaluate_schedule(s, *cost)
                    if best_schedule is None or max_bubble < best_bubble:
                        best_schedule, best_bubble = s, max_bubble
    res = transform_schedule(best_schedule, *cost)
    return res