Buggy python submission (verdict: Time Limit Exceeded):
s = list(map(lambda x: -1 if x == '?' else int(x), input()))

def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Runtime Error):
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))

def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Time Limit Exceeded):
from numba import njit
s = input()

@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == '1':
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == '0':
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True


l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Runtime Error):
from numba import njit
s = input()

@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == '1':
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == '0':
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True


l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()

l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == '1':
            if a == b == c:
                ok = False
                break
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == '0':
            if a == b == 0:
                ok = False
                break
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    if ok:
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()

l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == '1':
            if a == b == c:
                ok = False
                break
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == '0':
            if a == b == 0:
                ok = False
                break
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    if ok:
        r = c
    else:
        l = c
print(r)


Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()

l, r = 0, len(s)
while r - l > 1:
    c = (l + r) // 2
    
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == '1':
            if a == b == c:
                ok = False
                break
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == '0':
            if a == b == 0:
                ok = False
                break
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    if ok:
        r = c
    else:
        l = c
print(r)

Fixed submission:
from numba import njit
import numpy as np
s = np.array(list(map(lambda x: -1 if x == '?' else int(x), input())))
@njit
def test(c):
    # current point can be seen as xth smallest val, where x can be any value in [a, b] (subset of [0, c])
    # a <= b
    a, b = 0, c
    ok = True
    discrete = False # when True x = a, a+2, ..., b-2, b
    for si in s:
        if si == 1:
            if a == b == c:
                return False
            a += 1
            b += 1
            if b > c:
                b = c - 1 if discrete else c
        elif si == 0:
            if a == b == 0:
                return False
            a -= 1
            b -= 1
            if a < 0:
                a = 1 if discrete else 0
        else:
            if a == b == 0:
                a = b = 1
            elif a == b == c:
                a = b = c - 1
            elif a == b:
                discrete = True
                a -= 1
                b += 1
            else:
                a -= 1
                b += 1
                if a < 0:
                    a = 1 if discrete else 0
                if b > c:
                    b = c - 1 if discrete else c
    return True

l, r = 0, s.size
while r - l > 1:
    c = (l + r) // 2
    if test(c):
        r = c
    else:
        l = c
print(r)