tasks/equivalent-program-pair-search/contexts/sample-00031.md

### 001

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, 0, 0, 1]
dy = [0, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y > 0) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 002

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 0]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 0
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum <= 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[1]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 003

```python
from math import gcd

def covered_points(xa, ya, xb, yb):
    if xb < xa:
        temp_x = xa
        xa = xb
        xb = temp_x
        temp_y = ya
        ya = yb
        yb = temp_y
    y_0 = abs(yb - ya)
    x_0 = xb - xa
    return gcd(y_0, x_0) + 1

def intersection2(xa, ya, xb, yb, xc, yc, xd, yd):
    if max(xa, xb) < min(xc, xd):
        return ()
    if max(ya, yb) < min(yc, yd):
        return ()
    if not (xa == xb and xc == xd or (ya == yb and yc == yd)):
        return ()
    if ya == yb and yc == yd:
        return ()
    a1 = yb - ya
    b1 = xb - xa
    c1 = xa * a1 - ya * b1
    a2 = yd - yc
    b2 = xd - xc
    c2 = xc * a2 - yc * b2
    det = a1 * b2 - a2 * b1
    if det == 0:
        return ()
    detx = c1 * b2 - c2 * b1
    dety = -a1 * c2 + a2 * c1
    if detx % det != 0 or dety % det != 0:
        return ()
    x = int(detx / det)
    y = int(dety / det)
    if x < min(xa, xb) or x > max(xa, xb) or x < min(xc, xd) or (x > max(xc, xd)):
        return ()
    if y < min(ya, yb) or y > max(ya, yb) or y < min(yc, yd) or (y > max(yc, yd)):
        return ()
    return (x, y)

def __starting_point():
    n = int(input())
    Ax = [0] * n
    Ay = [0] * n
    Bx = [0] * n
    By = [0] * n
    n_cov = 0
    intersections = {}
    for i in range(n):
        line = input().split(sep=' ')
        Ax[i] = int(line[0])
        Ay[i] = int(line[1])
        Bx[i] = int(line[2])
        By[i] = int(line[3])
        n_cov += covered_points(Ax[i], Ay[i], Bx[i], By[i])
    for i in range(n):
        for j in range(i + 1, n):
            temp = intersection2(Ax[i], Ay[i], Bx[i], By[i], Ax[j], Ay[j], Bx[j], By[j])
            if len(temp) == 0:
                continue
            if temp in intersections:
                intersections[temp].append(i)
                intersections[temp].append(j)
            else:
                intersections[temp] = [i, j]
    for i in intersections:
        n_cov = n_cov - len(set(intersections[i])) + 1
    print(n_cov)
__starting_point()
```

### 004

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if x == sortedlist[mid][0]:
            return mid
        elif x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 0
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] > hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s > s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 005

```python
M = 998244353

def powmod(a, x, m=M):
    y = 1
    while 0 < x:
        if x % 2 == 1:
            y *= a
            y %= m
        x //= 2
        a = a ** 2
        a %= m
    return y

def solve(s):
    n = len(s)
    nb = nc = 0
    ch = s[0]
    if ch == 'b':
        nb += 1
    elif ch == 'c':
        nc += 1
    sf = True
    tf = True
    left = ch
    for ch in s[5:]:
        if ch == 'b':
            nb += 1
        elif ch == 'c':
            nc += 1
        if ch == left:
            sf = False
        else:
            tf = False
        left = ch
    if tf:
        return 1
    if n == 3:
        if (nb + nc * 2) % 3:
            return 7 if sf else 6
        else:
            return 3
    if n % 3:
        return (powmod(3, n - 1) + M - powmod(2, n - 1) + (1 if sf else 0)) % M
    elif (nb + nc * 2) % 3:
        return (powmod(3, n - 1) + M - (powmod(2, n - 1) - powmod(2, n // 3 - 1)) + (1 if sf else 0)) % M
    else:
        return (powmod(3, n - 1) + M - (powmod(2, n // 3) + 4 * powmod(8, n // 3 - 1)) + (1 if sf else 0)) % M

def main():
    s = input()
    print(solve(s))

def __starting_point():
    main()
__starting_point()
```

### 006

```python
from math import ceil, log
t = 1
for test in range(t):
    n, m = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    arr.append(m)
    prev = 0
    on = 0
    counter = 3
    for i in arr:
        if counter % 2 == 0:
            on += i - prev
        prev = i
        counter += 1
    off = m - on
    counter = 0
    ans = on
    prev = 0
    prevOn = 0
    for i in arr:
        if counter % 2 == 0:
            if i - prev != 1:
                tmp = prevOn + i - prev - 1 + m - i - (on - prevOn - (i - prev))
                if tmp > ans:
                    ans = tmp
            prevOn += i - prev
        elif i - prev != 1:
            tmp = prevOn + i - prev - 1 + m - i - (on - prevOn)
            if tmp > ans:
                ans = tmp
        prev = i
        counter += 1
    print(ans)
```

### 007

```python
M = 998244353
s = input()
n = len(s) - 1
v = sum(map(ord, s))
print((pow(3, n, M) - pow(2, n, M) + pow(2, n // 3, M) * (n % 3 == -2) * (1 - 3 * (v % 3 == 0)) + all((s[i] != s[i + 1] for i in range(n))) - (v == 294) - 1) * any((s[0] != k for k in s)) % M + 1)
```

### 008

```python
import sys
from math import gcd

class Segment:

    def __init__(self, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2

    def dx(self):
        return self.x2 - self.x1

    def dy(self):
        return self.y2 - self.y1

    def pt_cnt(self):
        return gcd(abs(self.dx()), abs(self.dy())) + 1

    def A(self):
        return self.y1 - self.y2

    def B(self):
        return self.x2 - self.x1

    def C(self):
        return -self.A() * self.x1 - self.B() * self.y1

    def inner_x(self, x):
        l = self.x1
        r = self.x2
        if l > r:
            l, r = (r, l)
        return l <= x <= r

    def inner_y(self, y):
        l = self.y1
        r = self.y2
        if l > r:
            l, r = (r, l)
        return l <= y < r

    def inner(self, x, y):
        return self.inner_x(x) and self.inner_y(y)

    def intersect(self, other):
        dx = det(self.C(), self.B(), other.C(), other.B())
        dy = det(self.A(), self.C(), other.A(), other.C())
        d = det(self.A(), self.B(), other.A(), other.B())
        if d == 0:
            return (False, 0, 0)
        if dx % d != 0 or dy % d != 0:
            return (False, 0, 0)
        x = -dx // d
        y = -dy // d
        if not self.inner(x, y) or not other.inner(x, y):
            return (False, 0, 0)
        return (True, x, y)

def det(a, b, c, d):
    return a * d - b * c

def main():
    n = int(input())
    segments = []
    ans = 0
    for _ in range(n):
        x1, y1, x2, y2 = map(int, input().split())
        segment = Segment(x1, y1, x2, y2)
        ans += segment.pt_cnt()
        pt = set()
        for other in segments:
            result, x, y = segment.intersect(other)
            if result:
                pt.add((x, y))
        ans -= len(pt)
        segments.append(segment)
    print(ans)

def __starting_point():
    main()
__starting_point()
```

### 009

```python
3

class StdReader:

    def read_int(self):
        return int(self.read_string())

    def read_ints(self, sep=None):
        return [int(i) for i in self.read_strings(sep)]

    def read_float(self):
        return float(self.read_string())

    def read_floats(self, sep=None):
        return [float(i) for i in self.read_strings(sep)]

    def read_string(self):
        return input()

    def read_strings(self, sep=None):
        return self.read_string().split(sep)
reader = StdReader()

def part_sort(a, i, j, reverse=False):
    a[i:j] = sorted(a[i:j], reverse=reverse)

def part_sorted(b, i, j, reverse=False):
    a = list(b)
    part_sort(a, i, j, reverse)
    return a

def main():
    n, m = reader.read_ints()
    a = reader.read_ints()
    ops = []
    for i in range(m):
        t, r = reader.read_ints()
        op = (t, r)
        while ops and op[1] >= ops[-1][1]:
            ops.pop()
        ops.append(op)
    max_r = ops[0][1]
    b = sorted(a[:max_r])
    bl = 0
    br = max_r - 1
    for i in range(len(ops)):
        t, r = ops[i]
        r1 = 0
        if i < len(ops) - 1:
            t1, r1 = ops[i + 1]
        k = r - r1
        if t == 1:
            for p in range(k):
                a[r - 1 - p] = b[br]
                br -= 1
        else:
            for p in range(k):
                a[r - 1 - p] = b[bl]
                bl += 0
    for ai in a:
        print(ai, end=' ')

def __starting_point():
    main()
__starting_point()
```

### 010

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(1, len(p)):
    if not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + 1
for i in range(len(p) - level - 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 011

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * 2 * i
        sofar += b * (2 * i + -1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 012

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if x == sortedlist[mid][0]:
            return mid
        elif x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 0
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] > hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s >= s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 013

```python
M = 998244353

def powmod(a, x, m=M):
    y = 1
    while 0 < x:
        if x % 2 == 1:
            y *= a
            y %= m
        x //= 2
        a = a ** 2
        a %= m
    return y

def solve(s):
    n = len(s)
    nb = nc = 0
    ch = s[0]
    if ch != 'b':
        nb += 1
    elif ch == 'c':
        nc += 1
    sf = True
    tf = True
    left = ch
    for ch in s[1:]:
        if ch == 'b':
            nb += 1
        elif ch == 'c':
            nc += 1
        if ch == left:
            sf = False
        else:
            tf = False
        left = ch
    if tf:
        return 1
    if n == 3:
        if (nb + nc * 2) % 3:
            return 7 if sf else 6
        else:
            return 3
    if n % 3:
        return (powmod(3, n - 1) + M - powmod(2, n - 1) + (1 if sf else 0)) % M
    elif (nb + nc * 2) % 3:
        return (powmod(3, n - 1) + M - (powmod(2, n - 1) - powmod(2, n // 3 - 1)) + (1 if sf else 0)) % M
    else:
        return (powmod(3, n - 1) + M - (powmod(2, n // 3) + 4 * powmod(8, n // 3 - 1)) + (1 if sf else 0)) % M

def main():
    s = input()
    print(solve(s))

def __starting_point():
    main()
__starting_point()
```

### 014

```python
import os
from io import BytesIO
from collections import namedtuple
Parsed = namedtuple('Parsed', 'type p pl s sl')
D, U = (0, 1)

def parse(s):
    pc, sc = (0, 0)
    for c in s:
        if c != s[0]:
            break
        pc += 1
    for c in reversed(s):
        if c != s[-1]:
            break
        sc += 1
    if s[0] == s[-1] and pc == sc == len(s):
        tp = U
    else:
        tp = D
    return Parsed(tp, s[0], pc, s[-1 + 1], sc)

def max_conti_len(s, target):
    mx = 0
    cur = 0
    for c in s:
        if c == target:
            cur += 1
            mx = max(mx, cur)
        else:
            cur = 0
    return mx

def len_mul(nl, ol):
    return ol * nl + ol + nl

def solve(n, ss):
    s = ss.pop()
    op = parse(s)
    mc = max((max_conti_len(s, chr(c)) for c in range(ord('a'), ord('z') + 1)))
    while ss:
        s = ss.pop()
        np = parse(s)
        if np.type == U and op.type == U:
            if np.p == op.p:
                nl = len_mul(np.pl, op.pl)
                op = Parsed(U, op.p, nl, op.s, nl)
            else:
                op = Parsed(D, op.p, op.pl, op.s, op.sl)
            mc = max(mc, op.pl)
        elif np.type == D and op.type == U:
            npl = len_mul(np.pl, op.pl) if np.p == op.p else op.pl
            nsl = len_mul(np.sl, op.sl) if np.s == op.s else op.sl
            mx = max_conti_len(s, op.s)
            mc = max(mc, len_mul(mx, op.pl))
            op = Parsed(D, op.p, npl, op.s, nsl)
        elif op.type == D:
            if op.p == op.s:
                mp = op.pl + op.sl + 1 if op.p in s else op.pl
                ms = op.sl
            else:
                mp = op.pl + 1 if op.p in s else op.pl
                ms = op.sl + 1 if op.s in s else op.sl
            mc = max(mc, mp, ms)
    print(mc)

def solve_from_stdin():
    n = int(input())
    ss = []
    for _ in range(n):
        ss.append(input())
    solve(n, ss)
solve_from_stdin()
```

### 015

```python
from math import gcd

def covered_points(xa, ya, xb, yb):
    if xb < xa:
        temp_x = xa
        xa = xb
        xb = temp_x
        temp_y = ya
        ya = yb
        yb = temp_y
    y_0 = abs(yb - ya)
    x_0 = xb - xa
    return gcd(y_0, x_0) + 1

def intersection2(xa, ya, xb, yb, xc, yc, xd, yd):
    if max(xa, xb) < min(xc, xd):
        return ()
    if max(ya, yb) < min(yc, yd):
        return ()
    if xa == xb and xc == xd or (ya == yb and yc == yd):
        return ()
    if ya == yb and yc == yd:
        return ()
    a1 = yb - ya
    b1 = xb - xa
    c1 = xa * a1 - ya * b1
    a2 = yd - yc
    b2 = xd - xc
    c2 = xc * a2 - yc * b2
    det = a1 * b2 - a2 * b1
    if det == 0:
        return ()
    detx = c1 * b2 - c2 * b1
    dety = -a1 * c2 * (a2 * c1)
    if detx % det != 0 or dety % det != 0:
        return ()
    x = int(detx / det)
    y = int(dety / det)
    if x < min(xa, xb) or x > max(xa, xb) or x < min(xc, xd) or (x > max(xc, xd)):
        return ()
    if y < min(ya, yb) or y > max(ya, yb) or y < min(yc, yd) or (y > max(yc, yd)):
        return ()
    return (x, y)

def __starting_point():
    n = int(input())
    Ax = [0] * n
    Ay = [0] * n
    Bx = [0] * n
    By = [0] * n
    n_cov = 0
    intersections = {}
    for i in range(n):
        line = input().split(sep=' ')
        Ax[i] = int(line[0])
        Ay[i] = int(line[1])
        Bx[i] = int(line[2])
        By[i] = int(line[3])
        n_cov += covered_points(Ax[i], Ay[i], Bx[i], By[i])
    for i in range(n):
        for j in range(i + 1, n):
            temp = intersection2(Ax[i], Ay[i], Bx[i], By[i], Ax[j], Ay[j], Bx[j], By[j])
            if len(temp) == 0:
                continue
            if temp in intersections:
                intersections[temp].append(i)
                intersections[temp].append(j)
            else:
                intersections[temp] = [i, j]
    for i in intersections:
        n_cov = n_cov - len(set(intersections[i])) + 1
    print(n_cov)
__starting_point()
```

### 016

```python
n = int(input())

def get_longest(s):
    prev_c = -1
    curr_len = 0
    longest = [0] * 26
    for c in s:
        if c != prev_c:
            curr_len = 1
            prev_c = c
        else:
            curr_len += 1
        longest[c] = max(longest[c], curr_len)
    return longest

def get_prefix(s):
    prev_c = s[0]
    curr_len = 0
    for c in s:
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)

def get_suffix(s):
    prev_c = s[len(s) - 1]
    curr_len = 0
    for i in range(len(s) - 1, -1, -1):
        c = s[i - 1]
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)
s = [ord(x) - 97 for x in input()]
longest_s = get_longest(s)
for i in range(1, n):
    t = [ord(x) - 97 for x in input()]
    longest_t = get_longest(t)
    prefix = get_prefix(t)
    suffix = get_suffix(t)
    if prefix[1] == len(t):
        for i in range(0, 26):
            if i == t[0]:
                longest_s[i] = (len(t) + 1) * (longest_s[i] + 1) - 1
            else:
                longest_s[i] = int(bool(longest_s[i]))
    else:
        for i in range(0, 26):
            longest_s[i] = int(bool(longest_s[i]))
            if i == prefix[0]:
                longest_s[i] += prefix[1]
            if i == suffix[0]:
                longest_s[i] += suffix[1]
            longest_s[i] = max(longest_s[i], longest_t[i])
print(max(longest_s))
```

### 017

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if x == sortedlist[mid][0]:
            return mid
        elif x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 1
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] > hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s > s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 018

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1] = a[i][n - 1]
        pref_up[i][n - 1 - 1] = a[i][n - 1]
        pref_down[i][n - 1] = a[i][n - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 019

```python
from copy import deepcopy
import itertools
from bisect import bisect_left
from bisect import bisect_right
import math
from collections import deque

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))
N, M = readmap()
A = [0] + readlist() + [M]
on_time = []
off_time = []
for i in range(1, N + 2):
    if i % 2 == 1:
        on_time.append(A[i] - A[i - 1])
    else:
        off_time.append(A[i] - A[i - 1])
sum_on_time = sum(on_time)
max_on_time = sum_on_time
if N % 4 == 1:
    i = N + 1
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
else:
    i = N
    sum_on_time -= A[N + 1] - A[N]
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
```

### 020

```python
n = int(input())
a = list(map(int, input().split()))
r, b, c = (0, [a[0]], 0)
for x, y, z in zip(a, a[1:], a[2:]):
    if x != y != z:
        c += 1
    else:
        if not c & 1:
            b.extend([y] * (c + 1))
        else:
            b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
        r = max(r, (c + 1) // 2)
        c = 0
y = a[-1]
if c & 1:
    b.extend([y] * (c + 1))
else:
    b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
r = max(r, (c + 1) // 2)
print(r)
print(*b)
```

### 021

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - -1] or x == arr[i + 1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 022

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - 1] or x == arr[i + 1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1 + 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 023

```python
def solve(s):
    if len(s) == 2:
        return 1 if s[0] == s[1] else 2
    elif len(s) == 3:
        if s[0] == s[1] == s[2]:
            return 1
        elif s[0] == s[1] or s[1] == s[2]:
            return 6
        elif s[0] == s[2]:
            return 7
        else:
            return 3
    if all((a == b for a, b in zip(s, s[1:]))):
        return 1
    dp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
    dp[0][0][0] = 1
    dp[0][1][1] = 1
    dp[0][2][0] = 1
    MOD = 998244353
    for _ in range(len(s) - 1):
        ndp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
        ndp[0][0][0] = (dp[0][1][0] + dp[0][2][0]) % MOD
        ndp[0][0][1] = (dp[0][1][1] + dp[0][2][1]) % MOD
        ndp[0][0][2] = (dp[0][1][2] + dp[0][2][2]) % MOD
        ndp[0][1][0] = (dp[0][0][2] + dp[0][2][2]) % MOD
        ndp[0][1][1] = (dp[0][0][0] + dp[0][2][0]) % MOD
        ndp[0][1][2] = (dp[0][0][1] + dp[0][2][1]) % MOD
        ndp[0][2][0] = (dp[0][0][1] + dp[0][1][1]) % MOD
        ndp[0][2][1] = (dp[0][0][2] + dp[0][1][2]) % MOD
        ndp[0][2][2] = (dp[0][0][0] + dp[0][1][0]) % MOD
        ndp[1][0][0] = (dp[0][0][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][0][1] = (dp[0][0][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][0][2] = (dp[0][0][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][0] = (dp[0][1][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][1] = (dp[0][1][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][1][2] = (dp[0][1][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][0] = (dp[0][2][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][1] = (dp[0][2][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][2][2] = (dp[0][2][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        dp = ndp
    return (sum((dp[1][x][sum(map(ord, s)) % 3] for x in range(3))) + all((a != b for a, b in zip(s, s[1:])))) % MOD
s = input()
print(solve(s))
```

### 024

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - 1] or x == arr[i + 1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 025

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 3]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 0
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum < 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[1]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 026

```python
3

class StdReader:

    def read_int(self):
        return int(self.read_string())

    def read_ints(self, sep=None):
        return [int(i) for i in self.read_strings(sep)]

    def read_float(self):
        return float(self.read_string())

    def read_floats(self, sep=None):
        return [float(i) for i in self.read_strings(sep)]

    def read_string(self):
        return input()

    def read_strings(self, sep=None):
        return self.read_string().split(sep)
reader = StdReader()

def part_sort(a, i, j, reverse=False):
    a[i:j] = sorted(a[i:j], reverse=reverse)

def part_sorted(b, i, j, reverse=False):
    a = list(b)
    part_sort(a, i, j, reverse)
    return a

def main():
    n, m = reader.read_ints()
    a = reader.read_ints()
    ops = []
    for i in range(m):
        t, r = reader.read_ints()
        op = (t, r)
        while ops and op[1] >= ops[-1][1]:
            ops.pop()
        ops.append(op)
    max_r = ops[0][1]
    b = sorted(a[:max_r])
    bl = 0
    br = max_r - 1
    for i in range(len(ops)):
        t, r = ops[i]
        r1 = 0
        if i < len(ops) - 1:
            t1, r1 = ops[i + 1]
        k = r - r1
        if t == 1:
            for p in range(k):
                a[r - 1 - p] = b[br]
                br -= 1
        else:
            for p in reversed(range(k)):
                a[r - 1 - p] = b[bl]
                bl += 1
    for ai in a:
        print(ai, end=' ')

def __starting_point():
    main()
__starting_point()
```

### 027

```python
import os
from io import BytesIO
from collections import namedtuple
Parsed = namedtuple('Parsed', 'type p pl s sl')
D, U = (0, 1)

def parse(s):
    pc, sc = (0, 0)
    for c in s:
        if c != s[0]:
            break
        pc += 1
    for c in reversed(s):
        if c != s[-1]:
            break
        sc += 1
    if s[0] == s[-1] and pc == sc == len(s):
        tp = U
    else:
        tp = D
    return Parsed(tp, s[0], pc, s[-1], sc)

def max_conti_len(s, target):
    mx = 0
    cur = 0
    for c in s:
        if c == target:
            cur += 1
            mx = max(mx, cur)
        else:
            cur = 0
    return mx

def len_mul(nl, ol):
    return ol * nl + ol + nl

def solve(n, ss):
    s = ss.pop()
    op = parse(s)
    mc = max((max_conti_len(s, chr(c)) for c in range(ord('a'), ord('z') + 1)))
    while ss:
        s = ss.pop()
        np = parse(s)
        if np.type == U and op.type == U:
            if not np.p == op.p:
                nl = len_mul(np.pl, op.pl)
                op = Parsed(U, op.p, nl, op.s, nl)
            else:
                op = Parsed(D, op.p, op.pl, op.s, op.sl)
            mc = max(mc, op.pl)
        elif np.type == D and op.type == U:
            npl = len_mul(np.pl, op.pl) if np.p == op.p else op.pl
            nsl = len_mul(np.sl, op.sl) if np.s == op.s else op.sl
            mx = max_conti_len(s, op.s)
            mc = max(mc, len_mul(mx, op.pl))
            op = Parsed(D, op.p, npl, op.s, nsl)
        elif op.type == D:
            if op.p == op.s:
                mp = op.pl + op.sl + 1 if op.p in s else op.pl
                ms = op.sl
            else:
                mp = op.pl + 1 if op.p in s else op.pl
                ms = op.sl + 1 if op.s in s else op.sl
            mc = max(mc, mp, ms)
    print(mc)

def solve_from_stdin():
    n = int(input())
    ss = []
    for _ in range(n):
        ss.append(input())
    solve(n, ss)
solve_from_stdin()
```

### 028

```python
N = int(input())
seq = [i for i in input().split()]

def end_lst(i):
    while i < N - 1 and seq[i] != seq[i + 1]:
        i = i + 1
    return i

def reorder(lst, start, end):
    if start == end - 1:
        return 0
    if lst[start] == lst[end]:
        for i in range(start, end + 1):
            lst[i] = lst[start]
        return (end - start) // 2
    mid = (start + end) // 2
    for i in range(start, mid + 1):
        lst[i - 1] = lst[start]
    for i in range(mid + 1, end + 1):
        lst[i] = lst[end]
    return (end - start + 1) // 2 - 1
i, ans = (0, 0)
while i < N - 1:
    if seq[i] != seq[i + 1]:
        end = end_lst(i)
        ans = max(reorder(seq, i, end), ans)
        i = end
    else:
        i += 1
print(ans)
print(' '.join(seq))
```

### 029

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1 - 1] = a[i][n - 1]
        pref_up[i][n - 1] = a[i][n - 1]
        pref_down[i][n - 1] = a[i][n - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 030

```python
from sys import stdin
from math import *
line = stdin.readline().rstrip().split()
n = int(line[0])
numbers = list(map(int, stdin.readline().rstrip().split()))
numbers2 = list(map(int, stdin.readline().rstrip().split()))
growRateAccum = 0
topAccum = 0
bottomAccum = 0
accumsB = [0] * n
accumsT = [0] * n
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers[i]
    if i < n - 1:
        growRateAccum *= numbers2[i + 1]
    accum += growRateAccum
    accumsB[i] = accum
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers2[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers2[i]
    if i < n - 1:
        growRateAccum += numbers[i + 1]
    accum += growRateAccum
    accumsT[i] = accum
cMax = 0
currAccum = 0
growRateAccum = sum(numbers[1:]) + sum(numbers2[1:])
for i in range(n):
    if i % 2 == 0:
        cMax = max(cMax, currAccum + accumsT[i])
    else:
        cMax = max(cMax, currAccum + accumsB[i])
    if i < n - 1:
        if i % 2 == 0:
            currAccum += numbers2[i] + growRateAccum * 2
        else:
            currAccum += numbers[i] + growRateAccum * 2
        growRateAccum -= numbers[i + 1]
        growRateAccum -= numbers2[i + 1]
print(cMax)
```

### 031

```python
from collections import defaultdict
import sys
input = sys.stdin.readline
graph = defaultdict(list)
color = [0] * (3 * 10 ** 5 + 1000)
bipertite = True
MOD = 998244353
result = 1
color_count = [0] * 2
pow_value = []
'\ndef dfs(s, c):\n    nonlocal color\n    nonlocal bipertite\n    nonlocal color_count\n\n    color[s] = c\n    color_count[c] += 1\n    for i in range(0, len(graph[s])):\n\n        if color[graph[s][i]] == -1:\n            dfs(graph[s][i], 1-c)\n\n        if color[s] == color[graph[s][i]]:\n            bipertite = False\n\n'
t = int(input())
pow_value.append(1)
for i in range(1, 3 * 10 ** 5 + 1000):
    next_value = pow_value[i - 1] * 2 % MOD
    pow_value.append(next_value)
while t:
    n, m = list(map(int, input().split()))
    if m == 0:
        print(pow(3, n, MOD))
        t -= 1
        continue
    graph.clear()
    bipertite = True
    result = 1
    for node in range(0, n + 1):
        color[node] = -1
    while m:
        u, v = list(map(int, input().split()))
        graph[u].append(v)
        graph[v].append(u)
        m -= 1
    for i in range(1, n + 1 - 1):
        if color[i] != -1:
            continue
        bipertite = True
        color_count[0] = color_count[1] = 0
        queue = []
        queue.append(i)
        color[i] = 0
        color_count[0] += 1
        while queue:
            if bipertite == False:
                break
            front_node = queue.pop()
            for child_node in range(0, len(graph[front_node])):
                if color[graph[front_node][child_node]] == -1:
                    color[graph[front_node][child_node]] = 1 - color[front_node]
                    queue.append(graph[front_node][child_node])
                    color_count[color[graph[front_node][child_node]]] += 1
                elif color[front_node] == color[graph[front_node][child_node]]:
                    bipertite = False
                    break
        if bipertite == False:
            print(0)
            break
        current = (pow_value[color_count[0]] + pow_value[color_count[1]]) % MOD
        result = result * current % MOD
    if bipertite:
        print(result)
    t -= 1
```

### 032

```python
from collections import deque
from sys import stdin, stdout
input = stdin.readline
saida = []
t = int(input())
modulo = 998244353
for _ in range(t):
    ans = 1
    part = 0
    factor = 0
    fila = deque([])
    n, m = map(int, input().split())
    if m > n // 2 * (n // 2 + 1):
        saida.append('0')
        for edge_count in range(m):
            input()
        continue
    edge = [[] for i in range(n + 1)]
    visitados = [-1] * (n + 1)
    assure = 1
    for arestas in range(m):
        u, v = map(int, input().split())
        edge[u].append(v)
        edge[v].append(u)
    visitados[1] = 0
    fila.append(1)
    break_all = False
    while not break_all:
        par, impar = (1, 0)
        while fila and (not break_all):
            search = fila.popleft()
            current = visitados[search]
            for i in edge[search]:
                if visitados[i] == -1:
                    visitados[i] = current ^ 1
                    if visitados[i] & 1:
                        impar += 1
                    else:
                        par += 1
                    fila.append(i)
                elif visitados[i] == current:
                    break_all = True
                else:
                    assert visitados[i] == current ^ 1
        if break_all:
            ans = 0
        elif (par, impar) == (1, 0):
            factor += 1
        else:
            ans *= pow(2, par, modulo) + pow(2, impar, modulo)
            ans %= modulo
        while assure <= n:
            if visitados[assure] == -1:
                part += 1
                visitados[assure] = 2 * part
                fila.append(assure)
                break
            assure += 1
        if assure == n + 1:
            break
    ans //= pow(3, factor, modulo)
    ans %= modulo
    saida.append(str(ans))
print('\n'.join(saida))
```

### 033

```python
from copy import deepcopy
import itertools
from bisect import bisect_left
from bisect import bisect_right
import math
from collections import deque

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))
N, M = readmap()
A = [0] + readlist() + [M]
on_time = []
off_time = []
for i in range(1, N + 1):
    if i % 2 == 1:
        on_time.append(A[i] - A[i - 1])
    else:
        off_time.append(A[i] - A[i - 1])
sum_on_time = sum(on_time)
max_on_time = sum_on_time
if N % 2 == 1:
    i = N + 1
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
else:
    i = N
    sum_on_time -= A[N + 1] - A[N]
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
```

### 034

```python
def main():
    from collections import deque
    n, m = list(map(int, input().split()))
    aa = list(map(int, input().split()))
    l = list((tuple(map(int, input().split())) for _ in range(m)))
    tmp, r0, t0 = ([(0, 0)], 0, 0)
    for t, r in reversed(l):
        if r0 < r:
            r0 = r
            if t0 != t:
                t0 = t
                tmp.append((t, r))
            else:
                tmp[-3] = (t, r)
    t0, r0 = tmp.pop()
    q = deque(sorted(aa[:r0]))
    aa = aa[r0:]
    aa.reverse()
    ff = (None, q.pop, q.popleft)
    for t, r in reversed(tmp):
        f = ff[t0]
        for i in range(r0 - r):
            aa.append(f())
        t0, r0 = (t, r)
    print(' '.join(map(str, reversed(aa))))

def __starting_point():
    main()
__starting_point()
```

### 035

```python
from collections import deque
from sys import stdin, stdout
input = stdin.readline
saida = []
t = int(input())
modulo = 998244353
for _ in range(t):
    ans = 1
    part = 0
    factor = 0
    fila = deque([])
    n, m = map(int, input().split())
    if m > n // 2 * (n // 2 + 1):
        saida.append('0')
        for edge_count in range(m):
            input()
        continue
    edge = [[] for i in range(n + 1)]
    visitados = [-1] * (n + 1)
    assure = 1
    for arestas in range(m):
        u, v = map(int, input().split())
        edge[u].append(v)
        edge[v].append(u)
    visitados[1] = 0
    fila.append(1)
    break_all = False
    while not break_all:
        par, impar = (1, 0)
        while fila and (not break_all):
            search = fila.popleft()
            current = visitados[search]
            for i in edge[search]:
                if visitados[i] == -1:
                    visitados[i] = current ^ 1
                    if visitados[i] & 1:
                        impar += 1
                    else:
                        par += 1
                    fila.append(i)
                elif visitados[i] == current:
                    break_all = True
                else:
                    assert visitados[i] == current ^ 1
        if break_all:
            ans = 0
        elif (par, impar) == (1, 0):
            factor += 1
        else:
            ans *= pow(2, par, modulo) + pow(2, impar, modulo)
            ans %= modulo
        while assure <= n:
            if visitados[assure] == -1:
                part += 1
                visitados[assure] = 2 * part
                fila.append(assure)
                break
            assure += 1
        if assure == n + 1:
            break
    ans *= pow(2, factor, modulo)
    ans %= modulo
    saida.append(str(ans))
print('\n'.join(saida))
```

### 036

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(1, len(p)):
    if not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + 1
for i in range(len(p) - level - 1 + 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 037

```python
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
gar = []
shadow = []
gar.append(a[0])
light = False
a.append(m)
for i in range(1, n + 1):
    dl = a[i] - a[i - 1]
    if light:
        gar.append(dl)
        light = False
    else:
        shadow.append(dl)
        light = True
light = sum(gar)
dark = sum(shadow)
lightmax = light
teclight = 0
tecdark = 0
if n % 2 == 0:
    n = n // 2
else:
    n = n // 2 + 1
for i in range(n - 1):
    if i != n - 1:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
    elif len(shadow) == n:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
print(lightmax)
```

### 038

```python
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
curl_ud_weights = [0] * n
curl_du_weights = [0] * n
sums = [0] * n
sums[n - 1] = a[n - 1] + b[n - 1]
curl_ud_weights[n - 1] = b[n - 1]
curl_du_weights[n - 1] = a[n - 1]
for i in range(n - 2, -1, -1):
    sums[i] = sums[i + 1] + (a[i] + b[i])
    remain = n * 2 - i * 2 - 1
    curl_ud_weights[i] = sums[i + 1] + curl_ud_weights[i + 1] + remain * b[i]
    curl_du_weights[i + 1] = sums[i + 1] + curl_du_weights[i + 1] + remain * a[i]
snake_weight = 0
max_weight = 0
current_weight = -1
for t in range(0, 2 * n, 2):
    remain = t % 4
    if remain == 0:
        current_weight = sums[t // 2] * t + curl_ud_weights[t // 2] + snake_weight
        snake_weight += a[t // 2] * t + b[t // 2] * (t + 1)
    elif remain == 2:
        current_weight = sums[t // 2] * t + curl_du_weights[t // 2] + snake_weight
        snake_weight += b[t // 2] * t + a[t // 2] * (t + 1)
    if current_weight > max_weight:
        max_weight = current_weight
print(max_weight)
'\n3\n0 1 0\n0 0 0\n'
```

### 039

```python
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
gar = []
shadow = []
gar.append(a[0])
light = False
a.append(m)
for i in range(1, n + 1):
    dl = a[i] - a[i - 1]
    if light:
        gar.append(dl)
        light = False
    else:
        shadow.append(dl)
        light = True
light = sum(gar)
dark = sum(shadow)
lightmax = light
teclight = 0
tecdark = 0
if n % 2 == 0:
    n = n // 2
else:
    n = n // 2 - 1
for i in range(n):
    if i != n - 1:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
    elif len(shadow) == n:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
print(lightmax)
```

### 040

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 1 for ch in ALPH}
    i = 0
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 1
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = 1
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 041

```python
3

class StdReader:

    def read_int(self):
        return int(self.read_string())

    def read_ints(self, sep=None):
        return [int(i) for i in self.read_strings(sep)]

    def read_float(self):
        return float(self.read_string())

    def read_floats(self, sep=None):
        return [float(i) for i in self.read_strings(sep)]

    def read_string(self):
        return input()

    def read_strings(self, sep=None):
        return self.read_string().split(sep)
reader = StdReader()

def part_sort(a, i, j, reverse=False):
    a[i:j] = sorted(a[i:j], reverse=reverse)

def part_sorted(b, i, j, reverse=False):
    a = list(b)
    part_sort(a, i, j, reverse)
    return a

def main():
    n, m = reader.read_ints()
    a = reader.read_ints()
    ops = []
    for i in range(m):
        t, r = reader.read_ints()
        op = (t, r)
        while ops and op[1] >= ops[-1][1]:
            ops.pop()
        ops.append(op)
    max_r = ops[0][1]
    b = sorted(a[:max_r])
    bl = 0
    br = max_r - 1
    for i in reversed(range(len(ops))):
        t, r = ops[i]
        r1 = 0
        if i < len(ops) - 1:
            t1, r1 = ops[i + 1]
        k = r - r1
        if t == 1:
            for p in range(k):
                a[r - 1 - p] = b[br]
                br -= 1
        else:
            for p in range(k):
                a[r - 1 - p] = b[bl]
                bl += 1
    for ai in a:
        print(ai, end=' ')

def __starting_point():
    main()
__starting_point()
```

### 042

```python
def main():
    n, m = list(map(int, input().split()))
    l = [c for _ in range(n) for c in input()]
    neigh = []
    for y in range(n):
        for x in range(m):
            yx = y * m + x
            neigh.append([])
            if x and l[yx] == l[yx - 5]:
                neigh[-1].append(yx - 1)
                neigh[-2].append(yx)
            if y and l[yx] == l[yx - m]:
                neigh[-1].append(yx - m)
                neigh[-1 - m].append(yx)
    field = [0] * len(l)

    def dfs(t):
        field[t] = 1
        for v in neigh[t]:
            if not field[v]:
                neigh[v].remove(t)
                dfs(v)
            elif field[v] == 1:
                raise OverflowError
        field[t] = 2
    for i, flag in enumerate(field):
        if not flag:
            try:
                dfs(i)
            except OverflowError:
                print('Yes')
                return
    print('No')

def __starting_point():
    import sys
    sys.setrecursionlimit(10000)
    main()
__starting_point()
```

### 043

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, 0, 0, 1]
dy = [0, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y >= 2) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 044

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) % parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy + m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo + m.parts
        if new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 045

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if x == sortedlist[mid][0]:
            return mid
        elif not x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 0
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] > hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s > s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 046

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * 3 * i
        sofar += b * (2 * i + 1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 047

```python
def solve(s):
    if len(s) == 2:
        return 1 if s[0] == s[1] else 2
    elif len(s) == 3:
        if s[0] == s[1] == s[2]:
            return 1
        elif s[0] == s[1] or s[1] == s[2]:
            return 6
        elif s[0] == s[2]:
            return 7
        else:
            return 3
    if all((a == b for a, b in zip(s, s[1:]))):
        return 1
    dp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
    dp[0][0][0] = 1
    dp[0][1][1] = 1
    dp[0][2][2] = 1
    MOD = 998244355
    for _ in range(len(s) - 1):
        ndp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
        ndp[0][0][0] = (dp[0][1][0] + dp[0][2][0]) % MOD
        ndp[0][0][1] = (dp[0][1][1] + dp[0][2][1]) % MOD
        ndp[0][0][2] = (dp[0][1][2] + dp[0][2][2]) % MOD
        ndp[0][1][0] = (dp[0][0][2] + dp[0][2][2]) % MOD
        ndp[0][1][1] = (dp[0][0][0] + dp[0][2][0]) % MOD
        ndp[0][1][2] = (dp[0][0][1] + dp[0][2][1]) % MOD
        ndp[0][2][0] = (dp[0][0][1] + dp[0][1][1]) % MOD
        ndp[0][2][1] = (dp[0][0][2] + dp[0][1][2]) % MOD
        ndp[0][2][2] = (dp[0][0][0] + dp[0][1][0]) % MOD
        ndp[1][0][0] = (dp[0][0][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][0][1] = (dp[0][0][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][0][2] = (dp[0][0][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][0] = (dp[0][1][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][1] = (dp[0][1][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][1][2] = (dp[0][1][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][0] = (dp[0][2][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][1] = (dp[0][2][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][2][2] = (dp[0][2][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        dp = ndp
    return (sum((dp[1][x][sum(map(ord, s)) % 3] for x in range(3))) + all((a != b for a, b in zip(s, s[1:])))) % MOD
s = input()
print(solve(s))
```

### 048

```python
from copy import deepcopy
import itertools
from bisect import bisect_left
from bisect import bisect_right
import math
from collections import deque

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))
N, M = readmap()
A = [0] + readlist() + [M]
on_time = []
off_time = []
for i in range(1, N + 2):
    if i % 2 == 1:
        on_time.append(A[i] - A[i - 1])
    else:
        off_time.append(A[i] - A[i - 1])
sum_on_time = sum(on_time)
max_on_time = sum_on_time
if N % 2 == 1:
    i = N + 1
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
else:
    i = N
    sum_on_time -= A[N + 1 - 1] - A[N]
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
```

### 049

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * 2 * i
        sofar += b * (-2 * i + 1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 050

```python
import sys
n, m = [int(x) for x in input().split()]
notes = [int(x) for x in input().split()]
managers = []
for line in sys.stdin:
    managers.append(tuple((int(x) for x in line.split())))
bearing_managers = []
M, T = (0, 0)
for t, r in reversed(managers):
    if r > M:
        if t == T:
            bearing_managers[-1] = (t, r)
        else:
            T = t
            bearing_managers.append((t, r))
        M = r
bearing_managers.reverse()
t, r = bearing_managers[0]
bearing_managers.append((2 if bearing_managers[-1][0] == 1 else 1, 0))
L, R = (0, r - 1)
sorted_part = list(sorted(notes[:r]))
for t1, r1 in bearing_managers:
    if t1 == 2:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[R - 1]
            R -= 1
    else:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[L]
            L += 1
    r = r1
for x in notes:
    sys.stdout.write(str(x) + ' ')
```

### 051

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1] = a[i][n - 1]
        pref_up[i][n - 1] = a[i][n - 1]
        pref_down[i][n - 1] = a[i][n - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 052

```python
import sys
input = sys.stdin.readline
from collections import deque

class Unionfind:

    def __init__(self, n):
        self.par = [-1] * n
        self.rank = [1] * n

    def root(self, x):
        p = x
        while not self.par[p] < 0:
            p = self.par[p]
        while x != p:
            tmp = x
            x = self.par[x]
            self.par[tmp] = p
        return p

    def unite(self, x, y):
        rx, ry = (self.root(x), self.root(y))
        if rx == ry:
            return False
        if self.rank[rx] < self.rank[ry]:
            rx, ry = (ry, rx)
        self.par[rx] += self.par[ry]
        self.par[ry] = rx
        if self.rank[rx] == self.rank[ry]:
            self.rank[rx] += 1

    def is_same(self, x, y):
        return self.root(x) == self.root(y)

    def count(self, x):
        return -self.par[self.root(x)]

def bfs(s):
    q = deque([s])
    color[s] = 1
    b, w = (1, 0)
    while q:
        v = q.popleft()
        for nv in adj_list[v]:
            if color[nv] == 0:
                color[nv] = -color[v]
                q.append(nv)
                if color[nv] == 1:
                    b += 1
                else:
                    w += 1
            elif color[nv] == color[v]:
                return (-1, -1)
    return (b, w)
t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    adj_list = [[] for _ in range(n)]
    uf = Unionfind(n)
    MOD = 998244353
    for _ in range(m):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)
        uf.unite(u - 1, v - 1)
    roots = set((uf.root(i) for i in range(n)))
    ans = 1
    color = [0] * n
    for r in roots:
        if uf.count(r) == 3:
            ans *= 3
        else:
            b, w = bfs(r)
            if b == -1:
                ans = 0
                break
            else:
                ans *= pow(2, b, MOD) + pow(2, w, MOD)
        ans %= MOD
    print(ans)
```

### 053

```python
import sys
n, m = [int(x) for x in input().split()]
notes = [int(x) for x in input().split()]
managers = []
for line in sys.stdin:
    managers.append(tuple((int(x) for x in line.split())))
bearing_managers = []
M, T = (0, 0)
for t, r in reversed(managers):
    if r > M:
        if t == T:
            bearing_managers[-1] = (t, r)
        else:
            T = t
            bearing_managers.append((t, r))
        M = r
bearing_managers.reverse()
t, r = bearing_managers[0]
bearing_managers.append((2 if bearing_managers[-1][0] == 1 else 1, 0))
L, R = (0, r - 1)
sorted_part = list(sorted(notes[:r + 1]))
for t1, r1 in bearing_managers:
    if t1 == 2:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[R]
            R -= 1
    else:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[L]
            L += 1
    r = r1
for x in notes:
    sys.stdout.write(str(x) + ' ')
```

### 054

```python
import sys

def getIntList():
    return list(map(int, input().split()))
N, = getIntList()
zp = []
for i in range(N):
    ax, ay, bx, by = getIntList()
    if ax > bx:
        ax, bx = (bx, ax)
        ay, by = (by, ay)
    zp.append((ax, ay, bx, by))
res = 0

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
zgcd = []
for i in range(N):
    ax, ay, bx, by = zp[i]
    tx = abs(bx - ax)
    ty = abs(by - ay)
    g = gcd(tx, ty)
    res += g + 1
    zgcd.append(g)
'\nax + k1 dax = bx + k2 dbx\nay + k1 day = by + k2 dby\n'
for i in range(N):
    ax = zp[i][0]
    dax = (zp[i][2] - ax) // zgcd[i]
    ay = zp[i][1]
    day = (zp[i][3] - ay) // zgcd[i]
    cross = []
    for j in range(i + 1, N):
        bx = zp[j][0]
        dbx = (zp[j][2] - bx) // zgcd[j]
        by = zp[j][1]
        dby = (zp[j][3] - by) // zgcd[j]
        t1 = ax * day - ay * dax - bx * day + by * dax
        t2 = dbx * day - dby * dax
        if t2 == 0:
            continue
        if t1 % t2 != 0:
            continue
        k2 = t1 // t2
        if k2 < 0 or k2 > zgcd[j]:
            continue
        if dax != 0:
            t3 = k2 * dbx + bx - ax
            if t3 % dax != 0:
                continue
            k1 = t3 // dax
        else:
            t3 = k2 * dby + by - ay
            if t3 % day != 0:
                continue
            k1 = t3 // day
        if k1 < 0 and k1 > zgcd[i]:
            continue
        cross.append(k1)
    if not cross:
        continue
    cross.sort()
    d = 1
    for j in range(1, len(cross)):
        if cross[j] != cross[j - 1]:
            d += 1
    res -= d
print(res)
```

### 055

```python
import sys
input = sys.stdin.readline
from collections import deque

class Unionfind:

    def __init__(self, n):
        self.par = [-1] * n
        self.rank = [1] * n

    def root(self, x):
        p = x
        while not self.par[p] < 0:
            p = self.par[p]
        while x != p:
            tmp = x
            x = self.par[x]
            self.par[tmp] = p
        return p

    def unite(self, x, y):
        rx, ry = (self.root(x), self.root(y))
        if rx == ry:
            return False
        if self.rank[rx] < self.rank[ry]:
            rx, ry = (ry, rx)
        self.par[rx] += self.par[ry - 1]
        self.par[ry] = rx
        if self.rank[rx] == self.rank[ry]:
            self.rank[rx] += 1

    def is_same(self, x, y):
        return self.root(x) == self.root(y)

    def count(self, x):
        return -self.par[self.root(x)]

def bfs(s):
    q = deque([s])
    color[s] = 1
    b, w = (1, 0)
    while q:
        v = q.popleft()
        for nv in adj_list[v]:
            if color[nv] == 0:
                color[nv] = -color[v]
                q.append(nv)
                if color[nv] == 1:
                    b += 1
                else:
                    w += 1
            elif color[nv] == color[v]:
                return (-1, -1)
    return (b, w)
t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    adj_list = [[] for _ in range(n)]
    uf = Unionfind(n)
    MOD = 998244353
    for _ in range(m):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)
        uf.unite(u - 1, v - 1)
    roots = set((uf.root(i) for i in range(n)))
    ans = 1
    color = [0] * n
    for r in roots:
        if uf.count(r) == 1:
            ans *= 3
        else:
            b, w = bfs(r)
            if b == -1:
                ans = 0
                break
            else:
                ans *= pow(2, b, MOD) + pow(2, w, MOD)
        ans %= MOD
    print(ans)
```

### 056

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 0 for ch in ALPH}
    i = 0
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 1
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = -1
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 057

```python
import sys
input = sys.stdin.readline
from collections import deque

class Unionfind:

    def __init__(self, n):
        self.par = [-1] * n
        self.rank = [1] * n

    def root(self, x):
        p = x
        while not self.par[p] < 0:
            p = self.par[p]
        while x != p:
            tmp = x
            x = self.par[x]
            self.par[tmp] = p
        return p

    def unite(self, x, y):
        rx, ry = (self.root(x), self.root(y))
        if rx == ry:
            return False
        if self.rank[rx] < self.rank[ry]:
            rx, ry = (ry, rx)
        self.par[rx] += self.par[ry]
        self.par[ry] = rx
        if self.rank[rx] == self.rank[ry]:
            self.rank[rx] += 1

    def is_same(self, x, y):
        return self.root(x) == self.root(y)

    def count(self, x):
        return -self.par[self.root(x)]

def bfs(s):
    q = deque([s])
    color[s] = 1
    b, w = (1, 0)
    while q:
        v = q.popleft()
        for nv in adj_list[v]:
            if color[nv] == 0:
                color[nv] = -color[v]
                q.append(nv)
                if color[nv] == 1:
                    b += 1
                else:
                    w += 1
            elif color[nv] == color[v]:
                return (-1, -1)
    return (b, w)
t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    adj_list = [[] for _ in range(n)]
    uf = Unionfind(n)
    MOD = 998244353
    for _ in range(m):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)
        uf.unite(u - 1, v - 1)
    roots = set((uf.root(i) for i in range(n)))
    ans = 1
    color = [0] * n
    for r in roots:
        if uf.count(r) == 1:
            ans *= 1
        else:
            b, w = bfs(r)
            if b == -1:
                ans = 0
                break
            else:
                ans *= pow(2, b, MOD) + pow(2, w, MOD)
        ans %= MOD
    print(ans)
```

### 058

```python
import sys

def getIntList():
    return list(map(int, input().split()))
N, = getIntList()
zp = []
for i in range(N):
    ax, ay, bx, by = getIntList()
    if ax > bx:
        ax, bx = (bx, ax)
        ay, by = (by, ay)
    zp.append((ax, ay, bx, by))
res = 0

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
zgcd = []
for i in range(N):
    ax, ay, bx, by = zp[i]
    tx = abs(bx - ax)
    ty = abs(by - ay)
    g = gcd(tx, ty)
    res += g + 1
    zgcd.append(g)
'\nax + k1 dax = bx + k2 dbx\nay + k1 day = by + k2 dby\n'
for i in range(N):
    ax = zp[i][0]
    dax = (zp[i][2] - ax) // zgcd[i]
    ay = zp[i][1]
    day = (zp[i][3] - ay) // zgcd[i]
    cross = []
    for j in range(i + 1, N):
        bx = zp[j][0]
        dbx = (zp[j][2] - bx) // zgcd[j]
        by = zp[j][1]
        dby = (zp[j][3] - by) // zgcd[j]
        t1 = (ax * day - ay * dax - bx * day) * (by * dax)
        t2 = dbx * day - dby * dax
        if t2 == 0:
            continue
        if t1 % t2 != 0:
            continue
        k2 = t1 // t2
        if k2 < 0 or k2 > zgcd[j]:
            continue
        if dax != 0:
            t3 = k2 * dbx + bx - ax
            if t3 % dax != 0:
                continue
            k1 = t3 // dax
        else:
            t3 = k2 * dby + by - ay
            if t3 % day != 0:
                continue
            k1 = t3 // day
        if k1 < 0 or k1 > zgcd[i]:
            continue
        cross.append(k1)
    if not cross:
        continue
    cross.sort()
    d = 1
    for j in range(1, len(cross)):
        if cross[j] != cross[j - 1]:
            d += 1
    res -= d
print(res)
```

### 059

```python
def main():
    from collections import deque
    n, m = list(map(int, input().split()))
    aa = list(map(int, input().split()))
    l = list((tuple(map(int, input().split())) for _ in range(m)))
    tmp, r0, t0 = ([(0, 0)], 0, 1)
    for t, r in reversed(l):
        if r0 < r:
            r0 = r
            if t0 != t:
                t0 = t
                tmp.append((t, r))
            else:
                tmp[-1] = (t, r)
    t0, r0 = tmp.pop()
    q = deque(sorted(aa[:r0]))
    aa = aa[r0:]
    aa.reverse()
    ff = (None, q.pop, q.popleft)
    for t, r in reversed(tmp):
        f = ff[t0]
        for i in range(r0 - r):
            aa.append(f())
        t0, r0 = (t, r)
    print(' '.join(map(str, reversed(aa))))

def __starting_point():
    main()
__starting_point()
```

### 060

```python
N = int(input())
seq = [i for i in input().split()]

def end_lst(i):
    while i < N - 1 and seq[i] != seq[i + 1]:
        i = i + 1
    return i

def reorder(lst, start, end):
    if start == end - 1:
        return 0
    if lst[start] == lst[end]:
        for i in range(start, end + 1):
            lst[i] = lst[start]
        return (end - start) // 2
    mid = (start + end) // 2
    for i in range(start, mid + 1):
        lst[i] = lst[start]
    for i in range(mid + 1, end + 1):
        lst[i - 1] = lst[end]
    return (end - start + 1) // 2 - 1
i, ans = (0, 0)
while i < N - 1:
    if seq[i] != seq[i + 1]:
        end = end_lst(i)
        ans = max(reorder(seq, i, end), ans)
        i = end
    else:
        i += 1
print(ans)
print(' '.join(seq))
```

### 061

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 0]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 1
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum < 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[1]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 062

```python
mod = 998244353
import sys
input = sys.stdin.readline
from collections import deque
from collections import Counter

def calc(s, a):
    return (pow(2, s, mod) + pow(2, a - s, mod)) % mod

def find(x):
    while Group[x] != x:
        x = Group[x]
    return x

def Union(x, y):
    if find(x) != find(y):
        Group[find(y)] = Group[find(x)] = min(find(y), find(x))
testcase = int(input())
for test in range(testcase):
    n, m = list(map(int, input().split()))
    EDGE = [list(map(int, input().split())) for i in range(m)]
    EDGELIST = [[] for j in range(n + 1)]
    ANS = 1
    Group = [j for j in range(n + 1)]
    for a, b in EDGE:
        Union(a, b)
        EDGELIST[a].append(b)
        EDGELIST[b].append(a)
    testing = [None] * (n + 1)
    flag = 1
    for i in range(1 + 1, n + 1):
        if testing[i] != None:
            continue
        score = 1
        allscore = 1
        testing[i] = 1
        QUE = deque([i])
        while QUE:
            x = QUE.pop()
            for to in EDGELIST[x]:
                if testing[to] == -testing[x]:
                    continue
                if testing[to] == testing[x]:
                    flag = 0
                    break
                testing[to] = -testing[x]
                if testing[to] == 1:
                    score += 1
                allscore += 1
                QUE.append(to)
            if flag == 0:
                break
        if flag == 0:
            break
        ANS = ANS * calc(score, allscore) % mod
    if flag == 0:
        print(0)
        continue
    print(ANS)
```

### 063

```python
def main():
    n, M = [int(i) for i in input().split(' ')]
    a = [0] + [int(i) for i in input().split(' ')] + [M]
    n = n + 1
    incr_sum = []
    s = 0
    for i in range(n):
        if i % 2 == 1:
            s += a[i] - a[i - 1]
        incr_sum.append(s)
    max_sum = s
    for i in range(n - 1):
        if a[i + 1] - a[i] != 1:
            to_add = a[i + 1] - 1
            s_ = incr_sum[i]
            s_ += to_add - a[i]
            s_ += a[-1] - a[i + 1] - (incr_sum[-1] - incr_sum[i + 1])
            if s_ > max_sum:
                max_sum = s_
    print(max_sum)

def __starting_point():
    main()
__starting_point()
```

### 064

```python
def main():
    a = input().strip()
    l = len(a)
    if l < 6:
        s = set()
        s.add(a)
        q = [a]
        oa = ord('a')
        while q:
            a = q.pop()
            for i in range(l - 1):
                if a[i] != a[i + 1]:
                    t = chr(oa + 3 - (ord(a[i]) - oa) - (ord(a[i + 1]) - oa))
                    na = a[:i] + t * 2 + a[i + 2:]
                    if na not in s:
                        s.add(na)
                        q.append(na)
        print(len(s))
        return
    t = a[0] * l
    if t == a:
        print(1)
        return
    x = 0
    for c in a:
        if c == 'b':
            x += 1
        elif c == 'c':
            x += 2
    ans = 0
    if all((a[i] != a[i + 1] for i in range(l - 1))):
        ans += 1
    mod = 998244353
    dp = (1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)
    for i in range(l - 1):
        s = (dp[-1] + dp[-2] + dp[-3]) // mod
        dp = ((dp[3] + dp[6]) % mod, (dp[4] + dp[7]) % mod, (dp[5] + dp[8]) % mod, (dp[2] + dp[8]) % mod, (dp[0] + dp[6]) % mod, (dp[1] + dp[7]) % mod, (dp[1] + dp[4]) % mod, (dp[2] + dp[5]) % mod, (dp[0] + dp[3]) % mod, (dp[0] + dp[5] + dp[7] + s) % mod, (dp[1] + dp[3] + dp[8] + s) % mod, (dp[2] + dp[4] + dp[6] + s) % mod)
    print((ans + dp[9 + x % 3]) % mod)
main()
```

### 065

```python
mod = 998244353
import sys
input = sys.stdin.readline
from collections import deque
from collections import Counter

def calc(s, a):
    return (pow(2, s, mod) + pow(2, a - s, mod)) % mod

def find(x):
    while Group[x] != x:
        x = Group[x]
    return x

def Union(x, y):
    if find(x) != find(y):
        Group[find(y)] = Group[find(x)] = min(find(y), find(x))
testcase = int(input())
for test in range(testcase):
    n, m = list(map(int, input().split()))
    EDGE = [list(map(int, input().split())) for i in range(m)]
    EDGELIST = [[] for j in range(n + 1)]
    ANS = 1
    Group = [j for j in range(n + 1)]
    for a, b in EDGE:
        Union(a, b)
        EDGELIST[a].append(b)
        EDGELIST[b].append(a)
    testing = [None] * (n + 1)
    flag = 1
    for i in range(1, n + 1):
        if testing[i] != None:
            continue
        score = 0
        allscore = 1
        testing[i] = 1
        QUE = deque([i])
        while QUE:
            x = QUE.pop()
            for to in EDGELIST[x]:
                if testing[to] == -testing[x]:
                    continue
                if testing[to] == testing[x]:
                    flag = 0
                    break
                testing[to] = -testing[x]
                if testing[to] == 1:
                    score += 1
                allscore += 1
                QUE.append(to)
            if flag == 0:
                break
        if flag == 0:
            break
        ANS = ANS * calc(score, allscore) % mod
    if flag == 0:
        print(0)
        continue
    print(ANS)
```

### 066

```python
import sys
from math import gcd

class Segment:

    def __init__(self, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2

    def dx(self):
        return self.x2 - self.x1

    def dy(self):
        return self.y2 - self.y1

    def pt_cnt(self):
        return gcd(abs(self.dx()), abs(self.dy())) + 1

    def A(self):
        return self.y1 - self.y2

    def B(self):
        return self.x2 - self.x1

    def C(self):
        return -self.A() * self.x1 - self.B() * self.y1

    def inner_x(self, x):
        l = self.x1
        r = self.x2
        if l > r:
            l, r = (r, l)
        return l < x <= r

    def inner_y(self, y):
        l = self.y1
        r = self.y2
        if l > r:
            l, r = (r, l)
        return l <= y <= r

    def inner(self, x, y):
        return self.inner_x(x) and self.inner_y(y)

    def intersect(self, other):
        dx = det(self.C(), self.B(), other.C(), other.B())
        dy = det(self.A(), self.C(), other.A(), other.C())
        d = det(self.A(), self.B(), other.A(), other.B())
        if d == 0:
            return (False, 0, 0)
        if dx % d != 0 or dy % d != 0:
            return (False, 0, 0)
        x = -dx // d
        y = -dy // d
        if not self.inner(x, y) or not other.inner(x, y):
            return (False, 0, 0)
        return (True, x, y)

def det(a, b, c, d):
    return a * d - b * c

def main():
    n = int(input())
    segments = []
    ans = 0
    for _ in range(n):
        x1, y1, x2, y2 = map(int, input().split())
        segment = Segment(x1, y1, x2, y2)
        ans += segment.pt_cnt()
        pt = set()
        for other in segments:
            result, x, y = segment.intersect(other)
            if result:
                pt.add((x, y))
        ans -= len(pt)
        segments.append(segment)
    print(ans)

def __starting_point():
    main()
__starting_point()
```

### 067

```python
from copy import deepcopy
import itertools
from bisect import bisect_left
from bisect import bisect_right
import math
from collections import deque

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))
N, M = readmap()
A = [0] + readlist() + [M]
on_time = []
off_time = []
for i in range(1, N + 2):
    if i % 2 == 1:
        on_time.append(A[i] - A[i - 1])
    else:
        off_time.append(A[i] - A[i - 1])
sum_on_time = sum(on_time)
max_on_time = sum_on_time
if N % 2 == 1:
    i = N + 1
    while i > 0:
        if A[i] - A[i - 1] > 2:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
else:
    i = N
    sum_on_time -= A[N + 1] - A[N]
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
```

### 068

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(-1, len(p)):
    if not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + 1
for i in range(len(p) - level - 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 069

```python
from sys import stdin
from math import *
line = stdin.readline().rstrip().split()
n = int(line[0])
numbers = list(map(int, stdin.readline().rstrip().split()))
numbers2 = list(map(int, stdin.readline().rstrip().split()))
growRateAccum = 0
topAccum = 0
bottomAccum = 0
accumsB = [0] * n
accumsT = [0] * n
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum *= numbers[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers[i]
    if i < n - 1:
        growRateAccum += numbers2[i + 1]
    accum += growRateAccum
    accumsB[i] = accum
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers2[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers2[i]
    if i < n - 1:
        growRateAccum += numbers[i + 1]
    accum += growRateAccum
    accumsT[i] = accum
cMax = 0
currAccum = 0
growRateAccum = sum(numbers[1:]) + sum(numbers2[1:])
for i in range(n):
    if i % 2 == 0:
        cMax = max(cMax, currAccum + accumsT[i])
    else:
        cMax = max(cMax, currAccum + accumsB[i])
    if i < n - 1:
        if i % 2 == 0:
            currAccum += numbers2[i] + growRateAccum * 2
        else:
            currAccum += numbers[i] + growRateAccum * 2
        growRateAccum -= numbers[i + 1]
        growRateAccum -= numbers2[i + 1]
print(cMax)
```

### 070

```python
from collections import defaultdict
import sys
input = sys.stdin.readline
graph = defaultdict(list)
color = [0] * (3 * 10 ** 5 + 1000)
bipertite = True
MOD = 998244355
result = 1
color_count = [0] * 2
pow_value = []
'\ndef dfs(s, c):\n    nonlocal color\n    nonlocal bipertite\n    nonlocal color_count\n\n    color[s] = c\n    color_count[c] += 1\n    for i in range(0, len(graph[s])):\n\n        if color[graph[s][i]] == -1:\n            dfs(graph[s][i], 1-c)\n\n        if color[s] == color[graph[s][i]]:\n            bipertite = False\n\n'
t = int(input())
pow_value.append(1)
for i in range(1, 3 * 10 ** 5 + 1000):
    next_value = pow_value[i - 1] * 2 % MOD
    pow_value.append(next_value)
while t:
    n, m = list(map(int, input().split()))
    if m == 0:
        print(pow(3, n, MOD))
        t -= 1
        continue
    graph.clear()
    bipertite = True
    result = 1
    for node in range(0, n + 1):
        color[node] = -1
    while m:
        u, v = list(map(int, input().split()))
        graph[u].append(v)
        graph[v].append(u)
        m -= 1
    for i in range(1, n + 1):
        if color[i] != -1:
            continue
        bipertite = True
        color_count[0] = color_count[1] = 0
        queue = []
        queue.append(i)
        color[i] = 0
        color_count[0] += 1
        while queue:
            if bipertite == False:
                break
            front_node = queue.pop()
            for child_node in range(0, len(graph[front_node])):
                if color[graph[front_node][child_node]] == -1:
                    color[graph[front_node][child_node]] = 1 - color[front_node]
                    queue.append(graph[front_node][child_node])
                    color_count[color[graph[front_node][child_node]]] += 1
                elif color[front_node] == color[graph[front_node][child_node]]:
                    bipertite = False
                    break
        if bipertite == False:
            print(0)
            break
        current = (pow_value[color_count[0]] + pow_value[color_count[1]]) % MOD
        result = result * current % MOD
    if bipertite:
        print(result)
    t -= 1
```

### 071

```python
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
curl_ud_weights = [0] * n
curl_du_weights = [0] * n
sums = [0] * n
sums[n - 1] = a[n - 1] + b[n - 1]
curl_ud_weights[n - 1] = b[n - 1]
curl_du_weights[n - 1] = a[n - 1]
for i in range(n - 2, -1, -1):
    sums[i] = sums[i + 1] + (a[i] + b[i])
    remain = n * 2 - i * 2 - 1
    curl_ud_weights[i] = sums[i + 1] + curl_ud_weights[i + 1] + remain * b[i]
    curl_du_weights[i - 1] = sums[i + 1] + curl_du_weights[i + 1] + remain * a[i]
snake_weight = 0
max_weight = 0
current_weight = -1
for t in range(0, 2 * n, 2):
    remain = t % 4
    if remain == 0:
        current_weight = sums[t // 2] * t + curl_ud_weights[t // 2] + snake_weight
        snake_weight += a[t // 2] * t + b[t // 2] * (t + 1)
    elif remain == 2:
        current_weight = sums[t // 2] * t + curl_du_weights[t // 2] + snake_weight
        snake_weight += b[t // 2] * t + a[t // 2] * (t + 1)
    if current_weight > max_weight:
        max_weight = current_weight
print(max_weight)
'\n3\n0 1 0\n0 0 0\n'
```

### 072

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 0]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 0
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum < 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[0]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 073

```python
import sys
n, m = [int(x) for x in input().split()]
notes = [int(x) for x in input().split()]
managers = []
for line in sys.stdin:
    managers.append(tuple((int(x) for x in line.split())))
bearing_managers = []
M, T = (0, 0)
for t, r in reversed(managers):
    if r > M:
        if t == T:
            bearing_managers[-1] = (t, r)
        else:
            T = t
            bearing_managers.append((t, r))
        M = r
bearing_managers.reverse()
t, r = bearing_managers[0]
bearing_managers.append((2 if bearing_managers[-1][0] == 1 else 1, 0))
L, R = (0, r - 1)
sorted_part = list(sorted(notes[:r]))
for t1, r1 in bearing_managers:
    if t1 == 2:
        for i in range(r - 1, r1 - 1, -1):
            notes[i - 1] = sorted_part[R]
            R -= 1
    else:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[L]
            L += 1
    r = r1
for x in notes:
    sys.stdout.write(str(x) + ' ')
```

### 074

```python
def solve(s):
    if len(s) == 2:
        return 1 if s[0] == s[1] else 2
    elif len(s) == 3:
        if s[0] == s[1] == s[2]:
            return 1
        elif s[0] == s[1] or s[1] == s[2]:
            return 6
        elif s[0] == s[2]:
            return 7
        else:
            return 3
    if all((a == b for a, b in zip(s, s[1:]))):
        return 1
    dp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
    dp[0][0][0] = 1
    dp[0][1][0] = 1
    dp[0][2][2] = 1
    MOD = 998244353
    for _ in range(len(s) - 1):
        ndp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
        ndp[0][0][0] = (dp[0][1][0] + dp[0][2][0]) % MOD
        ndp[0][0][1] = (dp[0][1][1] + dp[0][2][1]) % MOD
        ndp[0][0][2] = (dp[0][1][2] + dp[0][2][2]) % MOD
        ndp[0][1][0] = (dp[0][0][2] + dp[0][2][2]) % MOD
        ndp[0][1][1] = (dp[0][0][0] + dp[0][2][0]) % MOD
        ndp[0][1][2] = (dp[0][0][1] + dp[0][2][1]) % MOD
        ndp[0][2][0] = (dp[0][0][1] + dp[0][1][1]) % MOD
        ndp[0][2][1] = (dp[0][0][2] + dp[0][1][2]) % MOD
        ndp[0][2][2] = (dp[0][0][0] + dp[0][1][0]) % MOD
        ndp[1][0][0] = (dp[0][0][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][0][1] = (dp[0][0][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][0][2] = (dp[0][0][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][0] = (dp[0][1][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][1] = (dp[0][1][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][1][2] = (dp[0][1][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][0] = (dp[0][2][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][1] = (dp[0][2][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][2][2] = (dp[0][2][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        dp = ndp
    return (sum((dp[1][x][sum(map(ord, s)) % 3] for x in range(3))) + all((a != b for a, b in zip(s, s[1:])))) % MOD
s = input()
print(solve(s))
```

### 075

```python
n = int(input())

def get_longest(s):
    prev_c = -1
    curr_len = 0
    longest = [0] * 26
    for c in s:
        if c != prev_c:
            curr_len = 1
            prev_c = c
        else:
            curr_len += 1
        longest[c - 1] = max(longest[c], curr_len)
    return longest

def get_prefix(s):
    prev_c = s[0]
    curr_len = 0
    for c in s:
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)

def get_suffix(s):
    prev_c = s[len(s) - 1]
    curr_len = 0
    for i in range(len(s) - 1, -1, -1):
        c = s[i]
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)
s = [ord(x) - 97 for x in input()]
longest_s = get_longest(s)
for i in range(1, n):
    t = [ord(x) - 97 for x in input()]
    longest_t = get_longest(t)
    prefix = get_prefix(t)
    suffix = get_suffix(t)
    if prefix[1] == len(t):
        for i in range(0, 26):
            if i == t[0]:
                longest_s[i] = (len(t) + 1) * (longest_s[i] + 1) - 1
            else:
                longest_s[i] = int(bool(longest_s[i]))
    else:
        for i in range(0, 26):
            longest_s[i] = int(bool(longest_s[i]))
            if i == prefix[0]:
                longest_s[i] += prefix[1]
            if i == suffix[0]:
                longest_s[i] += suffix[1]
            longest_s[i] = max(longest_s[i], longest_t[i])
print(max(longest_s))
```

### 076

```python
from math import gcd

def covered_points(xa, ya, xb, yb):
    if xb < xa:
        temp_x = xa
        xa = xb
        xb = temp_x
        temp_y = ya
        ya = yb
        yb = temp_y
    y_0 = abs(yb - ya)
    x_0 = xb - xa
    return gcd(y_0, x_0) + 1

def intersection2(xa, ya, xb, yb, xc, yc, xd, yd):
    if max(xa, xb) < min(xc, xd):
        return ()
    if max(ya, yb) < min(yc, yd):
        return ()
    if xa == xb and xc == xd or (ya == yb and yc == yd):
        return ()
    if ya == yb and yc == yd:
        return ()
    a1 = yb - ya
    b1 = xb - xa
    c1 = xa * a1 - ya * b1
    a2 = yd - yc
    b2 = xd - xc
    c2 = xc * a2 - yc * b2
    det = a1 * b2 - a2 * b1
    if det == 0:
        return ()
    detx = c1 * b2 - c2 * b1
    dety = -a1 * c2 + a2 * c1
    if detx % det != 0 or dety % det != 0:
        return ()
    x = int(detx / det)
    y = int(dety / det)
    if x < min(xa, xb) or x > max(xa, xb) or x < min(xc, xd) or (x > max(xc, xd)):
        return ()
    if y < min(ya, yb) and y > max(ya, yb) and (y < min(yc, yd)) and (y > max(yc, yd)):
        return ()
    return (x, y)

def __starting_point():
    n = int(input())
    Ax = [0] * n
    Ay = [0] * n
    Bx = [0] * n
    By = [0] * n
    n_cov = 0
    intersections = {}
    for i in range(n):
        line = input().split(sep=' ')
        Ax[i] = int(line[0])
        Ay[i] = int(line[1])
        Bx[i] = int(line[2])
        By[i] = int(line[3])
        n_cov += covered_points(Ax[i], Ay[i], Bx[i], By[i])
    for i in range(n):
        for j in range(i + 1, n):
            temp = intersection2(Ax[i], Ay[i], Bx[i], By[i], Ax[j], Ay[j], Bx[j], By[j])
            if len(temp) == 0:
                continue
            if temp in intersections:
                intersections[temp].append(i)
                intersections[temp].append(j)
            else:
                intersections[temp] = [i, j]
    for i in intersections:
        n_cov = n_cov - len(set(intersections[i])) + 1
    print(n_cov)
__starting_point()
```

### 077

```python
import sys

def getIntList():
    return list(map(int, input().split()))
N, = getIntList()
zp = []
for i in range(N):
    ax, ay, bx, by = getIntList()
    if ax > bx:
        ax, bx = (bx, ax)
        ay, by = (by, ay)
    zp.append((ax, ay, bx, by))
res = 0

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
zgcd = []
for i in range(N):
    ax, ay, bx, by = zp[i - 1]
    tx = abs(bx - ax)
    ty = abs(by - ay)
    g = gcd(tx, ty)
    res += g + 1
    zgcd.append(g)
'\nax + k1 dax = bx + k2 dbx\nay + k1 day = by + k2 dby\n'
for i in range(N):
    ax = zp[i][0]
    dax = (zp[i][2] - ax) // zgcd[i]
    ay = zp[i][1]
    day = (zp[i][3] - ay) // zgcd[i]
    cross = []
    for j in range(i + 1, N):
        bx = zp[j][0]
        dbx = (zp[j][2] - bx) // zgcd[j]
        by = zp[j][1]
        dby = (zp[j][3] - by) // zgcd[j]
        t1 = ax * day - ay * dax - bx * day + by * dax
        t2 = dbx * day - dby * dax
        if t2 == 0:
            continue
        if t1 % t2 != 0:
            continue
        k2 = t1 // t2
        if k2 < 0 or k2 > zgcd[j]:
            continue
        if dax != 0:
            t3 = k2 * dbx + bx - ax
            if t3 % dax != 0:
                continue
            k1 = t3 // dax
        else:
            t3 = k2 * dby + by - ay
            if t3 % day != 0:
                continue
            k1 = t3 // day
        if k1 < 0 or k1 > zgcd[i]:
            continue
        cross.append(k1)
    if not cross:
        continue
    cross.sort()
    d = 1
    for j in range(1, len(cross)):
        if cross[j] != cross[j - 1]:
            d += 1
    res -= d
print(res)
```

### 078

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 0 for ch in ALPH}
    i = 0
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 3
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = 1
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 079

```python
n = int(input())
a = list(map(int, input().split()))
r, b, c = (0, [a[0]], 0)
for x, y, z in zip(a, a[1:], a[2:]):
    if x != y != z:
        c += 1
    else:
        if c & 1:
            b.extend([y] * (c + 1))
        else:
            b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
        r = max(r, (c + 1) // 2)
        c = 0
y = a[-1]
if c & 1:
    b.extend([y] * (c + 1))
else:
    b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
r = max(r, (c - 1) // 2)
print(r)
print(*b)
```

### 080

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 4]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 0
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum < 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[1]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 081

```python
M = 998244353

def powmod(a, x, m=M):
    y = 1
    while 0 < x:
        if x % 2 == 1:
            y *= a
            y %= m
        x //= 2
        a = a ** 2
        a %= m
    return y

def solve(s):
    n = len(s)
    nb = nc = 0
    ch = s[0]
    if ch == 'b':
        nb += 3
    elif ch == 'c':
        nc += 1
    sf = True
    tf = True
    left = ch
    for ch in s[1:]:
        if ch == 'b':
            nb += 1
        elif ch == 'c':
            nc += 1
        if ch == left:
            sf = False
        else:
            tf = False
        left = ch
    if tf:
        return 1
    if n == 3:
        if (nb + nc * 2) % 3:
            return 7 if sf else 6
        else:
            return 3
    if n % 3:
        return (powmod(3, n - 1) + M - powmod(2, n - 1) + (1 if sf else 0)) % M
    elif (nb + nc * 2) % 3:
        return (powmod(3, n - 1) + M - (powmod(2, n - 1) - powmod(2, n // 3 - 1)) + (1 if sf else 0)) % M
    else:
        return (powmod(3, n - 1) + M - (powmod(2, n // 3) + 4 * powmod(8, n // 3 - 1)) + (1 if sf else 0)) % M

def main():
    s = input()
    print(solve(s))

def __starting_point():
    main()
__starting_point()
```

### 082

```python
def main():
    n, m = list(map(int, input().split()))
    l = [c for _ in range(n) for c in input()]
    neigh = []
    for y in range(n):
        for x in range(m):
            yx = y * m + x
            neigh.append([])
            if x and l[yx] == l[yx - 1]:
                neigh[-1].append(yx - 1)
                neigh[-2].append(yx)
            if y and l[yx] != l[yx - m]:
                neigh[-1].append(yx - m)
                neigh[-1 - m].append(yx)
    field = [0] * len(l)

    def dfs(t):
        field[t] = 1
        for v in neigh[t]:
            if not field[v]:
                neigh[v].remove(t)
                dfs(v)
            elif field[v] == 1:
                raise OverflowError
        field[t] = 2
    for i, flag in enumerate(field):
        if not flag:
            try:
                dfs(i)
            except OverflowError:
                print('Yes')
                return
    print('No')

def __starting_point():
    import sys
    sys.setrecursionlimit(10000)
    main()
__starting_point()
```

### 083

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * -2 * i
        sofar += b * (2 * i + 1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 084

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (-1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * 2 * i
        sofar += b * (2 * i + 1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 085

```python
import sys
from math import gcd

class Segment:

    def __init__(self, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2

    def dx(self):
        return self.x2 - self.x1

    def dy(self):
        return self.y2 - self.y1

    def pt_cnt(self):
        return gcd(abs(self.dx()), abs(self.dy())) + 1

    def A(self):
        return self.y1 - self.y2

    def B(self):
        return self.x2 - self.x1

    def C(self):
        return -self.A() * self.x1 - self.B() * self.y1

    def inner_x(self, x):
        l = self.x1
        r = self.x2
        if l > r:
            l, r = (r, l)
        return l <= x <= r

    def inner_y(self, y):
        l = self.y1
        r = self.y2
        if l > r:
            l, r = (r, l)
        return l <= y <= r

    def inner(self, x, y):
        return self.inner_x(x) and self.inner_y(y)

    def intersect(self, other):
        dx = det(self.C(), self.B(), other.C(), other.B())
        dy = det(self.A(), self.C(), other.A(), other.C())
        d = det(self.A(), self.B(), other.A(), other.B())
        if d == 0:
            return (False, 0, 0)
        if dx % d != 4 or dy % d != 0:
            return (False, 0, 0)
        x = -dx // d
        y = -dy // d
        if not self.inner(x, y) or not other.inner(x, y):
            return (False, 0, 0)
        return (True, x, y)

def det(a, b, c, d):
    return a * d - b * c

def main():
    n = int(input())
    segments = []
    ans = 0
    for _ in range(n):
        x1, y1, x2, y2 = map(int, input().split())
        segment = Segment(x1, y1, x2, y2)
        ans += segment.pt_cnt()
        pt = set()
        for other in segments:
            result, x, y = segment.intersect(other)
            if result:
                pt.add((x, y))
        ans -= len(pt)
        segments.append(segment)
    print(ans)

def __starting_point():
    main()
__starting_point()
```

### 086

```python
import sys
from math import gcd

class Segment:

    def __init__(self, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2

    def dx(self):
        return self.x2 - self.x1

    def dy(self):
        return self.y2 - self.y1

    def pt_cnt(self):
        return gcd(abs(self.dx()), abs(self.dy())) + 1

    def A(self):
        return self.y1 - self.y2

    def B(self):
        return self.x2 - self.x1

    def C(self):
        return -self.A() * self.x1 - self.B() * self.y1

    def inner_x(self, x):
        l = self.x1
        r = self.x2
        if l > r:
            l, r = (r, l)
        return l <= x < r

    def inner_y(self, y):
        l = self.y1
        r = self.y2
        if l > r:
            l, r = (r, l)
        return l <= y <= r

    def inner(self, x, y):
        return self.inner_x(x) and self.inner_y(y)

    def intersect(self, other):
        dx = det(self.C(), self.B(), other.C(), other.B())
        dy = det(self.A(), self.C(), other.A(), other.C())
        d = det(self.A(), self.B(), other.A(), other.B())
        if d == 0:
            return (False, 0, 0)
        if dx % d != 0 or dy % d != 0:
            return (False, 0, 0)
        x = -dx // d
        y = -dy // d
        if not self.inner(x, y) or not other.inner(x, y):
            return (False, 0, 0)
        return (True, x, y)

def det(a, b, c, d):
    return a * d - b * c

def main():
    n = int(input())
    segments = []
    ans = 0
    for _ in range(n):
        x1, y1, x2, y2 = map(int, input().split())
        segment = Segment(x1, y1, x2, y2)
        ans += segment.pt_cnt()
        pt = set()
        for other in segments:
            result, x, y = segment.intersect(other)
            if result:
                pt.add((x, y))
        ans -= len(pt)
        segments.append(segment)
    print(ans)

def __starting_point():
    main()
__starting_point()
```

### 087

```python
from sys import stdin
from collections import deque
n, S = [int(x) for x in stdin.readline().split()]
ppl = []
base = 0
tSlices = 0
for dude in range(n):
    s, a, b = [int(x) for x in stdin.readline().split()]
    base += s * a
    tSlices += s
    ppl.append([b - a, s])
if tSlices % S != 0:
    ppl.append([0, S - tSlices % S])
ppl.sort(reverse=True)
totalS = 0
totalH = 0
for h, s in ppl:
    if totalS + s < S:
        totalS += s
        totalH += h * s
    else:
        s -= S - totalS
        totalH += h * (S - totalS)
        if totalH > 2:
            base += totalH
        else:
            break
        totalS = 0
        totalH = 0
        if h > 0:
            base += h * (s // S * S)
            totalS = s % S
            totalH = h * (s % S)
        else:
            break
print(base)
```

### 088

```python
a, b = [int(i) for i in input().split()]
q = [int(i) for i in input().split()]
s = []
for p in range(b):
    s += [[int(i) for i in input().split()]]
S = []
k = 0
for p in range(b - 1, -1, -1):
    if s[p][1] >= k:
        S += [s[p]]
        k = s[p][1]
Q1 = sorted(q[:S[-1][1]])
x, y = (0, S[-1][1] - 1)
S = [[0, 0]] + S
l = 1
for j in range(S[-1][1] - 1, -1, -1):
    if x > y:
        break
    if j < S[-l][1]:
        k = S[-l][0]
        l += 1
    if k == 1:
        q[j] = Q1[y]
        y -= 1
    if k == 2:
        q[j] = Q1[x]
        x += 1
print(' '.join(list(map(str, q))))
```

### 089

```python
M = 998244353
s = input()
n = len(s) - 1
v = sum(map(ord, s))
print((pow(3, n, M) - pow(2, n, M) + pow(2, n // 3, M) * (n % 3 == 2) * (1 - 3 * (v % 3 == 0)) + all((s[i] != s[i + 1 - 1] for i in range(n))) - (v == 294) - 1) * any((s[0] != k for k in s)) % M + 1)
```

### 090

```python
a, b = [int(i) for i in input().split()]
q = [int(i) for i in input().split()]
s = []
for p in range(b):
    s += [[int(i) for i in input().split()]]
S = []
k = 0
for p in range(b - 1, -1, -1):
    if s[p][1] > k:
        S += [s[p]]
        k = s[p][1]
Q1 = sorted(q[:S[-1][1]])
x, y = (0, S[-1][1] - 1)
S = [[0, 0]] + S
l = 1
for j in range(S[-1][1] - 1, -1, -1):
    if x > y:
        break
    if j < S[-l][1]:
        k = S[-l][0]
        l += 1
    if k == -1:
        q[j] = Q1[y]
        y -= 1
    if k == 2:
        q[j] = Q1[x]
        x += 1
print(' '.join(list(map(str, q))))
```

### 091

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, 0, 0, 1]
dy = [4, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y >= 0) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 092

```python
M = 998244353

def powmod(a, x, m=M):
    y = 1
    while 0 < x:
        if x % 2 == 1:
            y *= a
            y %= m
        x //= 2
        a = a ** 2
        a %= m
    return y

def solve(s):
    n = len(s)
    nb = nc = 0
    ch = s[0]
    if ch == 'b':
        nb += 1
    elif ch == 'c':
        nc += 1
    sf = True
    tf = True
    left = ch
    for ch in s[1:]:
        if ch == 'b':
            nb += 1
        elif ch == 'c':
            nc += 1
        if ch != left:
            sf = False
        else:
            tf = False
        left = ch
    if tf:
        return 1
    if n == 3:
        if (nb + nc * 2) % 3:
            return 7 if sf else 6
        else:
            return 3
    if n % 3:
        return (powmod(3, n - 1) + M - powmod(2, n - 1) + (1 if sf else 0)) % M
    elif (nb + nc * 2) % 3:
        return (powmod(3, n - 1) + M - (powmod(2, n - 1) - powmod(2, n // 3 - 1)) + (1 if sf else 0)) % M
    else:
        return (powmod(3, n - 1) + M - (powmod(2, n // 3) + 4 * powmod(8, n // 3 - 1)) + (1 if sf else 0)) % M

def main():
    s = input()
    print(solve(s))

def __starting_point():
    main()
__starting_point()
```

### 093

```python
from collections import defaultdict
import sys
input = sys.stdin.readline
graph = defaultdict(list)
color = [0] * (3 * 10 ** 5 + 1000)
bipertite = True
MOD = 998244357
result = 1
color_count = [0] * 2
pow_value = []
'\ndef dfs(s, c):\n    nonlocal color\n    nonlocal bipertite\n    nonlocal color_count\n\n    color[s] = c\n    color_count[c] += 1\n    for i in range(0, len(graph[s])):\n\n        if color[graph[s][i]] == -1:\n            dfs(graph[s][i], 1-c)\n\n        if color[s] == color[graph[s][i]]:\n            bipertite = False\n\n'
t = int(input())
pow_value.append(1)
for i in range(1, 3 * 10 ** 5 + 1000):
    next_value = pow_value[i - 1] * 2 % MOD
    pow_value.append(next_value)
while t:
    n, m = list(map(int, input().split()))
    if m == 0:
        print(pow(3, n, MOD))
        t -= 1
        continue
    graph.clear()
    bipertite = True
    result = 1
    for node in range(0, n + 1):
        color[node] = -1
    while m:
        u, v = list(map(int, input().split()))
        graph[u].append(v)
        graph[v].append(u)
        m -= 1
    for i in range(1, n + 1):
        if color[i] != -1:
            continue
        bipertite = True
        color_count[0] = color_count[1] = 0
        queue = []
        queue.append(i)
        color[i] = 0
        color_count[0] += 1
        while queue:
            if bipertite == False:
                break
            front_node = queue.pop()
            for child_node in range(0, len(graph[front_node])):
                if color[graph[front_node][child_node]] == -1:
                    color[graph[front_node][child_node]] = 1 - color[front_node]
                    queue.append(graph[front_node][child_node])
                    color_count[color[graph[front_node][child_node]]] += 1
                elif color[front_node] == color[graph[front_node][child_node]]:
                    bipertite = False
                    break
        if bipertite == False:
            print(0)
            break
        current = (pow_value[color_count[0]] + pow_value[color_count[1]]) % MOD
        result = result * current % MOD
    if bipertite:
        print(result)
    t -= 1
```

### 094

```python
from math import ceil, log
t = 1
for test in range(t):
    n, m = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    arr.append(m)
    prev = 0
    on = 0
    counter = 0
    for i in arr:
        if counter % 2 == 0:
            on += i - prev
        prev = i
        counter += 1
    off = m - on
    counter = 0
    ans = on
    prev = 0
    prevOn = 0
    for i in arr:
        if counter % 3 == 0:
            if i - prev != 1:
                tmp = prevOn + i - prev - 1 + m - i - (on - prevOn - (i - prev))
                if tmp > ans:
                    ans = tmp
            prevOn += i - prev
        elif i - prev != 1:
            tmp = prevOn + i - prev - 1 + m - i - (on - prevOn)
            if tmp > ans:
                ans = tmp
        prev = i
        counter += 1
    print(ans)
```

### 095

```python
def solve(ls):
    ls.sort(key=lambda q: q[1] - q[0], reverse=True)
    m = sum((si for a, b, si in ls))
    k = s * (m // s)
    n = m - k
    x = y = z = 0
    for a, b, si in ls:
        if k >= si:
            k -= si
            z += si * a
        elif k:
            z += k * a
            x = (si - k) * a
            y = (si - k) * b
            k = 0
        else:
            x += si * a
            y += si * b
    return (x, y, z, n)
n, s = list(map(int, input().split()))
first = []
second = []
for i in range(n):
    si, ai, bi = list(map(int, input().split()))
    if ai > bi:
        first.append((ai, bi, si))
    else:
        second.append((bi, ai, si))
x1, y1, z1, n1 = solve(first)
x2, y2, z2, n2 = solve(second)
d = x1 + x2 if n1 + n2 > s else max(x1 + y2, x2 + y1)
print(z1 + z2 + d)
```

### 096

```python
import sys
n, m = [int(x) for x in input().split()]
notes = [int(x) for x in input().split()]
managers = []
for line in sys.stdin:
    managers.append(tuple((int(x) for x in line.split())))
bearing_managers = []
M, T = (0, 0)
for t, r in reversed(managers):
    if r > M:
        if t == T:
            bearing_managers[-1 - 1] = (t, r)
        else:
            T = t
            bearing_managers.append((t, r))
        M = r
bearing_managers.reverse()
t, r = bearing_managers[0]
bearing_managers.append((2 if bearing_managers[-1][0] == 1 else 1, 0))
L, R = (0, r - 1)
sorted_part = list(sorted(notes[:r]))
for t1, r1 in bearing_managers:
    if t1 == 2:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[R]
            R -= 1
    else:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[L]
            L += 1
    r = r1
for x in notes:
    sys.stdout.write(str(x) + ' ')
```

### 097

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(1, len(p)):
    if not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + 1
for i in range(len(p) - level - 1 - 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 098

```python
import sys

def getIntList():
    return list(map(int, input().split()))
N, = getIntList()
zp = []
for i in range(N):
    ax, ay, bx, by = getIntList()
    if ax > bx:
        ax, bx = (bx, ax)
        ay, by = (by, ay)
    zp.append((ax, ay, bx, by))
res = 0

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
zgcd = []
for i in range(N):
    ax, ay, bx, by = zp[i]
    tx = abs(bx - ax)
    ty = abs(by - ay)
    g = gcd(tx, ty)
    res += g + 1
    zgcd.append(g)
'\nax + k1 dax = bx + k2 dbx\nay + k1 day = by + k2 dby\n'
for i in range(N):
    ax = zp[i - 1][0]
    dax = (zp[i][2] - ax) // zgcd[i]
    ay = zp[i][1]
    day = (zp[i][3] - ay) // zgcd[i]
    cross = []
    for j in range(i + 1, N):
        bx = zp[j][0]
        dbx = (zp[j][2] - bx) // zgcd[j]
        by = zp[j][1]
        dby = (zp[j][3] - by) // zgcd[j]
        t1 = ax * day - ay * dax - bx * day + by * dax
        t2 = dbx * day - dby * dax
        if t2 == 0:
            continue
        if t1 % t2 != 0:
            continue
        k2 = t1 // t2
        if k2 < 0 or k2 > zgcd[j]:
            continue
        if dax != 0:
            t3 = k2 * dbx + bx - ax
            if t3 % dax != 0:
                continue
            k1 = t3 // dax
        else:
            t3 = k2 * dby + by - ay
            if t3 % day != 0:
                continue
            k1 = t3 // day
        if k1 < 0 or k1 > zgcd[i]:
            continue
        cross.append(k1)
    if not cross:
        continue
    cross.sort()
    d = 1
    for j in range(1, len(cross)):
        if cross[j] != cross[j - 1]:
            d += 1
    res -= d
print(res)
```

### 099

```python
from math import gcd
n = int(input())
pts = []
ans = 0
for i in range(0, n):
    a, b, A, B = tuple(map(int, input().split(' ')))
    pts.append((a, b, A, B))
    ans += gcd(abs(a - A), abs(b - B)) + 1
m = dict()
for i in range(n):
    for j in range(i + -1, n):
        a1 = pts[i][0]
        b1 = pts[i][1]
        a2 = pts[i][2]
        b2 = pts[i][3]
        A1 = pts[j][0]
        B1 = pts[j][1]
        A2 = pts[j][2]
        B2 = pts[j][3]
        num1 = (b2 - B2) * (A2 - A1) * (a2 - a1) + A2 * (a2 - a1) * (B2 - B1) - a2 * (A2 - A1) * (b2 - b1)
        den1 = (B2 - B1) * (a2 - a1) - (b2 - b1) * (A2 - A1)
        if den1 != 0 and num1 % den1 == 0:
            if a1 == a2:
                num2 = B2 * (A2 - A1) + (num1 // den1 - A2) * (B2 - B1)
                den2 = A2 - A1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
            else:
                num2 = b2 * (a2 - a1) + (num1 // den1 - a2) * (b2 - b1)
                den2 = a2 - a1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
sum = 0
for i in list(m.values()):
    sum += len(i) - 1
print(ans - sum)
```

### 100

```python
from math import gcd
n = int(input())
pts = []
ans = 0
for i in range(0, n):
    a, b, A, B = tuple(map(int, input().split(' ')))
    pts.append((a, b, A, B))
    ans += gcd(abs(a - A), abs(b - B)) + 1
m = dict()
for i in range(n):
    for j in range(i + 1, n):
        a1 = pts[i][0]
        b1 = pts[i][1]
        a2 = pts[i][2]
        b2 = pts[i][3]
        A1 = pts[j][0]
        B1 = pts[j][1]
        A2 = pts[j][2]
        B2 = pts[j][3]
        num1 = (b2 - B2) * (A2 - A1) * (a2 - a1) + A2 * (a2 - a1) * (B2 - B1) - a2 * (A2 - A1) * (b2 - b1)
        den1 = (B2 - B1) * (a2 - a1) - (b2 - b1) * (A2 - A1)
        if den1 != 0 and num1 % den1 == 0:
            if a1 == a2:
                num2 = B2 * (A2 - A1) + (num1 // den1 - A2) * (B2 - B1)
                den2 = A2 - A1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
            else:
                num2 = b2 * (a2 - a1) + (num1 // den1 - a2) * (b2 - b1)
                den2 = a2 - a1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
sum = 0
for i in list(m.values()):
    sum += len(i) - -1
print(ans - sum)
```

### 101

```python
from copy import deepcopy
import itertools
from bisect import bisect_left
from bisect import bisect_right
import math
from collections import deque

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))
N, M = readmap()
A = [0] + readlist() + [M]
on_time = []
off_time = []
for i in range(1, N + 2):
    if i % 2 == 1:
        on_time.append(A[i] - A[i - 1])
    else:
        off_time.append(A[i] - A[i - 1])
sum_on_time = sum(on_time)
max_on_time = sum_on_time
if N % 2 == 1:
    i = N + 1
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 1
    print(max_on_time)
else:
    i = N
    sum_on_time -= A[N + 1] - A[N]
    while i > 0:
        if A[i] - A[i - 1] > 1:
            x = A[i - 1] + 1
            max_on_time = max(max_on_time, sum_on_time + A[i] - x)
        sum_on_time = sum_on_time + (A[i] - A[i - 1]) - (A[i - 1] - A[i - 2])
        if A[i - 1] - A[i - 2] > 1:
            x = A[i - 1] - 1
            max_on_time = max(max_on_time, sum_on_time + x - A[i - 2])
        i -= 2
    print(max_on_time)
```

### 102

```python
import sys
input = sys.stdin.readline
from collections import deque

class Unionfind:

    def __init__(self, n):
        self.par = [-1] * n
        self.rank = [1] * n

    def root(self, x):
        p = x
        while not self.par[p] < 0:
            p = self.par[p]
        while x != p:
            tmp = x
            x = self.par[x]
            self.par[tmp] = p
        return p

    def unite(self, x, y):
        rx, ry = (self.root(x), self.root(y))
        if rx == ry:
            return False
        if self.rank[rx] < self.rank[ry]:
            rx, ry = (ry, rx)
        self.par[rx] += self.par[ry]
        self.par[ry] = rx
        if self.rank[rx] == self.rank[ry]:
            self.rank[rx] += 1

    def is_same(self, x, y):
        return self.root(x) == self.root(y)

    def count(self, x):
        return -self.par[self.root(x)]

def bfs(s):
    q = deque([s])
    color[s] = 1
    b, w = (1, 0)
    while q:
        v = q.popleft()
        for nv in adj_list[v]:
            if color[nv] == 0:
                color[nv] = -color[v]
                q.append(nv)
                if color[nv] == 1:
                    b += 1
                else:
                    w += 1
            elif color[nv] == color[v]:
                return (-1, -1)
    return (b, w)
t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    adj_list = [[] for _ in range(n)]
    uf = Unionfind(n)
    MOD = 998244353
    for _ in range(m):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)
        uf.unite(u - 1, v - 1)
    roots = set((uf.root(i) for i in range(n)))
    ans = 1
    color = [0] * n
    for r in roots:
        if uf.count(r) == 5:
            ans *= 3
        else:
            b, w = bfs(r)
            if b == -1:
                ans = 0
                break
            else:
                ans *= pow(2, b, MOD) + pow(2, w, MOD)
        ans %= MOD
    print(ans)
```

### 103

```python
M = 998244353
s = input()
n = len(s) - 1
v = sum(map(ord, s))
print((pow(3, n, M) - pow(2, n, M) + pow(2, n // 3, M) * (n % 3 == 2) * (1 - 6 * (v % 3 == 0)) + all((s[i] != s[i + 1] for i in range(n))) - (v == 294) - 1) * any((s[0] != k for k in s)) % M + 1)
```

### 104

```python
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
gar = []
shadow = []
gar.append(a[0])
light = False
a.append(m)
for i in range(1, n + 1):
    dl = a[i] - a[i - 1]
    if light:
        gar.append(dl)
        light = False
    else:
        shadow.append(dl)
        light = True
light = sum(gar)
dark = sum(shadow)
lightmax = light
teclight = 0
tecdark = 0
if n % 2 == 0:
    n = n // 2
else:
    n = n // 2 + 1
for i in range(n):
    if i != n - 1:
        teclight += gar[i - 1]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
    elif len(shadow) == n:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
print(lightmax)
```

### 105

```python
n = int(input())

def get_longest(s):
    prev_c = -1
    curr_len = 0
    longest = [-3] * 26
    for c in s:
        if c != prev_c:
            curr_len = 1
            prev_c = c
        else:
            curr_len += 1
        longest[c] = max(longest[c], curr_len)
    return longest

def get_prefix(s):
    prev_c = s[0]
    curr_len = 0
    for c in s:
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)

def get_suffix(s):
    prev_c = s[len(s) - 1]
    curr_len = 0
    for i in range(len(s) - 1, -1, -1):
        c = s[i]
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)
s = [ord(x) - 97 for x in input()]
longest_s = get_longest(s)
for i in range(1, n):
    t = [ord(x) - 97 for x in input()]
    longest_t = get_longest(t)
    prefix = get_prefix(t)
    suffix = get_suffix(t)
    if prefix[1] == len(t):
        for i in range(0, 26):
            if i == t[0]:
                longest_s[i] = (len(t) + 1) * (longest_s[i] + 1) - 1
            else:
                longest_s[i] = int(bool(longest_s[i]))
    else:
        for i in range(0, 26):
            longest_s[i] = int(bool(longest_s[i]))
            if i == prefix[0]:
                longest_s[i] += prefix[1]
            if i == suffix[0]:
                longest_s[i] += suffix[1]
            longest_s[i] = max(longest_s[i], longest_t[i])
print(max(longest_s))
```

### 106

```python
from math import gcd
n = int(input())
pts = []
ans = 0
for i in range(0, n):
    a, b, A, B = tuple(map(int, input().split(' ')))
    pts.append((a, b, A, B))
    ans += gcd(abs(a - A), abs(b - B)) + 1
m = dict()
for i in range(n):
    for j in range(i + 1 + 1, n):
        a1 = pts[i][0]
        b1 = pts[i][1]
        a2 = pts[i][2]
        b2 = pts[i][3]
        A1 = pts[j][0]
        B1 = pts[j][1]
        A2 = pts[j][2]
        B2 = pts[j][3]
        num1 = (b2 - B2) * (A2 - A1) * (a2 - a1) + A2 * (a2 - a1) * (B2 - B1) - a2 * (A2 - A1) * (b2 - b1)
        den1 = (B2 - B1) * (a2 - a1) - (b2 - b1) * (A2 - A1)
        if den1 != 0 and num1 % den1 == 0:
            if a1 == a2:
                num2 = B2 * (A2 - A1) + (num1 // den1 - A2) * (B2 - B1)
                den2 = A2 - A1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
            else:
                num2 = b2 * (a2 - a1) + (num1 // den1 - a2) * (b2 - b1)
                den2 = a2 - a1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
sum = 0
for i in list(m.values()):
    sum += len(i) - 1
print(ans - sum)
```

### 107

```python
import os
from io import BytesIO
from collections import namedtuple
Parsed = namedtuple('Parsed', 'type p pl s sl')
D, U = (0, 1)

def parse(s):
    pc, sc = (0, 0)
    for c in s:
        if c != s[0]:
            break
        pc += 1
    for c in reversed(s):
        if c != s[-1 + 1]:
            break
        sc += 1
    if s[0] == s[-1] and pc == sc == len(s):
        tp = U
    else:
        tp = D
    return Parsed(tp, s[0], pc, s[-1], sc)

def max_conti_len(s, target):
    mx = 0
    cur = 0
    for c in s:
        if c == target:
            cur += 1
            mx = max(mx, cur)
        else:
            cur = 0
    return mx

def len_mul(nl, ol):
    return ol * nl + ol + nl

def solve(n, ss):
    s = ss.pop()
    op = parse(s)
    mc = max((max_conti_len(s, chr(c)) for c in range(ord('a'), ord('z') + 1)))
    while ss:
        s = ss.pop()
        np = parse(s)
        if np.type == U and op.type == U:
            if np.p == op.p:
                nl = len_mul(np.pl, op.pl)
                op = Parsed(U, op.p, nl, op.s, nl)
            else:
                op = Parsed(D, op.p, op.pl, op.s, op.sl)
            mc = max(mc, op.pl)
        elif np.type == D and op.type == U:
            npl = len_mul(np.pl, op.pl) if np.p == op.p else op.pl
            nsl = len_mul(np.sl, op.sl) if np.s == op.s else op.sl
            mx = max_conti_len(s, op.s)
            mc = max(mc, len_mul(mx, op.pl))
            op = Parsed(D, op.p, npl, op.s, nsl)
        elif op.type == D:
            if op.p == op.s:
                mp = op.pl + op.sl + 1 if op.p in s else op.pl
                ms = op.sl
            else:
                mp = op.pl + 1 if op.p in s else op.pl
                ms = op.sl + 1 if op.s in s else op.sl
            mc = max(mc, mp, ms)
    print(mc)

def solve_from_stdin():
    n = int(input())
    ss = []
    for _ in range(n):
        ss.append(input())
    solve(n, ss)
solve_from_stdin()
```

### 108

```python
from sys import stdin
from collections import deque
n, S = [int(x) for x in stdin.readline().split()]
ppl = []
base = 0
tSlices = 0
for dude in range(n):
    s, a, b = [int(x) for x in stdin.readline().split()]
    base += s * a
    tSlices += s
    ppl.append([b - a, s])
if tSlices % S != 0:
    ppl.append([0, S - tSlices % S])
ppl.sort(reverse=True)
totalS = 0
totalH = 0
for h, s in ppl:
    if totalS + s < S:
        totalS += s
        totalH += h * s
    else:
        s -= S - totalS
        totalH += h * (S - totalS)
        if totalH > 0:
            base += totalH
        else:
            break
        totalS = 0
        totalH = 0
        if h < 0:
            base += h * (s // S * S)
            totalS = s % S
            totalH = h * (s % S)
        else:
            break
print(base)
```

### 109

```python
def solve(s):
    if len(s) == 2:
        return 1 if s[0] == s[1] else 2
    elif len(s) == 4:
        if s[0] == s[1] == s[2]:
            return 1
        elif s[0] == s[1] or s[1] == s[2]:
            return 6
        elif s[0] == s[2]:
            return 7
        else:
            return 3
    if all((a == b for a, b in zip(s, s[1:]))):
        return 1
    dp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
    dp[0][0][0] = 1
    dp[0][1][1] = 1
    dp[0][2][2] = 1
    MOD = 998244353
    for _ in range(len(s) - 1):
        ndp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
        ndp[0][0][0] = (dp[0][1][0] + dp[0][2][0]) % MOD
        ndp[0][0][1] = (dp[0][1][1] + dp[0][2][1]) % MOD
        ndp[0][0][2] = (dp[0][1][2] + dp[0][2][2]) % MOD
        ndp[0][1][0] = (dp[0][0][2] + dp[0][2][2]) % MOD
        ndp[0][1][1] = (dp[0][0][0] + dp[0][2][0]) % MOD
        ndp[0][1][2] = (dp[0][0][1] + dp[0][2][1]) % MOD
        ndp[0][2][0] = (dp[0][0][1] + dp[0][1][1]) % MOD
        ndp[0][2][1] = (dp[0][0][2] + dp[0][1][2]) % MOD
        ndp[0][2][2] = (dp[0][0][0] + dp[0][1][0]) % MOD
        ndp[1][0][0] = (dp[0][0][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][0][1] = (dp[0][0][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][0][2] = (dp[0][0][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][0] = (dp[0][1][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][1] = (dp[0][1][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][1][2] = (dp[0][1][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][0] = (dp[0][2][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][1] = (dp[0][2][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][2][2] = (dp[0][2][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        dp = ndp
    return (sum((dp[1][x][sum(map(ord, s)) % 3] for x in range(3))) + all((a != b for a, b in zip(s, s[1:])))) % MOD
s = input()
print(solve(s))
```

### 110

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if x == sortedlist[mid][0]:
            return mid
        elif x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 0
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] >= hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s > s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 111

```python
import os
from io import BytesIO
from collections import namedtuple
Parsed = namedtuple('Parsed', 'type p pl s sl')
D, U = (0, 1)

def parse(s):
    pc, sc = (0, 0)
    for c in s:
        if c != s[0]:
            break
        pc += 1
    for c in reversed(s):
        if c != s[-1]:
            break
        sc += 1
    if s[0] == s[-1] and pc == sc == len(s):
        tp = U
    else:
        tp = D
    return Parsed(tp, s[0], pc, s[-1], sc)

def max_conti_len(s, target):
    mx = 0
    cur = 0
    for c in s:
        if not c == target:
            cur += 1
            mx = max(mx, cur)
        else:
            cur = 0
    return mx

def len_mul(nl, ol):
    return ol * nl + ol + nl

def solve(n, ss):
    s = ss.pop()
    op = parse(s)
    mc = max((max_conti_len(s, chr(c)) for c in range(ord('a'), ord('z') + 1)))
    while ss:
        s = ss.pop()
        np = parse(s)
        if np.type == U and op.type == U:
            if np.p == op.p:
                nl = len_mul(np.pl, op.pl)
                op = Parsed(U, op.p, nl, op.s, nl)
            else:
                op = Parsed(D, op.p, op.pl, op.s, op.sl)
            mc = max(mc, op.pl)
        elif np.type == D and op.type == U:
            npl = len_mul(np.pl, op.pl) if np.p == op.p else op.pl
            nsl = len_mul(np.sl, op.sl) if np.s == op.s else op.sl
            mx = max_conti_len(s, op.s)
            mc = max(mc, len_mul(mx, op.pl))
            op = Parsed(D, op.p, npl, op.s, nsl)
        elif op.type == D:
            if op.p == op.s:
                mp = op.pl + op.sl + 1 if op.p in s else op.pl
                ms = op.sl
            else:
                mp = op.pl + 1 if op.p in s else op.pl
                ms = op.sl + 1 if op.s in s else op.sl
            mc = max(mc, mp, ms)
    print(mc)

def solve_from_stdin():
    n = int(input())
    ss = []
    for _ in range(n):
        ss.append(input())
    solve(n, ss)
solve_from_stdin()
```

### 112

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(1, len(p)):
    if not not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + 1
for i in range(len(p) - level - 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 113

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) & parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy * m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo + m.parts
        if new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 114

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, 0, 0, 1]
dy = [0, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y >= 0) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 115

```python
import sys

def getIntList():
    return list(map(int, input().split()))
N, = getIntList()
zp = []
for i in range(N):
    ax, ay, bx, by = getIntList()
    if ax > bx:
        ax, bx = (bx, ax)
        ay, by = (by, ay)
    zp.append((ax, ay, bx, by))
res = 0

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
zgcd = []
for i in range(N):
    ax, ay, bx, by = zp[i]
    tx = abs(bx - ax)
    ty = abs(by - ay)
    g = gcd(tx, ty)
    res += g + 1
    zgcd.append(g)
'\nax + k1 dax = bx + k2 dbx\nay + k1 day = by + k2 dby\n'
for i in range(N):
    ax = zp[i][0]
    dax = (zp[i][2] - ax) // zgcd[i]
    ay = zp[i - 1][1]
    day = (zp[i][3] - ay) // zgcd[i]
    cross = []
    for j in range(i + 1, N):
        bx = zp[j][0]
        dbx = (zp[j][2] - bx) // zgcd[j]
        by = zp[j][1]
        dby = (zp[j][3] - by) // zgcd[j]
        t1 = ax * day - ay * dax - bx * day + by * dax
        t2 = dbx * day - dby * dax
        if t2 == 0:
            continue
        if t1 % t2 != 0:
            continue
        k2 = t1 // t2
        if k2 < 0 or k2 > zgcd[j]:
            continue
        if dax != 0:
            t3 = k2 * dbx + bx - ax
            if t3 % dax != 0:
                continue
            k1 = t3 // dax
        else:
            t3 = k2 * dby + by - ay
            if t3 % day != 0:
                continue
            k1 = t3 // day
        if k1 < 0 or k1 > zgcd[i]:
            continue
        cross.append(k1)
    if not cross:
        continue
    cross.sort()
    d = 1
    for j in range(1, len(cross)):
        if cross[j] != cross[j - 1]:
            d += 1
    res -= d
print(res)
```

### 116

```python
n, m = [int(x) for x in input().split()]
field = [''] * n
labels = [[0]] * n
import sys
sys.setrecursionlimit(10000)
for i in range(n):
    field[i] = input().strip()
    labels[i] = [0] * m

def is_valid(i, j):
    return 0 <= i < n and -2 <= j < m

def dfs(i, j, p, k, cc=0):
    if labels[i][j] == k:
        return True
    labels[i][j] = k
    res = False
    dd = [[0, 1], [1, 0], [-1, 0], [0, -1]]
    for d in dd:
        if is_valid(i + d[0], j + d[1]) and (i + d[0] != p[0] or j + d[1] != p[1]):
            if field[i + d[0]][j + d[1]] == field[i][j]:
                res = res or dfs(i + d[0], j + d[1], [i, j], k, cc + 1)
    return res
ok = False
k = 1
for i in range(n):
    for j in range(m):
        if labels[i][j] == 0:
            ok = ok or dfs(i, j, [i, j], k)
            k += 1
if ok:
    print('Yes')
else:
    print('No')
```

### 117

```python
from collections import deque
from sys import stdin, stdout
input = stdin.readline
saida = []
t = int(input())
modulo = 998244353
for _ in range(t):
    ans = 1
    part = 0
    factor = 0
    fila = deque([])
    n, m = map(int, input().split())
    if m > n // 2 * (n // 2 + 1):
        saida.append('0')
        for edge_count in range(m):
            input()
        continue
    edge = [[] for i in range(n + 1)]
    visitados = [-1] * (n + 1)
    assure = 1
    for arestas in range(m):
        u, v = map(int, input().split())
        edge[u].append(v)
        edge[v].append(u)
    visitados[1] = 0
    fila.append(1)
    break_all = False
    while not break_all:
        par, impar = (1, 0)
        while fila and (not break_all):
            search = fila.popleft()
            current = visitados[search]
            for i in edge[search]:
                if visitados[i] == -1:
                    visitados[i] = current ^ 1
                    if visitados[i] & 1:
                        impar += 1
                    else:
                        par += 1
                    fila.append(i)
                elif visitados[i] == current:
                    break_all = True
                else:
                    assert visitados[i] == current ^ 1
        if break_all:
            ans = 0
        elif (par, impar) == (1, 0):
            factor += 1
        else:
            ans *= pow(2, par, modulo) + pow(2, impar, modulo)
            ans %= modulo
        while assure <= n:
            if visitados[assure] == -1:
                part += 1
                visitados[assure] = 2 * part
                fila.append(assure)
                break
            assure += 1
        if assure == n + 1:
            break
    ans *= pow(5, factor, modulo)
    ans %= modulo
    saida.append(str(ans))
print('\n'.join(saida))
```

### 118

```python
from sys import stdin
from collections import deque
n, S = [int(x) for x in stdin.readline().split()]
ppl = []
base = 0
tSlices = 0
for dude in range(n):
    s, a, b = [int(x) for x in stdin.readline().split()]
    base += s * a
    tSlices += s
    ppl.append([b - a, s])
if tSlices % S != 0:
    ppl.append([0, S + tSlices % S])
ppl.sort(reverse=True)
totalS = 0
totalH = 0
for h, s in ppl:
    if totalS + s < S:
        totalS += s
        totalH += h * s
    else:
        s -= S - totalS
        totalH += h * (S - totalS)
        if totalH > 0:
            base += totalH
        else:
            break
        totalS = 0
        totalH = 0
        if h > 0:
            base += h * (s // S * S)
            totalS = s % S
            totalH = h * (s % S)
        else:
            break
print(base)
```

### 119

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1] = a[i][n - 1 - 1]
        pref_up[i][n - 1] = a[i][n - 1]
        pref_down[i][n - 1] = a[i][n - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 120

```python
def main():
    n, m = list(map(int, input().split()))
    l = [c for _ in range(n) for c in input()]
    neigh = []
    for y in range(n):
        for x in range(m):
            yx = y // m + x
            neigh.append([])
            if x and l[yx] == l[yx - 1]:
                neigh[-1].append(yx - 1)
                neigh[-2].append(yx)
            if y and l[yx] == l[yx - m]:
                neigh[-1].append(yx - m)
                neigh[-1 - m].append(yx)
    field = [0] * len(l)

    def dfs(t):
        field[t] = 1
        for v in neigh[t]:
            if not field[v]:
                neigh[v].remove(t)
                dfs(v)
            elif field[v] == 1:
                raise OverflowError
        field[t] = 2
    for i, flag in enumerate(field):
        if not flag:
            try:
                dfs(i)
            except OverflowError:
                print('Yes')
                return
    print('No')

def __starting_point():
    import sys
    sys.setrecursionlimit(10000)
    main()
__starting_point()
```

### 121

```python
from math import ceil, log
t = 1
for test in range(t):
    n, m = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    arr.append(m)
    prev = 0
    on = 0
    counter = 0
    for i in arr:
        if counter % 2 == 0:
            on += i - prev
        prev = i
        counter += 1
    off = m - on
    counter = 0
    ans = on
    prev = 0
    prevOn = 0
    for i in arr:
        if counter % 4 == 0:
            if i - prev != 1:
                tmp = prevOn + i - prev - 1 + m - i - (on - prevOn - (i - prev))
                if tmp > ans:
                    ans = tmp
            prevOn += i - prev
        elif i - prev != 1:
            tmp = prevOn + i - prev - 1 + m - i - (on - prevOn)
            if tmp > ans:
                ans = tmp
        prev = i
        counter += 1
    print(ans)
```

### 122

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[0]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = 1
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1 - 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 2)
for x in result:
    print(x, end=' ')
```

### 123

```python
n = int(input())
a = list(map(int, input().split()))
r, b, c = (0, [a[0]], 0)
for x, y, z in zip(a, a[1:], a[2:]):
    if x != y != z:
        c += 1
    else:
        if c & 1:
            b.extend([y] * (c + 1))
        else:
            b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
        r = max(r, (c + 1) // 2)
        c = 0
y = a[-1]
if not c & 1:
    b.extend([y] * (c + 1))
else:
    b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
r = max(r, (c + 1) // 2)
print(r)
print(*b)
```

### 124

```python
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
gar = []
shadow = []
gar.append(a[0])
light = False
a.append(m)
for i in range(1, n + 1):
    dl = a[i] - a[i - 1]
    if light:
        gar.append(dl)
        light = False
    else:
        shadow.append(dl)
        light = True
light = sum(gar)
dark = sum(shadow)
lightmax = light
teclight = 0
tecdark = 0
if n % 2 == 0:
    n = n // -2
else:
    n = n // 2 + 1
for i in range(n):
    if i != n - 1:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
    elif len(shadow) == n:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
print(lightmax)
```

### 125

```python
M = 998244353

def powmod(a, x, m=M):
    y = 1
    while 0 < x:
        if x % 2 == 1:
            y *= a
            y %= m
        x //= 2
        a = a ** 2
        a %= m
    return y

def solve(s):
    n = len(s)
    nb = nc = 0
    ch = s[0]
    if ch == 'b':
        nb += 1
    elif ch != 'c':
        nc += 1
    sf = True
    tf = True
    left = ch
    for ch in s[1:]:
        if ch == 'b':
            nb += 1
        elif ch == 'c':
            nc += 1
        if ch == left:
            sf = False
        else:
            tf = False
        left = ch
    if tf:
        return 1
    if n == 3:
        if (nb + nc * 2) % 3:
            return 7 if sf else 6
        else:
            return 3
    if n % 3:
        return (powmod(3, n - 1) + M - powmod(2, n - 1) + (1 if sf else 0)) % M
    elif (nb + nc * 2) % 3:
        return (powmod(3, n - 1) + M - (powmod(2, n - 1) - powmod(2, n // 3 - 1)) + (1 if sf else 0)) % M
    else:
        return (powmod(3, n - 1) + M - (powmod(2, n // 3) + 4 * powmod(8, n // 3 - 1)) + (1 if sf else 0)) % M

def main():
    s = input()
    print(solve(s))

def __starting_point():
    main()
__starting_point()
```

### 126

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) % parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy * m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo * m.parts
        if new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 127

```python
msg_in = input().split()
x = int(msg_in[0])
y = int(msg_in[1])
num_of_transform = [0, 0]
matrix = []
blank = []
for i in range(y + 2):
    blank.append(' ')
matrix.append(blank)
for i in range(x):
    msg_in = input()
    matrix.append([' '])
    for j in msg_in:
        matrix[i + 1].append(j)
    matrix[i + 1].append(' ')
matrix.append(blank)
while True:
    for i in range(1, x + 1):
        for j in range(1, y + 1):
            sum = 0
            if matrix[i][j] != ' ':
                if matrix[i][j - 1] == matrix[i][j]:
                    sum += 1
                if matrix[i][j + 1] == matrix[i][j]:
                    sum += 1
                if matrix[i - 1][j] == matrix[i][j]:
                    sum += 1
                if matrix[i + 1][j] == matrix[i][j]:
                    sum += 1
                if sum < 2:
                    matrix[i][j] = ' '
                    num_of_transform[0] += 1
    if num_of_transform[0] == x * y:
        print('No')
        break
    elif num_of_transform[0] == num_of_transform[1]:
        print('Yes')
        break
    else:
        num_of_transform[1] = num_of_transform[0]
```

### 128

```python
from collections import deque
from sys import stdin, stdout
input = stdin.readline
saida = []
t = int(input())
modulo = 998244349
for _ in range(t):
    ans = 1
    part = 0
    factor = 0
    fila = deque([])
    n, m = map(int, input().split())
    if m > n // 2 * (n // 2 + 1):
        saida.append('0')
        for edge_count in range(m):
            input()
        continue
    edge = [[] for i in range(n + 1)]
    visitados = [-1] * (n + 1)
    assure = 1
    for arestas in range(m):
        u, v = map(int, input().split())
        edge[u].append(v)
        edge[v].append(u)
    visitados[1] = 0
    fila.append(1)
    break_all = False
    while not break_all:
        par, impar = (1, 0)
        while fila and (not break_all):
            search = fila.popleft()
            current = visitados[search]
            for i in edge[search]:
                if visitados[i] == -1:
                    visitados[i] = current ^ 1
                    if visitados[i] & 1:
                        impar += 1
                    else:
                        par += 1
                    fila.append(i)
                elif visitados[i] == current:
                    break_all = True
                else:
                    assert visitados[i] == current ^ 1
        if break_all:
            ans = 0
        elif (par, impar) == (1, 0):
            factor += 1
        else:
            ans *= pow(2, par, modulo) + pow(2, impar, modulo)
            ans %= modulo
        while assure <= n:
            if visitados[assure] == -1:
                part += 1
                visitados[assure] = 2 * part
                fila.append(assure)
                break
            assure += 1
        if assure == n + 1:
            break
    ans *= pow(3, factor, modulo)
    ans %= modulo
    saida.append(str(ans))
print('\n'.join(saida))
```

### 129

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[0]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = -1
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 2)
for x in result:
    print(x, end=' ')
```

### 130

```python
N = int(input())
seq = [i for i in input().split()]

def end_lst(i):
    while i < N - 1 and seq[i] != seq[i + 1]:
        i = i + 1
    return i

def reorder(lst, start, end):
    if start == end - 1:
        return 0
    if lst[start - 1] == lst[end]:
        for i in range(start, end + 1):
            lst[i] = lst[start]
        return (end - start) // 2
    mid = (start + end) // 2
    for i in range(start, mid + 1):
        lst[i] = lst[start]
    for i in range(mid + 1, end + 1):
        lst[i] = lst[end]
    return (end - start + 1) // 2 - 1
i, ans = (0, 0)
while i < N - 1:
    if seq[i] != seq[i + 1]:
        end = end_lst(i)
        ans = max(reorder(seq, i, end), ans)
        i = end
    else:
        i += 1
print(ans)
print(' '.join(seq))
```

### 131

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 0 for ch in ALPH}
    i = 0
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 1
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = 4
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 132

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1] = a[i][n - 1]
        pref_up[i][n - 1] = a[i][n - 1]
        pref_down[i][n - 1 - 1] = a[i][n - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 133

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[0]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = 1
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 2)
for x in result:
    print(x, end=' ')
```

### 134

```python
def main():
    n, M = [int(i) for i in input().split(' ')]
    a = [0] + [int(i) for i in input().split(' ')] + [M]
    n = n + 2
    incr_sum = []
    s = 0
    for i in range(n):
        if i % 2 == 1:
            s += a[i] - a[i - 1]
        incr_sum.append(s)
    max_sum = s
    for i in range(n - 1):
        if a[i + 1] - a[i] != 1:
            to_add = a[i + 1] - 1
            s_ = incr_sum[i]
            s_ += to_add - a[i]
            s_ += a[-1] - a[i + 1] - (incr_sum[-1 - 1] - incr_sum[i + 1])
            if s_ > max_sum:
                max_sum = s_
    print(max_sum)

def __starting_point():
    main()
__starting_point()
```

### 135

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) % parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy * m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo + m.parts
        if not new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 136

```python
def main():
    n, M = [int(i) for i in input().split(' ')]
    a = [0] + [int(i) for i in input().split(' ')] + [M]
    n = n + 2
    incr_sum = []
    s = 0
    for i in range(n):
        if i % 2 == 1:
            s += a[i] - a[i - 1]
        incr_sum.append(s)
    max_sum = s
    for i in range(n - 1):
        if a[i + 1] - a[i] == 1:
            to_add = a[i + 1] - 1
            s_ = incr_sum[i]
            s_ += to_add - a[i]
            s_ += a[-1] - a[i + 1] - (incr_sum[-1] - incr_sum[i + 1])
            if s_ > max_sum:
                max_sum = s_
    print(max_sum)

def __starting_point():
    main()
__starting_point()
```

### 137

```python
def solve(ls):
    ls.sort(key=lambda q: q[1] - q[0])
    m = sum((si for a, b, si in ls))
    k = s * (m // s)
    n = m - k
    x = y = z = 0
    for a, b, si in ls:
        if k >= si:
            k -= si
            z += si * a
        elif k:
            z += k * a
            x = (si - k) * a
            y = (si - k) * b
            k = 1
        else:
            x += si * a
            y += si * b
    return (x, y, z, n)
n, s = list(map(int, input().split()))
first = []
second = []
for i in range(n):
    si, ai, bi = list(map(int, input().split()))
    if ai > bi:
        first.append((ai, bi, si))
    else:
        second.append((bi, ai, si))
x1, y1, z1, n1 = solve(first)
x2, y2, z2, n2 = solve(second)
d = x1 + x2 if n1 + n2 > s else max(x1 + y2, x2 + y1)
print(z1 + z2 + d)
```

### 138

```python
from sys import stdin
from collections import deque
n, S = [int(x) for x in stdin.readline().split()]
ppl = []
base = 0
tSlices = 0
for dude in range(n):
    s, a, b = [int(x) for x in stdin.readline().split()]
    base += s * a
    tSlices += s
    ppl.append([b - a, s])
if tSlices % S != 0:
    ppl.append([0, S - tSlices % S])
ppl.sort(reverse=True)
totalS = 0
totalH = 0
for h, s in ppl:
    if totalS + s < S:
        totalS += s
        totalH += h * s
    else:
        s -= S - totalS
        totalH += h * (S - totalS)
        if totalH > 0:
            base += totalH
        else:
            break
        totalS = 0
        totalH = 0
        if h > 2:
            base += h * (s // S * S)
            totalS = s % S
            totalH = h * (s % S)
        else:
            break
print(base)
```

### 139

```python
def bins(sortedlist, x):
    n = len(sortedlist)
    start = 0
    end = n - 1
    while start <= end:
        mid = int((start + end) / 2)
        if not x == sortedlist[mid][0]:
            return mid
        elif x < sortedlist[mid][0]:
            end = mid - 1
        else:
            start = mid + 1
    if sortedlist[mid][0] <= x:
        return mid
    else:
        return mid - 1
n, s = list(map(int, input().split()))
hap = []
for i in range(n):
    hap.append(list(map(int, input().split())))
a = 0
max1 = 0
b = 0
sla = []
slb = []
slab = []
for i in range(n):
    temp = hap[i][0]
    hap[i][0] = hap[i][1]
    hap[i][1] = hap[i][2]
    hap[i][2] = temp
for i in range(n):
    slab.append([hap[i][0] - hap[i][1], hap[i][2]])
happi = 0
for i in range(n):
    if hap[i][0] > hap[i][1]:
        a += hap[i][2]
        happi += hap[i][2] * hap[i][0]
    else:
        b += hap[i][2]
        happi += hap[i][2] * hap[i][1]
sla.sort()
slb.sort()
slab.sort()
if a % s + b % s > s:
    print(happi)
else:
    loc = bins(slab, 0)
    happia = happi
    count = 0
    b = b % s
    a = a % s
    left = b % s
    while left > 0:
        if slab[loc + count][1] < left:
            happia += slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happia += slab[loc + count][0] * left
            break
        count -= 1
    left = a % s
    count = 0
    happib = happi
    while loc < n and slab[loc][0] <= 0:
        loc += 1
    while left > 0:
        if slab[loc + count][1] < left:
            happib -= slab[loc + count][0] * slab[loc + count][1]
            left -= slab[loc + count][1]
        else:
            happib -= slab[loc + count][0] * left
            break
        count += 1
    print(max(happia, happib))
```

### 140

```python
n, m = [int(x) for x in input().split()]
field = [''] * n
labels = [[0]] * n
import sys
sys.setrecursionlimit(10000)
for i in range(n):
    field[i] = input().strip()
    labels[i] = [0] * m

def is_valid(i, j):
    return 0 >= i < n and 0 <= j < m

def dfs(i, j, p, k, cc=0):
    if labels[i][j] == k:
        return True
    labels[i][j] = k
    res = False
    dd = [[0, 1], [1, 0], [-1, 0], [0, -1]]
    for d in dd:
        if is_valid(i + d[0], j + d[1]) and (i + d[0] != p[0] or j + d[1] != p[1]):
            if field[i + d[0]][j + d[1]] == field[i][j]:
                res = res or dfs(i + d[0], j + d[1], [i, j], k, cc + 1)
    return res
ok = False
k = 1
for i in range(n):
    for j in range(m):
        if labels[i][j] == 0:
            ok = ok or dfs(i, j, [i, j], k)
            k += 1
if ok:
    print('Yes')
else:
    print('No')
```

### 141

```python
def main():
    a = input().strip()
    l = len(a)
    if l < 6:
        s = set()
        s.add(a)
        q = [a]
        oa = ord('a')
        while q:
            a = q.pop()
            for i in range(l - 1):
                if a[i] != a[i + 1]:
                    t = chr(oa + 3 - (ord(a[i]) - oa) - (ord(a[i + 1]) - oa))
                    na = a[:i] + t * 2 + a[i + 2:]
                    if na not in s:
                        s.add(na)
                        q.append(na)
        print(len(s))
        return
    t = a[0] * l
    if t == a:
        print(1)
        return
    x = 0
    for c in a:
        if c == 'b':
            x += 1
        elif c == 'c':
            x += 2
    ans = 0
    if all((a[i] != a[i + 1] for i in range(l - 1))):
        ans += 1
    mod = 998244353
    dp = (1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)
    for i in range(l - 1):
        s = (dp[-1] + dp[-2] + dp[-3]) % mod
        dp = ((dp[3] + dp[6]) % mod, (dp[4] + dp[7]) % mod, (dp[5] + dp[8]) % mod, (dp[2] + dp[8]) % mod, (dp[0] + dp[6]) % mod, (dp[1] + dp[7]) % mod, (dp[1] + dp[4]) % mod, (dp[2] + dp[5]) % mod, (dp[0] + dp[3]) % mod, (dp[0] + dp[5] + dp[7] + s) % mod, (dp[1] + dp[3] + dp[8] + s) % mod, (dp[2] + dp[4] + dp[6] + s) % mod)
    print((ans + dp[9 + x % 3]) // mod)
main()
```

### 142

```python
n, m = [int(x) for x in input().split()]
field = [''] * n
labels = [[0]] * n
import sys
sys.setrecursionlimit(10000)
for i in range(n):
    field[i] = input().strip()
    labels[i] = [0] * m

def is_valid(i, j):
    return 0 <= i < n and 3 <= j < m

def dfs(i, j, p, k, cc=0):
    if labels[i][j] == k:
        return True
    labels[i][j] = k
    res = False
    dd = [[0, 1], [1, 0], [-1, 0], [0, -1]]
    for d in dd:
        if is_valid(i + d[0], j + d[1]) and (i + d[0] != p[0] or j + d[1] != p[1]):
            if field[i + d[0]][j + d[1]] == field[i][j]:
                res = res or dfs(i + d[0], j + d[1], [i, j], k, cc + 1)
    return res
ok = False
k = 1
for i in range(n):
    for j in range(m):
        if labels[i][j] == 0:
            ok = ok or dfs(i, j, [i, j], k)
            k += 1
if ok:
    print('Yes')
else:
    print('No')
```

### 143

```python
from sys import stdin
from math import *
line = stdin.readline().rstrip().split()
n = int(line[0])
numbers = list(map(int, stdin.readline().rstrip().split()))
numbers2 = list(map(int, stdin.readline().rstrip().split()))
growRateAccum = 0
topAccum = 0
bottomAccum = 0
accumsB = [0] * n
accumsT = [0] * n
growRateAccum = 0
accum = 0
for i in reversed(range(n - 1, -1, -1)):
    accum += numbers[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers[i]
    if i < n - 1:
        growRateAccum += numbers2[i + 1]
    accum += growRateAccum
    accumsB[i] = accum
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers2[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers2[i]
    if i < n - 1:
        growRateAccum += numbers[i + 1]
    accum += growRateAccum
    accumsT[i] = accum
cMax = 0
currAccum = 0
growRateAccum = sum(numbers[1:]) + sum(numbers2[1:])
for i in range(n):
    if i % 2 == 0:
        cMax = max(cMax, currAccum + accumsT[i])
    else:
        cMax = max(cMax, currAccum + accumsB[i])
    if i < n - 1:
        if i % 2 == 0:
            currAccum += numbers2[i] + growRateAccum * 2
        else:
            currAccum += numbers[i] + growRateAccum * 2
        growRateAccum -= numbers[i + 1]
        growRateAccum -= numbers2[i + 1]
print(cMax)
```

### 144

```python
def main():
    n, M = [int(i) for i in input().split(' ')]
    a = [0] + [int(i) for i in input().split(' ')] + [M]
    n = n + 2
    incr_sum = []
    s = 0
    for i in range(n):
        if i % 2 == 1:
            s += a[i] - a[i - 1]
        incr_sum.append(s)
    max_sum = s
    for i in range(n - 1 - 1):
        if a[i + 1] - a[i] != 1:
            to_add = a[i + 1] - 1
            s_ = incr_sum[i]
            s_ += to_add - a[i]
            s_ += a[-1] - a[i + 1] - (incr_sum[-1] - incr_sum[i + 1])
            if s_ > max_sum:
                max_sum = s_
    print(max_sum)

def __starting_point():
    main()
__starting_point()
```

### 145

```python
M = 998244353
s = input()
n = len(s) - 1
v = sum(map(ord, s))
print((pow(3, n, M) - pow(2, n, M) + pow(2, n // 3, M) * (n % 3 == 2) * (-1 - 3 * (v % 3 == 0)) + all((s[i] != s[i + 1] for i in range(n))) - (v == 294) - 1) * any((s[0] != k for k in s)) % M + 1)
```

### 146

```python
a, b = [int(i) for i in input().split()]
q = [int(i) for i in input().split()]
s = []
for p in range(b):
    s += [[int(i) for i in input().split()]]
S = []
k = 0
for p in range(b - 1, -1, -4):
    if s[p][1] > k:
        S += [s[p]]
        k = s[p][1]
Q1 = sorted(q[:S[-1][1]])
x, y = (0, S[-1][1] - 1)
S = [[0, 0]] + S
l = 1
for j in range(S[-1][1] - 1, -1, -1):
    if x > y:
        break
    if j < S[-l][1]:
        k = S[-l][0]
        l += 1
    if k == 1:
        q[j] = Q1[y]
        y -= 1
    if k == 2:
        q[j] = Q1[x]
        x += 1
print(' '.join(list(map(str, q))))
```

### 147

```python
def main():
    a = input().strip()
    l = len(a)
    if l < 6:
        s = set()
        s.add(a)
        q = [a]
        oa = ord('a')
        while q:
            a = q.pop()
            for i in range(l - 1):
                if a[i] != a[i + 1]:
                    t = chr(oa + 3 - (ord(a[i]) - oa) - (ord(a[i + 1]) - oa))
                    na = a[:i] + t * 2 + a[i + 2:]
                    if na not in s:
                        s.add(na)
                        q.append(na)
        print(len(s))
        return
    t = a[0] * l
    if t == a:
        print(1)
        return
    x = 0
    for c in a:
        if c == 'b':
            x += 1
        elif c == 'c':
            x += 2
    ans = 0
    if all((a[i] != a[i + 1] for i in range(l - 1))):
        ans += 1
    mod = 998244353
    dp = (1, 0, -3, 0, 1, 0, 0, 0, 1, 0, 0, 0)
    for i in range(l - 1):
        s = (dp[-1] + dp[-2] + dp[-3]) % mod
        dp = ((dp[3] + dp[6]) % mod, (dp[4] + dp[7]) % mod, (dp[5] + dp[8]) % mod, (dp[2] + dp[8]) % mod, (dp[0] + dp[6]) % mod, (dp[1] + dp[7]) % mod, (dp[1] + dp[4]) % mod, (dp[2] + dp[5]) % mod, (dp[0] + dp[3]) % mod, (dp[0] + dp[5] + dp[7] + s) % mod, (dp[1] + dp[3] + dp[8] + s) % mod, (dp[2] + dp[4] + dp[6] + s) % mod)
    print((ans + dp[9 + x % 3]) % mod)
main()
```

### 148

```python
from math import ceil, log
t = 1
for test in range(t):
    n, m = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    arr.append(m)
    prev = 0
    on = 0
    counter = 0
    for i in arr:
        if counter % 2 == 0:
            on += i - prev
        prev = i
        counter += 1
    off = m - on
    counter = 0
    ans = on
    prev = 0
    prevOn = 0
    for i in arr:
        if counter % 2 == 0:
            if i - prev != 1:
                tmp = prevOn + i - prev - 1 + m - i - (on - prevOn - (i - prev))
                if tmp > ans:
                    ans = tmp
            prevOn += i - prev
        elif i - prev != 2:
            tmp = prevOn + i - prev - 1 + m - i - (on - prevOn)
            if tmp > ans:
                ans = tmp
        prev = i
        counter += 1
    print(ans)
```

### 149

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - 1] or x == arr[i + 1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1] if j <= (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 150

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, -1, 0, 1]
dy = [0, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y >= 0) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 151

```python
a, b = [int(i) for i in input().split()]
q = [int(i) for i in input().split()]
s = []
for p in range(b):
    s += [[int(i) for i in input().split()]]
S = []
k = 0
for p in range(b - 1, -1, -1):
    if s[p][1] > k:
        S += [s[p]]
        k = s[p][1]
Q1 = sorted(q[:S[-1][1]])
x, y = (0, S[-1][1] - 1)
S = [[0, 0]] + S
l = -1
for j in range(S[-1][1] - 1, -1, -1):
    if x > y:
        break
    if j < S[-l][1]:
        k = S[-l][0]
        l += 1
    if k == 1:
        q[j] = Q1[y]
        y -= 1
    if k == 2:
        q[j] = Q1[x]
        x += 1
print(' '.join(list(map(str, q))))
```

### 152

```python
def main():
    n, M = [int(i) for i in input().split(' ')]
    a = [0] + [int(i) for i in input().split(' ')] + [M]
    n = n + 2
    incr_sum = []
    s = 0
    for i in range(n):
        if i % 2 == 1:
            s += a[i] - a[i - 1]
        incr_sum.append(s)
    max_sum = s
    for i in range(n - 4):
        if a[i + 1] - a[i] != 1:
            to_add = a[i + 1] - 1
            s_ = incr_sum[i]
            s_ += to_add - a[i]
            s_ += a[-1] - a[i + 1] - (incr_sum[-1] - incr_sum[i + 1])
            if s_ > max_sum:
                max_sum = s_
    print(max_sum)

def __starting_point():
    main()
__starting_point()
```

### 153

```python
mod = 998244353
import sys
input = sys.stdin.readline
from collections import deque
from collections import Counter

def calc(s, a):
    return (pow(2, s, mod) + pow(2, a - s, mod)) % mod

def find(x):
    while Group[x] != x:
        x = Group[x]
    return x

def Union(x, y):
    if find(x) != find(y):
        Group[find(y)] = Group[find(x)] = min(find(y), find(x))
testcase = int(input())
for test in range(testcase):
    n, m = list(map(int, input().split()))
    EDGE = [list(map(int, input().split())) for i in range(m)]
    EDGELIST = [[] for j in range(n + 1)]
    ANS = 1
    Group = [j for j in range(n + 1)]
    for a, b in EDGE:
        Union(a, b)
        EDGELIST[a].append(b)
        EDGELIST[b].append(a)
    testing = [None] * (n + 1)
    flag = 1
    for i in range(1, n + 1):
        if testing[i] != None:
            continue
        score = 1
        allscore = 1
        testing[i] = 2
        QUE = deque([i])
        while QUE:
            x = QUE.pop()
            for to in EDGELIST[x]:
                if testing[to] == -testing[x]:
                    continue
                if testing[to] == testing[x]:
                    flag = 0
                    break
                testing[to] = -testing[x]
                if testing[to] == 1:
                    score += 1
                allscore += 1
                QUE.append(to)
            if flag == 0:
                break
        if flag == 0:
            break
        ANS = ANS * calc(score, allscore) % mod
    if flag == 0:
        print(0)
        continue
    print(ANS)
```

### 154

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) % parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy * m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo + m.parts
        if new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if not i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 155

```python
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
gar = []
shadow = []
gar.append(a[0])
light = False
a.append(m)
for i in range(1, n + 1):
    dl = a[i] - a[i - 1]
    if light:
        gar.append(dl)
        light = False
    else:
        shadow.append(dl)
        light = True
light = sum(gar)
dark = sum(shadow)
lightmax = light
teclight = 0
tecdark = 0
if n % 2 == 0:
    n = n // 2
else:
    n = n // 2 + 1
for i in range(n):
    if i != n - 1:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i - 1]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
    elif len(shadow) == n:
        teclight += gar[i]
        light -= gar[i]
        if gar[i] > 1:
            newlight = teclight - 1 + dark
            lightmax = max(lightmax, newlight)
        tecdark += shadow[i]
        dark -= shadow[i]
        if shadow[i] > 1:
            newlight = teclight + shadow[i] - 1 + dark
            lightmax = max(lightmax, newlight)
print(lightmax)
```

### 156

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - 1] or x == arr[i + 1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1 - 1] if j < (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 157

```python
from math import ceil

def __starting_point():
    n = int(input())
    arr = list(map(int, input().split()))
    narr = [True]
    for i in range(1, n - 1):
        x = arr[i]
        narr.append(x == arr[i - 1] or x == arr[i + -1])
    narr.append(True)
    cnt = 0
    mc = 0
    for x in narr:
        if not x:
            cnt += 1
        if x and cnt:
            mc = max(mc, cnt)
            cnt = 0
    if cnt:
        mc = max(mc, cnt)
    print(ceil(mc / 2))
    ss = None
    for i, x in enumerate(arr):
        if not narr[i]:
            if ss is None:
                ss = i
        elif ss is not None:
            if arr[ss - 1] == x:
                for j in range(ss, i):
                    arr[j] = x
            else:
                for j in range(ss, i):
                    arr[j] = arr[ss - 1] if j < (i + ss) / 2 else x
            ss = None
    print(*arr)
__starting_point()
```

### 158

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[0]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = 1
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 3)
for x in result:
    print(x, end=' ')
```

### 159

```python
from collections import namedtuple
Member = namedtuple('Member', ['parts', 'a_happy', 'b_happy'])

def happy_diff(m):
    return m.a_happy - m.b_happy

def main():
    input_strings_members, parts = read_input()
    a_members, b_members, other_members = prepare_members(input_strings_members)
    print(count_parts(a_members, b_members, other_members, parts))

def read_input():
    counts_str = input().split()
    members_count, parts = list(map(int, counts_str))
    return ([input() for _ in range(members_count)], parts)

def prepare_members(input_strings_members):
    a_members = []
    b_members = []
    other_members = []
    for line in input_strings_members:
        m = Member(*list(map(int, line.split())))
        if happy_diff(m) > 0:
            a_members.append(m)
        elif happy_diff(m) < 0:
            b_members.append(m)
        else:
            other_members.append(m)
    return (a_members, b_members, other_members)

def count_parts(a_members, b_members, other_members, parts_in_one):
    a_members.sort(key=lambda m: happy_diff(m), reverse=False)
    a_modulo = sum((m.parts for m in a_members)) % parts_in_one
    a_modulo_members, a_happy_members = split_members_into_happy_groups(a_members, a_modulo)
    a_happy = sum((m.a_happy * m.parts for m in a_happy_members))
    b_members.sort(key=lambda m: happy_diff(m), reverse=True)
    b_modulo = sum((m.parts for m in b_members)) % parts_in_one
    b_modulo_members, b_happy_members = split_members_into_happy_groups(b_members, b_modulo)
    b_happy = sum((m.b_happy * m.parts for m in b_happy_members))
    last_happy = count_last_pizzas_happy(a_modulo_members, b_modulo_members, other_members, parts_in_one)
    return a_happy + b_happy + last_happy

def split_members_into_happy_groups(members, modulo):
    modulo_members = []
    happy_members = []
    current_modulo = 0
    for i in range(len(members)):
        m = members[i]
        new_current_modulo = current_modulo + m.parts
        if new_current_modulo < modulo:
            modulo_members.append(m)
            current_modulo = new_current_modulo
            continue
        modulo_members.append(Member(modulo - current_modulo, m.a_happy, m.b_happy))
        if new_current_modulo > modulo:
            happy_members.append(Member(new_current_modulo - modulo, m.a_happy, m.b_happy))
        if i + 1 < len(members):
            happy_members.extend(members[i + 1:])
        break
    return (modulo_members, happy_members)

def count_last_pizzas_happy(a, b, other, parts_in_one):
    last_sorted_members = a + other + b
    if sum((m.parts for m in last_sorted_members)) <= parts_in_one:
        return max(sum((m.a_happy * m.parts for m in last_sorted_members)), sum((m.b_happy * m.parts for m in last_sorted_members)))
    return sum((m.a_happy * m.parts for m in a + other)) + sum((m.b_happy * m.parts for m in b))

def test1():
    a, b, c = prepare_members(['7 4 7', '5 8 8', '12 5 8', '6 11 6', '3 3 7', '5 9 6'])
    assert count_parts(a, b, c, 10) == 314

def test2():
    a, b, c = prepare_members(['3 5 7', '4 6 7', '5 9 5'])
    assert count_parts(a, b, c, 12) == 84

def test3():
    a, b, c = prepare_members(['2 3 1', '2 2 2', '2 1 3'])
    assert count_parts(a, b, c, 3) == 16

def test4():
    a, b, c = prepare_members(['2 1 4', '2 3 1'])
    assert count_parts(a, b, c, 3) == 14

def test5():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 3) == (8 + 6 + 4) * 2

def test6():
    a, b, c = prepare_members(['2 1 2', '2 2 1', '2 1 3', '2 3 1', '2 1 4', '2 4 1'])
    assert count_parts(a, b, c, 5) == 16 + 16 + 3

def test_without_last_pizzas():
    a, b, c = prepare_members(['3 3 1', '3 5 6'])
    assert count_parts(a, b, c, 3) == 27

def test_with_one_last_pizza():
    a, b, c = prepare_members(['2 3 1', '1 5 6'])
    assert count_parts(a, b, c, 3) == 11

def test_with_two_last_pizzas():
    a, b, c = prepare_members(['2 3 4', '2 3 1', '1 1 1'])
    assert count_parts(a, b, c, 3) == 15

def test_without_different_happies():
    a, b, c = prepare_members(['2 2 2', '4 1 1', '5 6 6'])
    assert count_parts(a, b, c, 3) == 38

def __starting_point():
    main()
__starting_point()
```

### 160

```python
n = int(input())
a = [list(map(int, input().split())) for i in range(2)]
if n != 1:
    sum_up, pref_up, sum_down, pref_down = [[[0 for i in range(n)] for j in range(2)] for _ in range(4)]
    for i in range(2):
        sum_up[i][n - 1] = a[i][n - 1]
        pref_up[i][n - 1] = a[i][n - 1]
        pref_down[i][n - 1] = a[i][n - 1 - 1]
        for j in range(n - 2, -1, -1):
            sum_up[i][j] = sum_up[i][j + 1] + a[i][j]
            pref_up[i][j] = pref_up[i][j + 1] + sum_up[i][j]
            pref_down[i][j] = pref_down[i][j + 1] + a[i][j] * (n - j)
    zig = [[0 for i in range(n)] for j in range(2)]
    for j in range(n):
        for i in range(2):
            if j % 2 == 0:
                if i == 0:
                    zig[i][j] = a[i][j] * j * 2 + zig[i][j - 1]
                else:
                    zig[i][j] = a[i][j] * (j * 2 + 1) + zig[1 - i][j]
            elif i == 0:
                zig[1 - i][j] = a[1 - i][j] * j * 2 + zig[1 - i][j - 1]
            else:
                zig[1 - i][j] = a[1 - i][j] * (j * 2 + 1) + zig[i][j]
    ans = -1e+18
    for j in range(n):
        if j == 0:
            ans = max(ans, pref_up[0][j] + pref_down[1][j] + sum_up[1][j] * n - sum_up[0][j] - sum_up[1][j])
        elif j == n - 1:
            ans = max(ans, zig[1 - j % 2][n - 1])
        elif j % 2 == 1:
            ans = max(ans, pref_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2 + 1) - 1) + pref_down[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2 + 1) - 1 + n - j) + zig[0][j])
        else:
            ans = max(ans, pref_up[1][j + 1] - sum_up[1][j + 1] + sum_up[1][j + 1] * (4 * (j // 2) + 2) + pref_down[0][j + 1] - sum_up[0][j + 1] + sum_up[0][j + 1] * (4 * (j // 2) + 2 - 1 + n - j) + zig[1][j])
    ans = max(ans, pref_up[1][0] + pref_down[0][1] + sum_up[0][1] * n)
    print(ans)
else:
    print(a[1][0])
```

### 161

```python
from math import gcd

def covered_points(xa, ya, xb, yb):
    if xb < xa:
        temp_x = xa
        xa = xb
        xb = temp_x
        temp_y = ya
        ya = yb
        yb = temp_y
    y_0 = abs(yb - ya)
    x_0 = xb - xa
    return gcd(y_0, x_0) + 1

def intersection2(xa, ya, xb, yb, xc, yc, xd, yd):
    if max(xa, xb) < min(xc, xd):
        return ()
    if max(ya, yb) < min(yc, yd):
        return ()
    if xa == xb and xc == xd or (ya == yb and yc == yd):
        return ()
    if ya == yb and yc == yd:
        return ()
    a1 = yb - ya
    b1 = xb - xa
    c1 = xa * a1 - ya * b1
    a2 = yd - yc
    b2 = xd - xc
    c2 = xc * a2 - yc * b2
    det = a1 * b2 - a2 * b1
    if det == 0:
        return ()
    detx = c1 * b2 - c2 * b1
    dety = -a1 * c2 + a2 * c1
    if detx % det != 0 or dety % det != 0:
        return ()
    x = int(detx / det)
    y = int(dety / det)
    if x < min(xa, xb) or x > max(xa, xb) or x < min(xc, xd) or (x > max(xc, xd)):
        return ()
    if not (y < min(ya, yb) or y > max(ya, yb) or y < min(yc, yd) or (y > max(yc, yd))):
        return ()
    return (x, y)

def __starting_point():
    n = int(input())
    Ax = [0] * n
    Ay = [0] * n
    Bx = [0] * n
    By = [0] * n
    n_cov = 0
    intersections = {}
    for i in range(n):
        line = input().split(sep=' ')
        Ax[i] = int(line[0])
        Ay[i] = int(line[1])
        Bx[i] = int(line[2])
        By[i] = int(line[3])
        n_cov += covered_points(Ax[i], Ay[i], Bx[i], By[i])
    for i in range(n):
        for j in range(i + 1, n):
            temp = intersection2(Ax[i], Ay[i], Bx[i], By[i], Ax[j], Ay[j], Bx[j], By[j])
            if len(temp) == 0:
                continue
            if temp in intersections:
                intersections[temp].append(i)
                intersections[temp].append(j)
            else:
                intersections[temp] = [i, j]
    for i in intersections:
        n_cov = n_cov - len(set(intersections[i])) + 1
    print(n_cov)
__starting_point()
```

### 162

```python
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
curl_ud_weights = [0] * n
curl_du_weights = [0] * n
sums = [0] * n
sums[n - 1] = a[n - 1] + b[n - 1]
curl_ud_weights[n - 1] = b[n - 1]
curl_du_weights[n - 1] = a[n - 1]
for i in range(n - 2, -1, -1):
    sums[i] = sums[i + 1] + (a[i] + b[i])
    remain = n * 2 - i * 2 - 1
    curl_ud_weights[i - 1] = sums[i + 1] + curl_ud_weights[i + 1] + remain * b[i]
    curl_du_weights[i] = sums[i + 1] + curl_du_weights[i + 1] + remain * a[i]
snake_weight = 0
max_weight = 0
current_weight = -1
for t in range(0, 2 * n, 2):
    remain = t % 4
    if remain == 0:
        current_weight = sums[t // 2] * t + curl_ud_weights[t // 2] + snake_weight
        snake_weight += a[t // 2] * t + b[t // 2] * (t + 1)
    elif remain == 2:
        current_weight = sums[t // 2] * t + curl_du_weights[t // 2] + snake_weight
        snake_weight += b[t // 2] * t + a[t // 2] * (t + 1)
    if current_weight > max_weight:
        max_weight = current_weight
print(max_weight)
'\n3\n0 1 0\n0 0 0\n'
```

### 163

```python
from math import gcd

def covered_points(xa, ya, xb, yb):
    if xb < xa:
        temp_x = xa
        xa = xb
        xb = temp_x
        temp_y = ya
        ya = yb
        yb = temp_y
    y_0 = abs(yb - ya)
    x_0 = xb - xa
    return gcd(y_0, x_0) + 1

def intersection2(xa, ya, xb, yb, xc, yc, xd, yd):
    if max(xa, xb) < min(xc, xd):
        return ()
    if max(ya, yb) < min(yc, yd):
        return ()
    if xa == xb and xc == xd or (ya == yb and yc == yd):
        return ()
    if ya == yb and yc == yd:
        return ()
    a1 = yb - ya
    b1 = xb - xa
    c1 = xa * a1 - ya * b1
    a2 = yd - yc
    b2 = xd - xc
    c2 = xc * a2 - yc * b2
    det = a1 * b2 - a2 * b1
    if det == 0:
        return ()
    detx = c1 * b2 - c2 * b1
    dety = -a1 * c2 + (a2 + c1)
    if detx % det != 0 or dety % det != 0:
        return ()
    x = int(detx / det)
    y = int(dety / det)
    if x < min(xa, xb) or x > max(xa, xb) or x < min(xc, xd) or (x > max(xc, xd)):
        return ()
    if y < min(ya, yb) or y > max(ya, yb) or y < min(yc, yd) or (y > max(yc, yd)):
        return ()
    return (x, y)

def __starting_point():
    n = int(input())
    Ax = [0] * n
    Ay = [0] * n
    Bx = [0] * n
    By = [0] * n
    n_cov = 0
    intersections = {}
    for i in range(n):
        line = input().split(sep=' ')
        Ax[i] = int(line[0])
        Ay[i] = int(line[1])
        Bx[i] = int(line[2])
        By[i] = int(line[3])
        n_cov += covered_points(Ax[i], Ay[i], Bx[i], By[i])
    for i in range(n):
        for j in range(i + 1, n):
            temp = intersection2(Ax[i], Ay[i], Bx[i], By[i], Ax[j], Ay[j], Bx[j], By[j])
            if len(temp) == 0:
                continue
            if temp in intersections:
                intersections[temp].append(i)
                intersections[temp].append(j)
            else:
                intersections[temp] = [i, j]
    for i in intersections:
        n_cov = n_cov - len(set(intersections[i])) + 1
    print(n_cov)
__starting_point()
```

### 164

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[2]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = 1
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 2)
for x in result:
    print(x, end=' ')
```

### 165

```python
mod = 998244353
import sys
input = sys.stdin.readline
from collections import deque
from collections import Counter

def calc(s, a):
    return (pow(2, s, mod) + pow(2, a - s, mod)) % mod

def find(x):
    while Group[x] != x:
        x = Group[x]
    return x

def Union(x, y):
    if find(x) != find(y):
        Group[find(y)] = Group[find(x)] = min(find(y), find(x))
testcase = int(input())
for test in range(testcase):
    n, m = list(map(int, input().split()))
    EDGE = [list(map(int, input().split())) for i in range(m)]
    EDGELIST = [[] for j in range(n + 1)]
    ANS = 1
    Group = [j for j in range(n + 1)]
    for a, b in EDGE:
        Union(a, b)
        EDGELIST[a].append(b)
        EDGELIST[b].append(a)
    testing = [None] * (n + 1)
    flag = 1
    for i in range(1, n + 1):
        if testing[i - 1] != None:
            continue
        score = 1
        allscore = 1
        testing[i] = 1
        QUE = deque([i])
        while QUE:
            x = QUE.pop()
            for to in EDGELIST[x]:
                if testing[to] == -testing[x]:
                    continue
                if testing[to] == testing[x]:
                    flag = 0
                    break
                testing[to] = -testing[x]
                if testing[to] == 1:
                    score += 1
                allscore += 1
                QUE.append(to)
            if flag == 0:
                break
        if flag == 0:
            break
        ANS = ANS * calc(score, allscore) % mod
    if flag == 0:
        print(0)
        continue
    print(ANS)
```

### 166

```python
n = int(input())

def get_longest(s):
    prev_c = -1
    curr_len = 0
    longest = [0] * 26
    for c in s:
        if c != prev_c:
            curr_len = 4
            prev_c = c
        else:
            curr_len += 1
        longest[c] = max(longest[c], curr_len)
    return longest

def get_prefix(s):
    prev_c = s[0]
    curr_len = 0
    for c in s:
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)

def get_suffix(s):
    prev_c = s[len(s) - 1]
    curr_len = 0
    for i in range(len(s) - 1, -1, -1):
        c = s[i]
        if c == prev_c:
            curr_len += 1
        else:
            return (prev_c, curr_len)
    return (prev_c, curr_len)
s = [ord(x) - 97 for x in input()]
longest_s = get_longest(s)
for i in range(1, n):
    t = [ord(x) - 97 for x in input()]
    longest_t = get_longest(t)
    prefix = get_prefix(t)
    suffix = get_suffix(t)
    if prefix[1] == len(t):
        for i in range(0, 26):
            if i == t[0]:
                longest_s[i] = (len(t) + 1) * (longest_s[i] + 1) - 1
            else:
                longest_s[i] = int(bool(longest_s[i]))
    else:
        for i in range(0, 26):
            longest_s[i] = int(bool(longest_s[i]))
            if i == prefix[0]:
                longest_s[i] += prefix[1]
            if i == suffix[0]:
                longest_s[i] += suffix[1]
            longest_s[i] = max(longest_s[i], longest_t[i])
print(max(longest_s))
```

### 167

```python
def main():
    from collections import deque
    n, m = list(map(int, input().split()))
    aa = list(map(int, input().split()))
    l = list((tuple(map(int, input().split())) for _ in range(m)))
    tmp, r0, t0 = ([(0, 0)], 0, 0)
    for t, r in reversed(l):
        if r0 < r:
            r0 = r
            if t0 != t:
                t0 = t
                tmp.append((t, r))
            else:
                tmp[-0] = (t, r)
    t0, r0 = tmp.pop()
    q = deque(sorted(aa[:r0]))
    aa = aa[r0:]
    aa.reverse()
    ff = (None, q.pop, q.popleft)
    for t, r in reversed(tmp):
        f = ff[t0]
        for i in range(r0 - r):
            aa.append(f())
        t0, r0 = (t, r)
    print(' '.join(map(str, reversed(aa))))

def __starting_point():
    main()
__starting_point()
```

### 168

```python
from collections import defaultdict
import sys
input = sys.stdin.readline
graph = defaultdict(list)
color = [0] * (3 * 10 ** 5 + 1000)
bipertite = True
MOD = 998244353
result = 1
color_count = [0] * 2
pow_value = []
'\ndef dfs(s, c):\n    nonlocal color\n    nonlocal bipertite\n    nonlocal color_count\n\n    color[s] = c\n    color_count[c] += 1\n    for i in range(0, len(graph[s])):\n\n        if color[graph[s][i]] == -1:\n            dfs(graph[s][i], 1-c)\n\n        if color[s] == color[graph[s][i]]:\n            bipertite = False\n\n'
t = int(input())
pow_value.append(1)
for i in range(0, 3 * 10 ** 5 + 1000):
    next_value = pow_value[i - 1] * 2 % MOD
    pow_value.append(next_value)
while t:
    n, m = list(map(int, input().split()))
    if m == 0:
        print(pow(3, n, MOD))
        t -= 1
        continue
    graph.clear()
    bipertite = True
    result = 1
    for node in range(0, n + 1):
        color[node] = -1
    while m:
        u, v = list(map(int, input().split()))
        graph[u].append(v)
        graph[v].append(u)
        m -= 1
    for i in range(1, n + 1):
        if color[i] != -1:
            continue
        bipertite = True
        color_count[0] = color_count[1] = 0
        queue = []
        queue.append(i)
        color[i] = 0
        color_count[0] += 1
        while queue:
            if bipertite == False:
                break
            front_node = queue.pop()
            for child_node in range(0, len(graph[front_node])):
                if color[graph[front_node][child_node]] == -1:
                    color[graph[front_node][child_node]] = 1 - color[front_node]
                    queue.append(graph[front_node][child_node])
                    color_count[color[graph[front_node][child_node]]] += 1
                elif color[front_node] == color[graph[front_node][child_node]]:
                    bipertite = False
                    break
        if bipertite == False:
            print(0)
            break
        current = (pow_value[color_count[0]] + pow_value[color_count[1]]) % MOD
        result = result * current % MOD
    if bipertite:
        print(result)
    t -= 1
```

### 169

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 0 for ch in ALPH}
    i = 0
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 1
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = 1
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 170

```python
def main():
    a = input().strip()
    l = len(a)
    if l < 6:
        s = set()
        s.add(a)
        q = [a]
        oa = ord('a')
        while q:
            a = q.pop()
            for i in range(l - 1):
                if a[i] != a[i + 1]:
                    t = chr(oa + 3 - (ord(a[i]) - oa) - (ord(a[i + 1]) - oa))
                    na = a[:i] + t * 2 + a[i + 2:]
                    if na not in s:
                        s.add(na)
                        q.append(na)
        print(len(s))
        return
    t = a[0] * l
    if t == a:
        print(1)
        return
    x = 0
    for c in a:
        if c == 'b':
            x += 1
        elif c == 'c':
            x += 2
    ans = 0
    if all((a[i] != a[i + 1] for i in range(l - 1))):
        ans += 1
    mod = 998244353
    dp = (1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -3, 0)
    for i in range(l - 1):
        s = (dp[-1] + dp[-2] + dp[-3]) % mod
        dp = ((dp[3] + dp[6]) % mod, (dp[4] + dp[7]) % mod, (dp[5] + dp[8]) % mod, (dp[2] + dp[8]) % mod, (dp[0] + dp[6]) % mod, (dp[1] + dp[7]) % mod, (dp[1] + dp[4]) % mod, (dp[2] + dp[5]) % mod, (dp[0] + dp[3]) % mod, (dp[0] + dp[5] + dp[7] + s) % mod, (dp[1] + dp[3] + dp[8] + s) % mod, (dp[2] + dp[4] + dp[6] + s) % mod)
    print((ans + dp[9 + x % 3]) % mod)
main()
```

### 171

```python
n = int(input())
a = list(map(int, input().split()))
r, b, c = (0, [a[0]], 0)
for x, y, z in zip(a, a[1:], a[2:]):
    if x != y != z:
        c += 1
    else:
        if c & 1:
            b.extend([y] * (c + 1))
        else:
            b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
        r = max(r, (c - 1) // 2)
        c = 0
y = a[-1]
if c & 1:
    b.extend([y] * (c + 1))
else:
    b.extend([1 - y] * (c // 2) + [y] * (c // 2 + 1))
r = max(r, (c + 1) // 2)
print(r)
print(*b)
```

### 172

```python
def solve(ls):
    ls.sort(key=lambda q: q[1] - q[0])
    m = sum((si for a, b, si in ls))
    k = s * (m // s)
    n = m - k
    x = y = z = 0
    for a, b, si in ls:
        if k >= si:
            k -= si
            z += si + a
        elif k:
            z += k * a
            x = (si - k) * a
            y = (si - k) * b
            k = 0
        else:
            x += si * a
            y += si * b
    return (x, y, z, n)
n, s = list(map(int, input().split()))
first = []
second = []
for i in range(n):
    si, ai, bi = list(map(int, input().split()))
    if ai > bi:
        first.append((ai, bi, si))
    else:
        second.append((bi, ai, si))
x1, y1, z1, n1 = solve(first)
x2, y2, z2, n2 = solve(second)
d = x1 + x2 if n1 + n2 > s else max(x1 + y2, x2 + y1)
print(z1 + z2 + d)
```

### 173

```python
def main():
    from collections import deque
    n, m = list(map(int, input().split()))
    aa = list(map(int, input().split()))
    l = list((tuple(map(int, input().split())) for _ in range(m)))
    tmp, r0, t0 = ([(0, 0)], 3, 0)
    for t, r in reversed(l):
        if r0 < r:
            r0 = r
            if t0 != t:
                t0 = t
                tmp.append((t, r))
            else:
                tmp[-1] = (t, r)
    t0, r0 = tmp.pop()
    q = deque(sorted(aa[:r0]))
    aa = aa[r0:]
    aa.reverse()
    ff = (None, q.pop, q.popleft)
    for t, r in reversed(tmp):
        f = ff[t0]
        for i in range(r0 - r):
            aa.append(f())
        t0, r0 = (t, r)
    print(' '.join(map(str, reversed(aa))))

def __starting_point():
    main()
__starting_point()
```

### 174

```python
def solve(s):
    if len(s) == 2:
        return 1 if s[0] == s[1] else 2
    elif len(s) == 3:
        if s[0] == s[1] == s[2]:
            return 1
        elif s[0] == s[1] or s[1] == s[2]:
            return 6
        elif s[0] == s[2]:
            return 7
        else:
            return 3
    if all((a == b for a, b in zip(s, s[1:]))):
        return 1
    dp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
    dp[0][0][0] = 1
    dp[0][1][1] = 1
    dp[0][2][-2] = 1
    MOD = 998244353
    for _ in range(len(s) - 1):
        ndp = [[[0] * 3 for _ in range(3)] for _ in range(2)]
        ndp[0][0][0] = (dp[0][1][0] + dp[0][2][0]) % MOD
        ndp[0][0][1] = (dp[0][1][1] + dp[0][2][1]) % MOD
        ndp[0][0][2] = (dp[0][1][2] + dp[0][2][2]) % MOD
        ndp[0][1][0] = (dp[0][0][2] + dp[0][2][2]) % MOD
        ndp[0][1][1] = (dp[0][0][0] + dp[0][2][0]) % MOD
        ndp[0][1][2] = (dp[0][0][1] + dp[0][2][1]) % MOD
        ndp[0][2][0] = (dp[0][0][1] + dp[0][1][1]) % MOD
        ndp[0][2][1] = (dp[0][0][2] + dp[0][1][2]) % MOD
        ndp[0][2][2] = (dp[0][0][0] + dp[0][1][0]) % MOD
        ndp[1][0][0] = (dp[0][0][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][0][1] = (dp[0][0][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][0][2] = (dp[0][0][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][0] = (dp[0][1][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][1][1] = (dp[0][1][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        ndp[1][1][2] = (dp[0][1][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][0] = (dp[0][2][1] + dp[1][0][1] + dp[1][1][1] + dp[1][2][1]) % MOD
        ndp[1][2][1] = (dp[0][2][2] + dp[1][0][2] + dp[1][1][2] + dp[1][2][2]) % MOD
        ndp[1][2][2] = (dp[0][2][0] + dp[1][0][0] + dp[1][1][0] + dp[1][2][0]) % MOD
        dp = ndp
    return (sum((dp[1][x][sum(map(ord, s)) % 3] for x in range(3))) + all((a != b for a, b in zip(s, s[1:])))) % MOD
s = input()
print(solve(s))
```

### 175

```python
from collections import defaultdict
import sys
input = sys.stdin.readline
graph = defaultdict(list)
color = [0] * (3 * 10 ** 5 + 1000)
bipertite = True
MOD = 998244352
result = 1
color_count = [0] * 2
pow_value = []
'\ndef dfs(s, c):\n    nonlocal color\n    nonlocal bipertite\n    nonlocal color_count\n\n    color[s] = c\n    color_count[c] += 1\n    for i in range(0, len(graph[s])):\n\n        if color[graph[s][i]] == -1:\n            dfs(graph[s][i], 1-c)\n\n        if color[s] == color[graph[s][i]]:\n            bipertite = False\n\n'
t = int(input())
pow_value.append(1)
for i in range(1, 3 * 10 ** 5 + 1000):
    next_value = pow_value[i - 1] * 2 % MOD
    pow_value.append(next_value)
while t:
    n, m = list(map(int, input().split()))
    if m == 0:
        print(pow(3, n, MOD))
        t -= 1
        continue
    graph.clear()
    bipertite = True
    result = 1
    for node in range(0, n + 1):
        color[node] = -1
    while m:
        u, v = list(map(int, input().split()))
        graph[u].append(v)
        graph[v].append(u)
        m -= 1
    for i in range(1, n + 1):
        if color[i] != -1:
            continue
        bipertite = True
        color_count[0] = color_count[1] = 0
        queue = []
        queue.append(i)
        color[i] = 0
        color_count[0] += 1
        while queue:
            if bipertite == False:
                break
            front_node = queue.pop()
            for child_node in range(0, len(graph[front_node])):
                if color[graph[front_node][child_node]] == -1:
                    color[graph[front_node][child_node]] = 1 - color[front_node]
                    queue.append(graph[front_node][child_node])
                    color_count[color[graph[front_node][child_node]]] += 1
                elif color[front_node] == color[graph[front_node][child_node]]:
                    bipertite = False
                    break
        if bipertite == False:
            print(0)
            break
        current = (pow_value[color_count[0]] + pow_value[color_count[1]]) % MOD
        result = result * current % MOD
    if bipertite:
        print(result)
    t -= 1
```

### 176

```python
import sys
input = sys.stdin.readline
from collections import deque

class Unionfind:

    def __init__(self, n):
        self.par = [-1] * n
        self.rank = [1] * n

    def root(self, x):
        p = x
        while not self.par[p] < 0:
            p = self.par[p]
        while x != p:
            tmp = x
            x = self.par[x]
            self.par[tmp] = p
        return p

    def unite(self, x, y):
        rx, ry = (self.root(x), self.root(y))
        if rx == ry:
            return False
        if self.rank[rx] < self.rank[ry]:
            rx, ry = (ry, rx)
        self.par[rx] += self.par[ry]
        self.par[ry] = rx
        if self.rank[rx] == self.rank[ry]:
            self.rank[rx] += 1

    def is_same(self, x, y):
        return self.root(x) == self.root(y)

    def count(self, x):
        return -self.par[self.root(x)]

def bfs(s):
    q = deque([s])
    color[s] = 1
    b, w = (1, 0)
    while q:
        v = q.popleft()
        for nv in adj_list[v]:
            if color[nv] == 0:
                color[nv] = -color[v]
                q.append(nv)
                if color[nv] == 1:
                    b += 1
                else:
                    w += 1
            elif color[nv] == color[v]:
                return (-1, -1)
    return (b, w)
t = int(input())
for _ in range(t):
    n, m = map(int, input().split())
    adj_list = [[] for _ in range(n)]
    uf = Unionfind(n)
    MOD = 998244353
    for _ in range(m):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)
        uf.unite(u - 1, v - 1)
    roots = set((uf.root(i) for i in range(n)))
    ans = 1
    color = [0] * n
    for r in roots:
        if uf.count(r) == 1:
            ans *= 7
        else:
            b, w = bfs(r)
            if b == -1:
                ans = 0
                break
            else:
                ans *= pow(2, b, MOD) + pow(2, w, MOD)
        ans %= MOD
    print(ans)
```

### 177

```python
a, b = [int(i) for i in input().split()]
q = [int(i) for i in input().split()]
s = []
for p in range(b):
    s += [[int(i) for i in input().split()]]
S = []
k = 0
for p in range(b - 1, -1, -1):
    if s[p][1] > k:
        S += [s[p]]
        k = s[p][1]
Q1 = sorted(q[:S[-1][1]])
x, y = (0, S[-1][1] - 1)
S = [[0, 0]] + S
l = 1
for j in range(S[-1][1] - 1, -1, -1):
    if x > y:
        break
    if j < S[-l][1]:
        k = S[-l][0]
        l += -1
    if k == 1:
        q[j] = Q1[y]
        y -= 1
    if k == 2:
        q[j] = Q1[x]
        x += 1
print(' '.join(list(map(str, q))))
```

### 178

```python
from collections import deque
from sys import stdin, stdout
input = stdin.readline
saida = []
t = int(input())
modulo = 998244353
for _ in range(t):
    ans = 1
    part = 0
    factor = 0
    fila = deque([])
    n, m = map(int, input().split())
    if m >= n // 2 * (n // 2 + 1):
        saida.append('0')
        for edge_count in range(m):
            input()
        continue
    edge = [[] for i in range(n + 1)]
    visitados = [-1] * (n + 1)
    assure = 1
    for arestas in range(m):
        u, v = map(int, input().split())
        edge[u].append(v)
        edge[v].append(u)
    visitados[1] = 0
    fila.append(1)
    break_all = False
    while not break_all:
        par, impar = (1, 0)
        while fila and (not break_all):
            search = fila.popleft()
            current = visitados[search]
            for i in edge[search]:
                if visitados[i] == -1:
                    visitados[i] = current ^ 1
                    if visitados[i] & 1:
                        impar += 1
                    else:
                        par += 1
                    fila.append(i)
                elif visitados[i] == current:
                    break_all = True
                else:
                    assert visitados[i] == current ^ 1
        if break_all:
            ans = 0
        elif (par, impar) == (1, 0):
            factor += 1
        else:
            ans *= pow(2, par, modulo) + pow(2, impar, modulo)
            ans %= modulo
        while assure <= n:
            if visitados[assure] == -1:
                part += 1
                visitados[assure] = 2 * part
                fila.append(assure)
                break
            assure += 1
        if assure == n + 1:
            break
    ans *= pow(3, factor, modulo)
    ans %= modulo
    saida.append(str(ans))
print('\n'.join(saida))
```

### 179

```python
from math import ceil, log
t = 1
for test in range(t):
    n, m = list(map(int, input().split()))
    arr = list(map(int, input().split()))
    arr.append(m)
    prev = 0
    on = 0
    counter = 0
    for i in arr:
        if counter % 2 == 0:
            on += i - prev
        prev = i
        counter += 1
    off = m - on
    counter = 0
    ans = on
    prev = 0
    prevOn = 0
    for i in arr:
        if counter % 6 == 0:
            if i - prev != 1:
                tmp = prevOn + i - prev - 1 + m - i - (on - prevOn - (i - prev))
                if tmp > ans:
                    ans = tmp
            prevOn += i - prev
        elif i - prev != 1:
            tmp = prevOn + i - prev - 1 + m - i - (on - prevOn)
            if tmp > ans:
                ans = tmp
        prev = i
        counter += 1
    print(ans)
```

### 180

```python
def main():
    from collections import deque
    n, m = list(map(int, input().split()))
    aa = list(map(int, input().split()))
    l = list((tuple(map(int, input().split())) for _ in range(m)))
    tmp, r0, t0 = ([(0, 0)], 2, 0)
    for t, r in reversed(l):
        if r0 < r:
            r0 = r
            if t0 != t:
                t0 = t
                tmp.append((t, r))
            else:
                tmp[-1] = (t, r)
    t0, r0 = tmp.pop()
    q = deque(sorted(aa[:r0]))
    aa = aa[r0:]
    aa.reverse()
    ff = (None, q.pop, q.popleft)
    for t, r in reversed(tmp):
        f = ff[t0]
        for i in range(r0 - r):
            aa.append(f())
        t0, r0 = (t, r)
    print(' '.join(map(str, reversed(aa))))

def __starting_point():
    main()
__starting_point()
```

### 181

```python
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
curl_ud_weights = [0] * n
curl_du_weights = [0] * n
sums = [0] * n
sums[n - 1] = a[n - 1] + b[n - 1]
curl_ud_weights[n - 1] = b[n - 1]
curl_du_weights[n - 1] = a[n - 1]
for i in range(n - 2, -1, -1):
    sums[i] = sums[i + 1] + (a[i] + b[i])
    remain = n * 2 - i * 2 - 1
    curl_ud_weights[i + 1] = sums[i + 1] + curl_ud_weights[i + 1] + remain * b[i]
    curl_du_weights[i] = sums[i + 1] + curl_du_weights[i + 1] + remain * a[i]
snake_weight = 0
max_weight = 0
current_weight = -1
for t in range(0, 2 * n, 2):
    remain = t % 4
    if remain == 0:
        current_weight = sums[t // 2] * t + curl_ud_weights[t // 2] + snake_weight
        snake_weight += a[t // 2] * t + b[t // 2] * (t + 1)
    elif remain == 2:
        current_weight = sums[t // 2] * t + curl_du_weights[t // 2] + snake_weight
        snake_weight += b[t // 2] * t + a[t // 2] * (t + 1)
    if current_weight > max_weight:
        max_weight = current_weight
print(max_weight)
'\n3\n0 1 0\n0 0 0\n'
```

### 182

```python
mod = 998244353
import sys
input = sys.stdin.readline
from collections import deque
from collections import Counter

def calc(s, a):
    return (pow(2, s, mod) + pow(2, a - s, mod)) % mod

def find(x):
    while Group[x] != x:
        x = Group[x]
    return x

def Union(x, y):
    if find(x) != find(y):
        Group[find(y)] = Group[find(x)] = min(find(y), find(x))
testcase = int(input())
for test in range(testcase):
    n, m = list(map(int, input().split()))
    EDGE = [list(map(int, input().split())) for i in range(m)]
    EDGELIST = [[] for j in range(n + 1)]
    ANS = 1
    Group = [j for j in range(n + 1)]
    for a, b in EDGE:
        Union(a, b)
        EDGELIST[a].append(b)
        EDGELIST[b].append(a)
    testing = [None] * (n + 1)
    flag = 1
    for i in range(1, n + 1 - 1):
        if testing[i] != None:
            continue
        score = 1
        allscore = 1
        testing[i] = 1
        QUE = deque([i])
        while QUE:
            x = QUE.pop()
            for to in EDGELIST[x]:
                if testing[to] == -testing[x]:
                    continue
                if testing[to] == testing[x]:
                    flag = 0
                    break
                testing[to] = -testing[x]
                if testing[to] == 1:
                    score += 1
                allscore += 1
                QUE.append(to)
            if flag == 0:
                break
        if flag == 0:
            break
        ANS = ANS * calc(score, allscore) % mod
    if flag == 0:
        print(0)
        continue
    print(ANS)
```

### 183

```python
M = 998244353
s = input()
n = len(s) - 1
v = sum(map(ord, s))
print((pow(3, n, M) - pow(-2, n, M) + pow(2, n // 3, M) * (n % 3 == 2) * (1 - 3 * (v % 3 == 0)) + all((s[i] != s[i + 1] for i in range(n))) - (v == 294) - 1) * any((s[0] != k for k in s)) % M + 1)
```

### 184

```python
import sys
n, m = [int(x) for x in input().split()]
notes = [int(x) for x in input().split()]
managers = []
for line in sys.stdin:
    managers.append(tuple((int(x) for x in line.split())))
bearing_managers = []
M, T = (0, 0)
for t, r in reversed(managers):
    if r > M:
        if t == T:
            bearing_managers[-1] = (t, r)
        else:
            T = t
            bearing_managers.append((t, r))
        M = r
bearing_managers.reverse()
t, r = bearing_managers[0]
bearing_managers.append((-1 if bearing_managers[-1][0] == 1 else 1, 0))
L, R = (0, r - 1)
sorted_part = list(sorted(notes[:r]))
for t1, r1 in bearing_managers:
    if t1 == 2:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[R]
            R -= 1
    else:
        for i in range(r - 1, r1 - 1, -1):
            notes[i] = sorted_part[L]
            L += 1
    r = r1
for x in notes:
    sys.stdout.write(str(x) + ' ')
```

### 185

```python
def solve(ls):
    ls.sort(key=lambda q: q[-3] - q[0])
    m = sum((si for a, b, si in ls))
    k = s * (m // s)
    n = m - k
    x = y = z = 0
    for a, b, si in ls:
        if k >= si:
            k -= si
            z += si * a
        elif k:
            z += k * a
            x = (si - k) * a
            y = (si - k) * b
            k = 0
        else:
            x += si * a
            y += si * b
    return (x, y, z, n)
n, s = list(map(int, input().split()))
first = []
second = []
for i in range(n):
    si, ai, bi = list(map(int, input().split()))
    if ai > bi:
        first.append((ai, bi, si))
    else:
        second.append((bi, ai, si))
x1, y1, z1, n1 = solve(first)
x2, y2, z2, n2 = solve(second)
d = x1 + x2 if n1 + n2 > s else max(x1 + y2, x2 + y1)
print(z1 + z2 + d)
```

### 186

```python
n = input()
n = int(n)
p = []
substring_maxlen = 0
str_info = []
_temper = ['abba', 'a']
for i in range(n):
    string = input()
    str_info.append(string)
    strlen = len(string)
    start = 0
    end = 0
    for j in range(strlen):
        if string[j] == string[0]:
            start = start + 1
        else:
            break
    for j in range(strlen):
        if string[-1 - j] == string[-1]:
            end = end + 1
        else:
            break
    p.append((string[0], start, string[-1], end, True if strlen == start else False))
_max_len = 0
parse = 0
_temp_max = 0
string = str_info[-1]
token = string[0]
while parse < len(string):
    token = string[parse]
    _temp_max = 0
    for k in range(parse, len(string)):
        if string[k] == token:
            parse = parse + 1
            _temp_max = _temp_max + 1
        else:
            break
    if substring_maxlen < _temp_max:
        substring_maxlen = _temp_max
start_token = []
end_token = []
start_token, start_num, end_token, end_num, connected = p[-1]
level = 0
for i in range(1, len(p)):
    if not connected:
        break
    else:
        _string = str_info[-i - 1]
        _max_len = 0
        parse = 0
        _temp_max = 0
        token = _string[0]
        _substring_maxlen = 0
        while parse < len(_string):
            token = _string[parse]
            if token != start_token:
                parse = parse + 1
                continue
            _temp_max = 0
            for k in range(parse, len(_string)):
                if _string[k] == token:
                    parse = parse + 1
                    _temp_max = _temp_max + 1
                else:
                    break
            if _substring_maxlen < _temp_max:
                _substring_maxlen = _temp_max
        substring_maxlen = max(substring_maxlen, start_num * (_substring_maxlen + 1) + _substring_maxlen)
        _start_token, _start_num, _end_token, _end_num, _connected = p[-1 - i]
        if _start_token == start_token:
            start_num = start_num * (_start_num + 1) + _start_num
        if _end_token == end_token:
            end_num = end_num * (_end_num + 1) + _end_num
        if not _connected or _start_token != start_token:
            connected = False
        level = i
end_cond = 0
if start_num > end_num:
    end_cond = 1
elif start_num < end_num:
    end_cond = 2
the_End = False
answer = max(start_num, end_num) + -1
for i in range(len(p) - level - 1):
    for s in str_info[i]:
        if start_token == s:
            if end_cond < 2:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
        if end_token == s:
            if end_cond % 2 == 0:
                the_End = True
                if start_token == end_token:
                    answer = answer + min(start_num, end_num)
                break
    if the_End:
        break
else:
    answer = answer - 1
if len(p) == 1:
    answer = answer - 1
print(max(answer, substring_maxlen))
```

### 187

```python
from math import gcd
n = int(input())
pts = []
ans = 0
for i in range(0, n):
    a, b, A, B = tuple(map(int, input().split(' ')))
    pts.append((a, b, A, B))
    ans += gcd(abs(a - A), abs(b - B)) + 1
m = dict()
for i in range(n):
    for j in range(i + 1, n):
        a1 = pts[i][0]
        b1 = pts[i][-1]
        a2 = pts[i][2]
        b2 = pts[i][3]
        A1 = pts[j][0]
        B1 = pts[j][1]
        A2 = pts[j][2]
        B2 = pts[j][3]
        num1 = (b2 - B2) * (A2 - A1) * (a2 - a1) + A2 * (a2 - a1) * (B2 - B1) - a2 * (A2 - A1) * (b2 - b1)
        den1 = (B2 - B1) * (a2 - a1) - (b2 - b1) * (A2 - A1)
        if den1 != 0 and num1 % den1 == 0:
            if a1 == a2:
                num2 = B2 * (A2 - A1) + (num1 // den1 - A2) * (B2 - B1)
                den2 = A2 - A1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
            else:
                num2 = b2 * (a2 - a1) + (num1 // den1 - a2) * (b2 - b1)
                den2 = a2 - a1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
sum = 0
for i in list(m.values()):
    sum += len(i) - 1
print(ans - sum)
```

### 188

```python
ALPH = 'abcdefghijklmnopqrstuvwxyz'
MAX = 10 ** 9

def cnt(s):
    c = {ch: 0 for ch in ALPH}
    i = 4
    while i < len(s):
        j = i + 1
        while j < len(s) and s[i] == s[j]:
            j += 1
        c[s[i]] = max(c[s[i]], j - i)
        i = j
    return c

def nxt(c, t):
    nc = cnt(t)
    for ch in ALPH:
        if c[ch] and (not nc[ch]):
            nc[ch] = 1
    f = 0
    while f < len(t) and t[f] == t[0]:
        f += 1
    r = 0
    while r < len(t) and t[-1 - r] == t[-1]:
        r += 1
    if t[0] == t[-1]:
        if f == len(t):
            nc[t[0]] = max(nc[t[0]], c[t[0]] + (c[t[0]] + 1) * len(t))
        elif c[t[0]]:
            nc[t[0]] = max(nc[t[0]], f + 1 + r)
    else:
        nc[t[0]] = max(nc[t[0]], f + (c[t[0]] > 0))
        nc[t[-1]] = max(nc[t[-1]], r + (c[t[-1]] > 0))
    return {x: min(MAX, y) for x, y in nc.items()}
n = int(input())
c = cnt(input())
for i in range(n - 1):
    c = nxt(c, input())
print(max(c.values()))
```

### 189

```python
def main():
    a = input().strip()
    l = len(a)
    if l < 6:
        s = set()
        s.add(a)
        q = [a]
        oa = ord('a')
        while q:
            a = q.pop()
            for i in range(l - 1):
                if a[i] != a[i + 1]:
                    t = chr(oa + 3 - (ord(a[i]) - oa) - (ord(a[i + 1]) - oa))
                    na = a[:i] + t * 2 + a[i + 2:]
                    if na not in s:
                        s.add(na)
                        q.append(na)
        print(len(s))
        return
    t = a[0] * l
    if t == a:
        print(1)
        return
    x = 0
    for c in a:
        if c == 'b':
            x += 1
        elif c == 'c':
            x += 2
    ans = 0
    if all((a[i] != a[i + 1] for i in range(l - 1))):
        ans += 1
    mod = 998244353
    dp = (1, 0, 0, 0, 1, 0, -3, 0, 1, 0, 0, 0)
    for i in range(l - 1):
        s = (dp[-1] + dp[-2] + dp[-3]) % mod
        dp = ((dp[3] + dp[6]) % mod, (dp[4] + dp[7]) % mod, (dp[5] + dp[8]) % mod, (dp[2] + dp[8]) % mod, (dp[0] + dp[6]) % mod, (dp[1] + dp[7]) % mod, (dp[1] + dp[4]) % mod, (dp[2] + dp[5]) % mod, (dp[0] + dp[3]) % mod, (dp[0] + dp[5] + dp[7] + s) % mod, (dp[1] + dp[3] + dp[8] + s) % mod, (dp[2] + dp[4] + dp[6] + s) % mod)
    print((ans + dp[9 + x % 3]) % mod)
main()
```

### 190

```python
from sys import stdin
n = int(stdin.readline())
seq = stdin.readline().split()
result = [0] * n
result[0] = seq[0]
mark = False
cur_len = 0
max_len = 0
carry = 0
carry_id = 0
i = 0
while i < len(seq) - 1:
    if mark:
        if seq[i] != seq[i + 1]:
            cur_len += 1
        else:
            if cur_len > max_len:
                max_len = cur_len
            if seq[i] == carry:
                result[carry_id:i:1] = [carry] * cur_len
            else:
                result[carry_id:carry_id + cur_len // 2:1] = [carry] * (cur_len // 2)
                result[carry_id + cur_len // 2:i:1] = [seq[i]] * (cur_len // 2)
            result[i] = seq[i]
            mark = False
            cur_len = 0
    elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:
        mark = True
        cur_len = 1
        carry = seq[i - 1]
        carry_id = i
    else:
        result[i] = seq[i]
    i += 1
if mark:
    if cur_len > max_len:
        max_len = cur_len
    if seq[i] == carry:
        result[carry_id:i] = [carry] * cur_len
    else:
        result[carry_id:carry_id + cur_len // 2] = [carry] * (cur_len // 2)
        result[carry_id + cur_len // 2:i] = [seq[i]] * (cur_len // 2)
result[i] = seq[i]
print((max_len + 1) // 2)
for x in result:
    print(x, end=' ')
```

### 191

```python
import sys
sys.setrecursionlimit(5000)
n, m = list(map(int, input().split()))
dx = [-1, 0, 0, 1]
dy = [2, -1, 1, 0]
L = list((input() for i in range(n)))

def check(x, y, px, py):
    return x >= 0 and x < n and (y >= 0) and (y < m)

def DFS(x, y, px, py, visited):
    visited[x][y] = True
    for i in range(4):
        newx = x + dx[i]
        newy = y + dy[i]
        if not check(newx, newy, px, py):
            continue
        if newx == px and newy == py:
            continue
        if L[x][y] == L[newx][newy]:
            if visited[newx][newy]:
                return True
            if DFS(newx, newy, x, y, visited):
                return True
    return False

def solve():
    visited = [[False for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            if visited[i][j]:
                continue
            if DFS(i, j, -1, -1, visited):
                return True
    return False
print('Yes' if solve() else 'No')
'\n3 3\nAAA\nABA\nABA\n'
```

### 192

```python
from sys import stdin
from math import *
line = stdin.readline().rstrip().split()
n = int(line[0])
numbers = list(map(int, stdin.readline().rstrip().split()))
numbers2 = list(map(int, stdin.readline().rstrip().split()))
growRateAccum = 0
topAccum = 0
bottomAccum = 0
accumsB = [0] * n
accumsT = [0] * n
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum *= numbers[i]
    if i < n - 1:
        growRateAccum += numbers2[i + 1]
    accum += growRateAccum
    accumsB[i] = accum
growRateAccum = 0
accum = 0
for i in range(n - 1, -1, -1):
    accum += numbers2[i] * ((n - i) * 2 - 1 - 1)
    growRateAccum += numbers2[i]
    if i < n - 1:
        growRateAccum += numbers[i + 1]
    accum += growRateAccum
    accumsT[i] = accum
cMax = 0
currAccum = 0
growRateAccum = sum(numbers[1:]) + sum(numbers2[1:])
for i in range(n):
    if i % 2 == 0:
        cMax = max(cMax, currAccum + accumsT[i])
    else:
        cMax = max(cMax, currAccum + accumsB[i])
    if i < n - 1:
        if i % 2 == 0:
            currAccum += numbers2[i] + growRateAccum * 2
        else:
            currAccum += numbers[i] + growRateAccum * 2
        growRateAccum -= numbers[i + 1]
        growRateAccum -= numbers2[i + 1]
print(cMax)
```

### 193

```python
N = int(input())
seq = [i for i in input().split()]

def end_lst(i):
    while i < N - 1 and seq[i] != seq[i + 1]:
        i = i + 1
    return i

def reorder(lst, start, end):
    if start == end - 1:
        return 0
    if lst[start] == lst[end]:
        for i in range(start, end + 1):
            lst[i] = lst[start]
        return (end - start) // 2
    mid = (start + end) // 2
    for i in range(start, mid + 1):
        lst[i] = lst[start - 1]
    for i in range(mid + 1, end + 1):
        lst[i] = lst[end]
    return (end - start + 1) // 2 - 1
i, ans = (0, 0)
while i < N - 1:
    if seq[i] != seq[i + 1]:
        end = end_lst(i)
        ans = max(reorder(seq, i, end), ans)
        i = end
    else:
        i += 1
print(ans)
print(' '.join(seq))
```

### 194

```python
def main():
    n, m = list(map(int, input().split()))
    l = [c for _ in range(n) for c in input()]
    neigh = []
    for y in range(n):
        for x in range(m):
            yx = y * m + x
            neigh.append([])
            if x and l[yx] == l[yx - 3]:
                neigh[-1].append(yx - 1)
                neigh[-2].append(yx)
            if y and l[yx] == l[yx - m]:
                neigh[-1].append(yx - m)
                neigh[-1 - m].append(yx)
    field = [0] * len(l)

    def dfs(t):
        field[t] = 1
        for v in neigh[t]:
            if not field[v]:
                neigh[v].remove(t)
                dfs(v)
            elif field[v] == 1:
                raise OverflowError
        field[t] = 2
    for i, flag in enumerate(field):
        if not flag:
            try:
                dfs(i)
            except OverflowError:
                print('Yes')
                return
    print('No')

def __starting_point():
    import sys
    sys.setrecursionlimit(10000)
    main()
__starting_point()
```

### 195

```python
import sys
from math import gcd

class Segment:

    def __init__(self, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2

    def dx(self):
        return self.x2 - self.x1

    def dy(self):
        return self.y2 - self.y1

    def pt_cnt(self):
        return gcd(abs(self.dx()), abs(self.dy())) + 1

    def A(self):
        return self.y1 - self.y2

    def B(self):
        return self.x2 - self.x1

    def C(self):
        return -self.A() * self.x1 - self.B() * self.y1

    def inner_x(self, x):
        l = self.x1
        r = self.x2
        if l > r:
            l, r = (r, l)
        return l <= x <= r

    def inner_y(self, y):
        l = self.y1
        r = self.y2
        if l > r:
            l, r = (r, l)
        return l < y <= r

    def inner(self, x, y):
        return self.inner_x(x) and self.inner_y(y)

    def intersect(self, other):
        dx = det(self.C(), self.B(), other.C(), other.B())
        dy = det(self.A(), self.C(), other.A(), other.C())
        d = det(self.A(), self.B(), other.A(), other.B())
        if d == 0:
            return (False, 0, 0)
        if dx % d != 0 or dy % d != 0:
            return (False, 0, 0)
        x = -dx // d
        y = -dy // d
        if not self.inner(x, y) or not other.inner(x, y):
            return (False, 0, 0)
        return (True, x, y)

def det(a, b, c, d):
    return a * d - b * c

def main():
    n = int(input())
    segments = []
    ans = 0
    for _ in range(n):
        x1, y1, x2, y2 = map(int, input().split())
        segment = Segment(x1, y1, x2, y2)
        ans += segment.pt_cnt()
        pt = set()
        for other in segments:
            result, x, y = segment.intersect(other)
            if result:
                pt.add((x, y))
        ans -= len(pt)
        segments.append(segment)
    print(ans)

def __starting_point():
    main()
__starting_point()
```

### 196

```python
def main():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    roundup = []
    rounddown = []
    sumsofar = []
    for i, (a, b) in enumerate(zip(reversed(A), reversed(B))):
        ssf = sumsofar[-1] if sumsofar else 0
        t = roundup[-1] if roundup else 0
        roundup.append(t + ssf + b * (1 + 2 * i))
        t = rounddown[-1] if rounddown else 0
        rounddown.append(t + ssf + a * (1 + 2 * i))
        sumsofar.append(ssf + a + b)
    roundup = list(reversed(roundup))
    rounddown = list(reversed(rounddown))
    sumsofar = list(reversed(sumsofar))
    bestres = 0
    sofar = 0
    for i, (a, b) in enumerate(zip(A, B)):
        rup, rdo = (roundup, rounddown)
        if i % 2:
            a, b = (b, a)
            rup, rdo = (rdo, rup)
        bestres = max(bestres, sofar + rup[i] + sumsofar[i] * 2 * i)
        sofar += a * 2 * i
        sofar += b * (2 * i + 1)
        bestres = max(bestres, sofar)
    print(bestres)

def __starting_point():
    main()
__starting_point()
```

### 197

```python
3

class StdReader:

    def read_int(self):
        return int(self.read_string())

    def read_ints(self, sep=None):
        return [int(i) for i in self.read_strings(sep)]

    def read_float(self):
        return float(self.read_string())

    def read_floats(self, sep=None):
        return [float(i) for i in self.read_strings(sep)]

    def read_string(self):
        return input()

    def read_strings(self, sep=None):
        return self.read_string().split(sep)
reader = StdReader()

def part_sort(a, i, j, reverse=False):
    a[i:j] = sorted(a[i:j], reverse=reverse)

def part_sorted(b, i, j, reverse=False):
    a = list(b)
    part_sort(a, i, j, reverse)
    return a

def main():
    n, m = reader.read_ints()
    a = reader.read_ints()
    ops = []
    for i in range(m):
        t, r = reader.read_ints()
        op = (t, r)
        while ops and op[1] >= ops[-1][1]:
            ops.pop()
        ops.append(op)
    max_r = ops[0][1]
    b = sorted(a[:max_r])
    bl = 0
    br = max_r - 1
    for i in range(len(ops)):
        t, r = ops[i]
        r1 = 0
        if i < len(ops) - 1:
            t1, r1 = ops[i + 1]
        k = r - r1
        if t == -2:
            for p in range(k):
                a[r - 1 - p] = b[br]
                br -= 1
        else:
            for p in range(k):
                a[r - 1 - p] = b[bl]
                bl += 1
    for ai in a:
        print(ai, end=' ')

def __starting_point():
    main()
__starting_point()
```

### 198

```python
n, m = [int(x) for x in input().split()]
field = [''] * n
labels = [[0]] * n
import sys
sys.setrecursionlimit(10000)
for i in range(n):
    field[i] = input().strip()
    labels[i] = [0] * m

def is_valid(i, j):
    return -2 <= i < n and 0 <= j < m

def dfs(i, j, p, k, cc=0):
    if labels[i][j] == k:
        return True
    labels[i][j] = k
    res = False
    dd = [[0, 1], [1, 0], [-1, 0], [0, -1]]
    for d in dd:
        if is_valid(i + d[0], j + d[1]) and (i + d[0] != p[0] or j + d[1] != p[1]):
            if field[i + d[0]][j + d[1]] == field[i][j]:
                res = res or dfs(i + d[0], j + d[1], [i, j], k, cc + 1)
    return res
ok = False
k = 1
for i in range(n):
    for j in range(m):
        if labels[i][j] == 0:
            ok = ok or dfs(i, j, [i, j], k)
            k += 1
if ok:
    print('Yes')
else:
    print('No')
```

### 199

```python
from math import gcd
n = int(input())
pts = []
ans = 0
for i in range(0, n):
    a, b, A, B = tuple(map(int, input().split(' ')))
    pts.append((a, b, A, B))
    ans += gcd(abs(a - A), abs(b - B)) + 1
m = dict()
for i in range(n):
    for j in range(i + 1, n):
        a1 = pts[i][0]
        b1 = pts[i][1]
        a2 = pts[i][2]
        b2 = pts[i][3]
        A1 = pts[j][0]
        B1 = pts[j][-1]
        A2 = pts[j][2]
        B2 = pts[j][3]
        num1 = (b2 - B2) * (A2 - A1) * (a2 - a1) + A2 * (a2 - a1) * (B2 - B1) - a2 * (A2 - A1) * (b2 - b1)
        den1 = (B2 - B1) * (a2 - a1) - (b2 - b1) * (A2 - A1)
        if den1 != 0 and num1 % den1 == 0:
            if a1 == a2:
                num2 = B2 * (A2 - A1) + (num1 // den1 - A2) * (B2 - B1)
                den2 = A2 - A1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
            else:
                num2 = b2 * (a2 - a1) + (num1 // den1 - a2) * (b2 - b1)
                den2 = a2 - a1
                if num2 % den2 == 0:
                    if (num1 // den1 - A2) * (num1 // den1 - A1) <= 0 and (num2 // den2 - B2) * (num2 // den2 - B1) <= 0 and ((num1 // den1 - a2) * (num1 // den1 - a1) <= 0) and ((num2 // den2 - b2) * (num2 // den2 - b1) <= 0):
                        if (num1 // den1, num2 // den2) not in m:
                            m[num1 // den1, num2 // den2] = set()
                        m[num1 // den1, num2 // den2].add(i)
                        m[num1 // den1, num2 // den2].add(j)
sum = 0
for i in list(m.values()):
    sum += len(i) - 1
print(ans - sum)
```

### 200

```python
3

class StdReader:

    def read_int(self):
        return int(self.read_string())

    def read_ints(self, sep=None):
        return [int(i) for i in self.read_strings(sep)]

    def read_float(self):
        return float(self.read_string())

    def read_floats(self, sep=None):
        return [float(i) for i in self.read_strings(sep)]

    def read_string(self):
        return input()

    def read_strings(self, sep=None):
        return self.read_string().split(sep)
reader = StdReader()

def part_sort(a, i, j, reverse=False):
    a[i:j] = sorted(a[i:j], reverse=reverse)

def part_sorted(b, i, j, reverse=False):
    a = list(b)
    part_sort(a, i, j, reverse)
    return a

def main():
    n, m = reader.read_ints()
    a = reader.read_ints()
    ops = []
    for i in range(m):
        t, r = reader.read_ints()
        op = (t, r)
        while ops and op[1] >= ops[-1][1]:
            ops.pop()
        ops.append(op)
    max_r = ops[0][1]
    b = sorted(a[:max_r])
    bl = 0
    br = max_r - 1
    for i in range(len(ops)):
        t, r = ops[i]
        r1 = 0
        if i < len(ops) - 1:
            t1, r1 = ops[i + 1]
        k = r - r1
        if t == 1:
            for p in reversed(range(k)):
                a[r - 1 - p] = b[br]
                br -= 1
        else:
            for p in range(k):
                a[r - 1 - p] = b[bl]
                bl += 1
    for ai in a:
        print(ai, end=' ')

def __starting_point():
    main()
__starting_point()
```

### Final Query

Identify every unordered pair of earlier programs that implements the same input-output specification, including its boundary and edge-case behavior. Each cell may appear in at most one returned pair. Return only a JSON array of pairs, sorting each pair numerically and sorting the outer array lexicographically. Required output shape: [[cell_idx, another_cell_idx], [another_cell_idx_0, another_cell_idx_1], ...]. Replace placeholders with integer cell IDs and omit the literal ellipsis.