Problem:
Score : 800 points

Problem Statement

Given is a string S, where each character is 0, 1, or ?.

Consider making a string S' by replacing each occurrence of ? with 0 or 1 (we can choose the character for each ? independently).
Let us define the unbalancedness of S' as follows:

(The unbalancedness of S') = \max \{ The absolute difference between the number of occurrences of 0 and 1 between the l-th and r-th character of S (inclusive) :\ 1 \leq l \leq r \leq |S|\}

Find the minimum possible unbalancedness of S'.

Constraints

1 \leq |S| \leq 10^6

Each character of S is 0, 1, or ?.

Input

Input is given from Standard Input in the following format:

S

Output

Print the minimum possible unbalancedness of S'.

Sample Input 1

0??

Sample Output 1

1

We can make S'= 010 and achieve the minimum possible unbalancedness of 1.

Sample Input 2

0??0

Sample Output 2

2

Sample Input 3

??00????0??0????0?0??00??1???11?1?1???1?11?111???1

Sample Output 3

4

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
$s = str();
$max = 1;
//if(strpos($s, '0??0') !== false)$max = 2;
//if(strpos($s, '1??1') !== false)$max = 2;
$zero = 0;
$one = 0;
for($i = 0, $I = strlen($s); $i < $I; $i++){
    $t = $s[$i];
    if($t == "0"){
        $zero++;
        if($one > 0)$one--;
    }elseif($t == "1"){
        $one++;
        if($zero > 0)$zero--;
    }else{
        if($zero > 0){
            $zero--;
            $one = 1;
        }elseif($one > 0){
            $one--;
            $zero = 1;
        }
    }
//    o($zero, $one);
    $max = max($max, $zero, $one);
}
echo $max;

function str(){return trim(fgets(STDIN));}
function ints($n = false){
  if($n===false){
    return array_map('intval',explode(' ',trim(fgets(STDIN))));
  }else{$ret = [];for($i = 0; $i < $n; $i++)foreach(array_map('intval',explode(' ',trim(fgets(STDIN)))) as $j => $v)$ret[$j][] = $v;return $ret;}
}
function int(){return intval(trim(fgets(STDIN)));}
function chmax(&$a,$b){if($a<$b){$a=$b;return 1;}return 0;}
function chmin(&$a,$b){if($a>$b){$a=$b;return 1;}return 0;}
function popcount($x){$c=0;while($x){$x&=$x-1;++$c;}return$c;}
function o(...$val){
    if(count($val)==1)$val=array_shift($val);
    echo debug_backtrace()[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0)echo "empty array";
        elseif(!is_array(current($val)))echo "array: ",implode(" ", addIndex($val)),"\n";
        else{
            echo "array:array\n";
            if(isCleanArray($val))foreach($val as $row)echo implode(" ", addIndex($row)),"\n";
            else foreach($val as $i => $row)echo "[".$i."] ".implode(" ", addIndex($row)),"\n";
        }
    }else echo $val."\n";
}
function addIndex($val){if(!isCleanArray($val)){$val = array_map(function($k, $v){return $k.":".$v;}, array_keys($val), $val);}return $val;}
function isCleanArray($array){$clean=true;$i = 0;foreach($array as $k=>$v){if($k != $i++)$clean = false;}return $clean;}
// 座圧対象の配列 -> [圧縮された配列,復元用のMap,圧縮用のMap]
function atsu($array){$a = array_flip($array);$fuku=array_flip($a);sort($fuku);$atsu = array_flip($fuku);foreach($array as $i=>$val)$array[$i]=$atsu[$val];return [$array, $fuku, $atsu];}
function gcdAll($array){$gcd=$array[0];for($i=1,$I=count($array);$i<$I;++$i){$gcd=gcd($gcd,$array[$i]);}return $gcd;}
function gcd($m, $n){if(!$n)return $m;return gcd($n, $m % $n);}
function lcmAll($array){$lcm=$array[0];for($i=1,$I=count($array);$i<$I;++$i){$lcm=lcm($lcm,$array[$i]);}return $lcm;}
function lcm($a, $b) {return $a / gcd($a, $b) * $b;}

function dfs($current, $from = -1, $d = 0){
  global $G, $distance;
  $distance[$current] = $d;
  foreach($G[$current] as $to){
    if($from != $to){
      dfs($to, $current, $d + 1);
    }
  }
}

function loadTree($N = false){
  if($N === false)$N = $GLOBALS['N'];
  return loadGraph($N, $N-1);
}
function loadGraph($N = false, $M = false, $both = true){
  if($N === false)$N = $GLOBALS['N'];
  if($M === false)$M = $GLOBALS['M'];
  $G = array_fill(1, $N, []);
  for($i = 0; $i < $M; $i++){
    $values = ints();
    if(count($values) == 2){
      list($a, $b) = $values;
      if($both == 0){
        $G[$a][] = $b;
      }elseif($both == 1){
        $G[$a][] = $b;
        $G[$b][] = $a;
      }else{
        $G[$b][] = $a;
      }
    }else{
      list($a, $b, $d) = $values;
      if($both == 0){
        $G[$a][] = [$b, $d];
      }elseif($both == 1){
        $G[$a][] = [$b, $d];
        $G[$b][] = [$a, $d];
      }else{
        $G[$b][] = [$a, $d];
      }
    }
  }
  return $G;
}